%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU529^1 : 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 : n006.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 08:26:36 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 : SEU529^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n006.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:48:09 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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.aFamDrpcOH/E---3.1_744493.p
% 0.22/0.28 % Version: 3.5.1-ho
% 0.22/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 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_1 with pid 744508 completed with status 0
% 0.22/0.28 % Result found by new_bool_1
% 0.22/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 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 % (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-FFMS31-SHFSMSBN
% 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 744510 completed with status 0
% 0.22/0.28 % Result found by SubtermCWHack
% 0.22/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 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 % (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-FFMS31-SHFSMSBN
% 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, epred1_0: $o).
% 0.22/0.28 thf(decl_80, type, esk1_2: $i > $i > $i).
% 0.22/0.28 thf(decl_81, type, esk2_2: $i > $i > $i).
% 0.22/0.28 thf(decl_82, type, esk3_2: $i > $i > $i).
% 0.22/0.28 thf(decl_83, type, esk4_1: $i > $i).
% 0.22/0.28 thf(decl_84, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.22/0.28 thf(decl_85, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.28 thf(decl_86, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.22/0.28 thf(decl_87, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.28 thf(decl_88, type, esk9_1: $i > $i).
% 0.22/0.28 thf(decl_89, type, esk10_2: ($i > $o) > $i > $i).
% 0.22/0.28 thf(decl_90, type, esk11_1: ($i > $o) > $i).
% 0.22/0.28 thf(decl_91, type, esk12_2: ($i > $o) > $i > $i).
% 0.22/0.28 thf(decl_92, type, esk13_1: ($i > $o) > $i).
% 0.22/0.28 thf(decl_93, type, esk14_2: $i > $i > $i).
% 0.22/0.28 thf(decl_94, type, esk15_2: $i > $i > $i).
% 0.22/0.28 thf(decl_95, type, esk16_1: $i > $i).
% 0.22/0.28 thf(decl_96, type, esk17_1: $i > $i).
% 0.22/0.28 thf(decl_97, type, esk18_1: $i > $i).
% 0.22/0.28 thf(decl_98, type, esk19_2: $i > $i > $i).
% 0.22/0.28 thf(decl_99, type, esk20_3: $i > $i > $o > $i).
% 0.22/0.28 thf(decl_100, type, esk21_2: ($i > $o) > $i > $i).
% 0.22/0.28 thf(decl_101, type, esk22_1: ($i > $o) > $i).
% 0.22/0.28 thf(decl_102, type, esk23_1: $i > $i).
% 0.22/0.28 thf(decl_103, type, esk24_0: $i).
% 0.22/0.28 thf(decl_104, type, esk25_0: $i).
% 0.22/0.28 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', exuE2)).
% 0.22/0.28 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', exu)).
% 0.22/0.28 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', nonempty)).
% 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', replAx)).
% 0.22/0.28 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', exuE3e)).
% 0.22/0.28 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', prop2set)).
% 0.22/0.28 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', exuE1)).
% 0.22/0.28 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', nonemptyI)).
% 0.22/0.28 thf(eqinunit, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', eqinunit)).
% 0.22/0.28 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', nonemptyImpWitness)).
% 0.22/0.28 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', dsetconstrEL)).
% 0.22/0.28 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', dsetconstrI)).
% 0.22/0.28 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', dsetconstrER)).
% 0.22/0.28 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', prop2setE)).
% 0.22/0.28 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', nonemptyI1)).
% 0.22/0.28 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', nonemptyE1)).
% 0.22/0.28 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', setbeta)).
% 0.22/0.28 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', setoftrueEq)).
% 0.22/0.28 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', emptyinPowerset)).
% 0.22/0.28 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', emptyInPowerset)).
% 0.22/0.28 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', powersetE)).
% 0.22/0.28 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', setunionAx)).
% 0.22/0.28 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', setunionI)).
% 0.22/0.28 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', powersetAx)).
% 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/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', setunionE)).
% 0.22/0.28 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', setadjoinAx)).
% 0.22/0.28 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', subPowSU)).
% 0.22/0.28 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', emptysetAx)).
% 0.22/0.28 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', setextAx)).
% 0.22/0.28 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', omega0Ax)).
% 0.22/0.28 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', uniqinunit)).
% 0.22/0.28 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', notinsingleton)).
% 0.22/0.28 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', wellorderingAx)).
% 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/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', foundationAx)).
% 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:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', omegaIndAx)).
% 0.22/0.28 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', omegaSAx)).
% 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/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', setext)).
% 0.22/0.28 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', notinemptyset)).
% 0.22/0.28 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', emptysetimpfalse)).
% 0.22/0.28 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', emptysetE)).
% 0.22/0.28 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', emptyI)).
% 0.22/0.28 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', emptyinunitempty)).
% 0.22/0.28 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', setadjoinIL)).
% 0.22/0.28 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', noeltsimpempty)).
% 0.22/0.28 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', setadjoinE)).
% 0.22/0.28 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', setadjoinOr)).
% 0.22/0.28 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', powersetI)).
% 0.22/0.28 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.aFamDrpcOH/E---3.1_744493.p', setadjoinIR)).
% 0.22/0.28 thf(c_0_48, 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_49, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.22/0.28 thf(c_0_50, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.22/0.28 thf(c_0_51, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.22/0.28 thf(c_0_52, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.22/0.28 thf(c_0_53, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.22/0.28 thf(c_0_54, plain, ((exuE1)<=>![X1:$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_55, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.22/0.28 thf(c_0_56, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[eqinunit])).
% 0.22/0.28 thf(c_0_57, plain, ((exuE2)=(![X1:$i > $o]:((((?[X146:$i]:(((((X1 @ X146)))&(![X147:$i]:(((((X1 @ X147)))=>(((X146)=(X147))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_48, c_0_49])).
% 0.22/0.28 thf(c_0_58, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_50])).
% 0.22/0.28 thf(c_0_59, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.22/0.28 thf(c_0_60, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.22/0.28 thf(c_0_61, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X140:$i]:(((((X6 @ X2 @ X140)))&(![X141:$i]:(((((X6 @ X2 @ X141)))=>(((X140)=(X141)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_51, c_0_49])).
% 0.22/0.28 thf(c_0_62, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.22/0.28 thf(c_0_63, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X144:$i]:(((((X1 @ X144)))&(![X145:$i]:(((((X1 @ X145)))=>(((X144)=(X145))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_52, c_0_49])).
% 0.22/0.28 thf(c_0_64, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_53])).
% 0.22/0.28 thf(c_0_65, plain, ((exuE1)=(![X1:$i > $o]:((((?[X142:$i]:(((((X1 @ X142)))&(![X143:$i]:(((((X1 @ X143)))=>(((X142)=(X143))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_54, c_0_49])).
% 0.22/0.28 thf(c_0_66, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_50])).
% 0.22/0.28 thf(c_0_67, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_55, c_0_50])).
% 0.22/0.28 thf(c_0_68, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_50])).
% 0.22/0.28 thf(c_0_69, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.22/0.28 thf(c_0_70, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.22/0.28 thf(c_0_71, plain, ((epred1_0)<=>![X177:$i]:(?[X178:$i]:((((![X179:$i]:(((in @ X179 @ X178)=>![X180:$i]:(((in @ X180 @ X179)=>(in @ X180 @ X177)))))&![X181:$i, X182:$i]:((((in @ X181 @ X177)&(in @ X182 @ X177))=>(![X183:$i]:(((in @ X183 @ X178)=>((in @ X181 @ X183)<=>(in @ X182 @ X183))))=>((X181)=(X182))))))&![X184:$i, X185:$i]:((((in @ X184 @ X178)&(in @ X185 @ X178))=>(![X186:$i]:(((in @ X186 @ X184)=>(in @ X186 @ X185)))|![X187:$i]:(((in @ X187 @ X185)=>(in @ X187 @ X184)))))))&![X188:$i]:(((![X189:$i]:(((in @ X189 @ X188)=>(in @ X189 @ X177)))&?[X190:$i]:((in @ X190 @ X188)))=>?[X191:$i, X192:$i]:(((((in @ X191 @ X178)&(in @ X192 @ X188))&~(?[X193:$i]:(((in @ X193 @ X191)&(in @ X193 @ X188)))))&![X194:$i]:(((in @ X194 @ X178)=>(![X195:$i]:(((in @ X195 @ X194)=>(in @ X195 @ X191)))|(in @ X192 @ X194)))))))))))), introduced(definition)).
% 0.22/0.28 thf(c_0_72, negated_conjecture, ~((![X148:$i, X149:$i]:((![X150:$i]:(((in @ X150 @ X148)<=>(in @ X150 @ X149)))=>((X148)=(X149))))=>(![X151:$i]:(~(in @ X151 @ emptyset))=>(![X152:$i, X153:$i, X154:$i]:(((in @ X154 @ (setadjoin @ X152 @ X153))<=>(((X154)=(X152))|(in @ X154 @ X153))))=>(![X155:$i, X156:$i]:(((in @ X156 @ (powerset @ X155))<=>![X157:$i]:(((in @ X157 @ X156)=>(in @ X157 @ X155)))))=>(![X158:$i, X159:$i]:(((in @ X159 @ (setunion @ X158))<=>?[X160:$i]:(((in @ X159 @ X160)&(in @ X160 @ X158)))))=>((in @ emptyset @ omega)=>(![X161:$i]:(((in @ X161 @ omega)=>(in @ (setadjoin @ X161 @ X161) @ omega)))=>(![X162:$i]:((((in @ emptyset @ X162)&![X163:$i]:((((in @ X163 @ omega)&(in @ X163 @ X162))=>(in @ (setadjoin @ X163 @ X163) @ X162))))=>![X164:$i]:(((in @ X164 @ omega)=>(in @ X164 @ X162)))))=>(![X165:$i > $i > $o, X166:$i]:((![X167:$i]:(((in @ X167 @ X166)=>?[X168:$i]:(((X165 @ X167 @ X168)&![X169:$i]:(((X165 @ X167 @ X169)=>((X168)=(X169))))))))=>?[X170:$i]:(![X171:$i]:(((in @ X171 @ X170)<=>?[X172:$i]:(((in @ X172 @ X166)&(X165 @ X172 @ X171))))))))=>(![X173:$i]:((?[X174:$i]:((in @ X174 @ X173))=>?[X175:$i]:(((in @ X175 @ X173)&~(?[X176:$i]:(((in @ X176 @ X175)&(in @ X176 @ X173))))))))=>((epred1_0)=>((descrp)=>(![X196:$i, X197:$i > $o, X198:$i]:(((in @ X198 @ X196)=>((X197 @ X198)=>(in @ X198 @ (dsetconstr @ X196 @ X197)))))=>(![X199:$i, X200:$i > $o, X201:$i]:(((in @ X201 @ (dsetconstr @ X199 @ X200))=>(in @ X201 @ X199)))=>(![X202:$i, X203:$i > $o, X204:$i]:(((in @ X204 @ (dsetconstr @ X202 @ X203))=>(X203 @ X204)))=>(![X205:$i > $o]:((?[X206:$i]:(((X205 @ X206)&![X207:$i]:(((X205 @ X207)=>((X206)=(X207))))))=>?[X208:$i]:(((X205 @ X208)&![X209:$i]:(((X205 @ X209)=>((X208)=(X209))))))))=>(![X210:$o, X211:$i]:(((in @ X211 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X210)))))=>(X210)))=>(![X212:$i]:(((in @ X212 @ emptyset)=>![X213:$o]:((X213))))=>(![X214:$i]:(((in @ X214 @ emptyset)=>~($true)))=>(![X215:$i]:(~(in @ X215 @ emptyset))=>(![X216:$i > $o]:((?[X217:$i]:(((X216 @ X217)&![X218:$i]:(((X216 @ X218)=>((X217)=(X218))))))=>?[X219:$i]:((X216 @ X219))))=>(![X220:$i, X221:$i]:((![X222:$i]:(((in @ X222 @ X220)=>(in @ X222 @ X221)))=>(![X223:$i]:(((in @ X223 @ X221)=>(in @ X223 @ X220)))=>((X220)=(X221)))))=>(![X224:$i]:((![X225:$i]:(~(in @ X225 @ X224))=>((X224)=(emptyset))))=>(![X226:$i]:((![X227:$i]:(~(in @ X227 @ X226))=>((X226)=(emptyset))))=>(![X228:$i, X229:$i > $o, X230:$i]:(((in @ X230 @ X228)=>((in @ X230 @ (dsetconstr @ X228 @ X229))<=>(X229 @ X230))))=>(![X231:$i]:((((X231)!=(emptyset))=>?[X232:$i]:((in @ X232 @ X231))))=>(![X233:$i, X234:$i > $o, X235:$i]:(((in @ X235 @ X233)=>((X234 @ X235)=>((dsetconstr @ X233 @ X234)!=(emptyset)))))=>(![X236:$i]:((?[X237:$i]:((in @ X237 @ X236))=>((X236)!=(emptyset))))=>(![X238:$i, X239:$i]:((in @ X238 @ (setadjoin @ X238 @ X239)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X240:$i, X241:$i, X242:$i]:(((in @ X242 @ X241)=>(in @ X242 @ (setadjoin @ X240 @ X241))))=>(![X243:$i, X244:$i, X245:$i]:(((in @ X245 @ (setadjoin @ X243 @ X244))=>![X246:$o]:(((((X245)=(X243))=>(X246))=>(((in @ X245 @ X244)=>(X246))=>(X246))))))=>(![X247:$i, X248:$i, X249:$i]:(((in @ X249 @ (setadjoin @ X247 @ X248))=>(((X249)=(X247))|(in @ X249 @ X248))))=>(![X250:$i]:(((dsetconstr @ X250 @ (^[Z0:$i]:($true)))=(X250)))=>(![X251:$i, X252:$i]:((![X253:$i]:(((in @ X253 @ X252)=>(in @ X253 @ X251)))=>(in @ X252 @ (powerset @ X251))))=>(![X254:$i]:((in @ emptyset @ (powerset @ X254)))=>(![X255:$i]:((in @ emptyset @ (powerset @ X255)))=>(![X256:$i, X257:$i, X258:$i]:(((in @ X257 @ (powerset @ X256))=>((in @ X258 @ X257)=>(in @ X258 @ X256))))=>(![X259:$i, X260:$i, X261:$i]:(((in @ X260 @ X261)=>((in @ X261 @ X259)=>(in @ X260 @ (setunion @ X259)))))=>(![X262:$i, X263:$i]:(((in @ X263 @ (setunion @ X262))=>![X264:$o]:((![X265:$i]:(((in @ X263 @ X265)=>((in @ X265 @ X262)=>(X264))))=>(X264)))))=>(![X266:$i, X267:$i]:(((in @ X267 @ X266)=>(in @ X267 @ (powerset @ (setunion @ X266)))))=>(![X268:$i > $o]:((?[X269:$i]:(((X268 @ X269)&![X270:$i]:(((X268 @ X270)=>((X269)=(X270))))))=>?[X271:$i]:(![X272:$i]:(((X268 @ X272)<=>((X272)=(X271)))))))=>(![X273:$i]:((((X273)!=(emptyset))=>?[X274:$i]:(((in @ X274 @ X273)&$true))))=>(![X275:$i, X276:$i]:(((in @ X275 @ (setadjoin @ X276 @ emptyset))=>((X275)=(X276))))=>(![X277:$i, X278:$i]:((((X277)!=(X278))=>~(in @ X278 @ (setadjoin @ X277 @ emptyset))))=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_56, emptyinPowerset]), emptyInPowerset]), powersetE]), setunionAx]), setunionI]), powersetAx]), setunionE]), setadjoinAx]), subPowSU]), emptysetAx]), c_0_57]), setextAx]), c_0_58]), omega0Ax]), uniqinunit]), notinsingleton]), c_0_59]), c_0_60]), wellorderingAx]), foundationAx]), c_0_61]), omegaIndAx]), omegaSAx]), c_0_62]), setext]), c_0_63]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_64]), c_0_65]), emptyI]), emptyinunitempty]), setadjoinIL]), c_0_66]), c_0_67]), c_0_68]), c_0_69]), noeltsimpempty]), setadjoinE]), setadjoinOr]), c_0_70]), powersetI]), setadjoinIR])])]), c_0_71])).
% 0.22/0.28 thf(c_0_73, negated_conjecture, ![X279:$i, X280:$i, X282:$i, X283:$i, X284:$i, X285:$i, X286:$i, X287:$i, X288:$i, X289:$i, X290:$i, X292:$i, X293:$i, X295:$i, X296:$i, X297:$i, X298:$i, X299:$i, X301:$i, X302:$i > $i > $o, X303:$i, X305:$i, X308:$i, X310:$i, X311:$i, X312:$i, X313:$i, X315:$i, X316:$i, X317:$i > $o, X318:$i, X319:$i, X320:$i > $o, X321:$i, X322:$i, X323:$i > $o, X324:$i, X325:$i > $o, X326:$i, X329:$i, X330:$o, X331:$i, X332:$i, X333:$o, X334:$i, X335:$i, X336:$i > $o, X337:$i, X340:$i, X341:$i, X344:$i, X346:$i, X348:$i, X349:$i > $o, X350:$i, X351:$i, X353:$i, X354:$i > $o, X355:$i, X356:$i, X357:$i, X358:$i, X359:$i, X360:$i, X361:$i, X362:$i, X363:$i, X364:$i, X365:$i, X366:$o, X367:$i, X368:$i, X369:$i, X370:$i, X371:$i, X372:$i, X374:$i, X375:$i, X376:$i, X377:$i, X378:$i, X379:$i, X380:$i, X381:$i, X382:$i, X383:$i, X384:$o, X386:$i, X387:$i, X388:$i > $o, X389:$i, X392:$i, X393:$i, X394:$i, X396:$i, X397:$i, X398:$i, X399:$i]:((((~(in @ (esk1_2 @ X279 @ X280) @ X279)|~(in @ (esk1_2 @ X279 @ X280) @ X280)|((X279)=(X280)))&((in @ (esk1_2 @ X279 @ X280) @ X279)|(in @ (esk1_2 @ X279 @ X280) @ X280)|((X279)=(X280))))&(~(in @ X282 @ emptyset)&(((~(in @ X285 @ (setadjoin @ X283 @ X284))|(((X285)=(X283))|(in @ X285 @ X284)))&((((X285)!=(X283))|(in @ X285 @ (setadjoin @ X283 @ X284)))&(~(in @ X285 @ X284)|(in @ X285 @ (setadjoin @ X283 @ X284)))))&(((~(in @ X287 @ (powerset @ X286))|(~(in @ X288 @ X287)|(in @ X288 @ X286)))&(((in @ (esk2_2 @ X289 @ X290) @ X290)|(in @ X290 @ (powerset @ X289)))&(~(in @ (esk2_2 @ X289 @ X290) @ X289)|(in @ X290 @ (powerset @ X289)))))&(((((in @ X293 @ (esk3_2 @ X292 @ X293))|~(in @ X293 @ (setunion @ X292)))&((in @ (esk3_2 @ X292 @ X293) @ X292)|~(in @ X293 @ (setunion @ X292))))&(~(in @ X296 @ X297)|~(in @ X297 @ X295)|(in @ X296 @ (setunion @ X295))))&((in @ emptyset @ omega)&((~(in @ X298 @ omega)|(in @ (setadjoin @ X298 @ X298) @ omega))&(((((in @ (esk4_1 @ X299) @ omega)|~(in @ emptyset @ X299)|(~(in @ X301 @ omega)|(in @ X301 @ X299)))&((in @ (esk4_1 @ X299) @ X299)|~(in @ emptyset @ X299)|(~(in @ X301 @ omega)|(in @ X301 @ X299))))&(~(in @ (setadjoin @ (esk4_1 @ X299) @ (esk4_1 @ X299)) @ X299)|~(in @ emptyset @ X299)|(~(in @ X301 @ omega)|(in @ X301 @ X299))))&((((((in @ (esk8_3 @ X302 @ X303 @ X308) @ X303)|~(in @ X308 @ (esk7_2 @ X302 @ X303))|(in @ (esk5_2 @ X302 @ X303) @ X303))&((X302 @ (esk8_3 @ X302 @ X303 @ X308) @ X308)|~(in @ X308 @ (esk7_2 @ X302 @ X303))|(in @ (esk5_2 @ X302 @ X303) @ X303)))&(~(in @ X311 @ X303)|~(X302 @ X311 @ X310)|(in @ X310 @ (esk7_2 @ X302 @ X303))|(in @ (esk5_2 @ X302 @ X303) @ X303)))&(((((in @ (esk8_3 @ X302 @ X303 @ X308) @ X303)|~(in @ X308 @ (esk7_2 @ X302 @ X303))|((X302 @ (esk5_2 @ X302 @ X303) @ (esk6_3 @ X302 @ X303 @ X305))|~(X302 @ (esk5_2 @ X302 @ X303) @ X305)))&((X302 @ (esk8_3 @ X302 @ X303 @ X308) @ X308)|~(in @ X308 @ (esk7_2 @ X302 @ X303))|((X302 @ (esk5_2 @ X302 @ X303) @ (esk6_3 @ X302 @ X303 @ X305))|~(X302 @ (esk5_2 @ X302 @ X303) @ X305))))&(~(in @ X311 @ X303)|~(X302 @ X311 @ X310)|(in @ X310 @ (esk7_2 @ X302 @ X303))|((X302 @ (esk5_2 @ X302 @ X303) @ (esk6_3 @ X302 @ X303 @ X305))|~(X302 @ (esk5_2 @ X302 @ X303) @ X305))))&((((in @ (esk8_3 @ X302 @ X303 @ X308) @ X303)|~(in @ X308 @ (esk7_2 @ X302 @ X303))|(((X305)!=(esk6_3 @ X302 @ X303 @ X305))|~(X302 @ (esk5_2 @ X302 @ X303) @ X305)))&((X302 @ (esk8_3 @ X302 @ X303 @ X308) @ X308)|~(in @ X308 @ (esk7_2 @ X302 @ X303))|(((X305)!=(esk6_3 @ X302 @ X303 @ X305))|~(X302 @ (esk5_2 @ X302 @ X303) @ X305))))&(~(in @ X311 @ X303)|~(X302 @ X311 @ X310)|(in @ X310 @ (esk7_2 @ X302 @ X303))|(((X305)!=(esk6_3 @ X302 @ X303 @ X305))|~(X302 @ (esk5_2 @ X302 @ X303) @ X305))))))&((((in @ (esk9_1 @ X312) @ X312)|~(in @ X313 @ X312))&(~(in @ X315 @ (esk9_1 @ X312))|~(in @ X315 @ X312)|~(in @ X313 @ X312)))&((epred1_0)&((descrp)&((~(in @ X318 @ X316)|(~(X317 @ X318)|(in @ X318 @ (dsetconstr @ X316 @ X317))))&((~(in @ X321 @ (dsetconstr @ X319 @ X320))|(in @ X321 @ X319))&((~(in @ X324 @ (dsetconstr @ X322 @ X323))|(X323 @ X324))&(((((X325 @ (esk11_1 @ X325))|((X325 @ (esk10_2 @ X325 @ X326))|~(X325 @ X326)))&(~(X325 @ X329)|((esk11_1 @ X325)=(X329))|((X325 @ (esk10_2 @ X325 @ X326))|~(X325 @ X326))))&(((X325 @ (esk11_1 @ X325))|(((X326)!=(esk10_2 @ X325 @ X326))|~(X325 @ X326)))&(~(X325 @ X329)|((esk11_1 @ X325)=(X329))|(((X326)!=(esk10_2 @ X325 @ X326))|~(X325 @ X326)))))&((~(in @ X331 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X330)))))|(X330))&((~(in @ X332 @ emptyset)|(X333))&((~(in @ X334 @ emptyset)|~($true))&(~(in @ X335 @ emptyset)&((((X336 @ (esk12_2 @ X336 @ X337))|~(X336 @ X337)|(X336 @ (esk13_1 @ X336)))&(((X337)!=(esk12_2 @ X336 @ X337))|~(X336 @ X337)|(X336 @ (esk13_1 @ X336))))&(((((in @ (esk15_2 @ X340 @ X341) @ X341)|((X340)=(X341))|(in @ (esk14_2 @ X340 @ X341) @ X340))&(~(in @ (esk15_2 @ X340 @ X341) @ X340)|((X340)=(X341))|(in @ (esk14_2 @ X340 @ X341) @ X340)))&(((in @ (esk15_2 @ X340 @ X341) @ X341)|((X340)=(X341))|~(in @ (esk14_2 @ X340 @ X341) @ X341))&(~(in @ (esk15_2 @ X340 @ X341) @ X340)|((X340)=(X341))|~(in @ (esk14_2 @ X340 @ X341) @ X341))))&(((in @ (esk16_1 @ X344) @ X344)|((X344)=(emptyset)))&(((in @ (esk17_1 @ X346) @ X346)|((X346)=(emptyset)))&(((~(in @ X350 @ (dsetconstr @ X348 @ X349))|(X349 @ X350)|~(in @ X350 @ X348))&(~(X349 @ X350)|(in @ X350 @ (dsetconstr @ X348 @ X349))|~(in @ X350 @ X348)))&((((X351)=(emptyset))|(in @ (esk18_1 @ X351) @ X351))&((~(in @ X355 @ X353)|(~(X354 @ X355)|((dsetconstr @ X353 @ X354)!=(emptyset))))&((~(in @ X357 @ X356)|((X356)!=(emptyset)))&((in @ X358 @ (setadjoin @ X358 @ X359))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X362 @ X361)|(in @ X362 @ (setadjoin @ X360 @ X361)))&(((((in @ X365 @ X364)|(X366)|((X365)=(X363))|~(in @ X365 @ (setadjoin @ X363 @ X364)))&(~(X366)|(X366)|((X365)=(X363))|~(in @ X365 @ (setadjoin @ X363 @ X364))))&(((in @ X365 @ X364)|(X366)|~(X366)|~(in @ X365 @ (setadjoin @ X363 @ X364)))&(~(X366)|(X366)|~(X366)|~(in @ X365 @ (setadjoin @ X363 @ X364)))))&((~(in @ X369 @ (setadjoin @ X367 @ X368))|(((X369)=(X367))|(in @ X369 @ X368)))&(((dsetconstr @ X370 @ (^[Z0:$i]:($true)))=(X370))&((((in @ (esk19_2 @ X371 @ X372) @ X372)|(in @ X372 @ (powerset @ X371)))&(~(in @ (esk19_2 @ X371 @ X372) @ X371)|(in @ X372 @ (powerset @ X371))))&((in @ emptyset @ (powerset @ X374))&((in @ emptyset @ (powerset @ X375))&((~(in @ X377 @ (powerset @ X376))|(~(in @ X378 @ X377)|(in @ X378 @ X376)))&((~(in @ X380 @ X381)|(~(in @ X381 @ X379)|(in @ X380 @ (setunion @ X379))))&((((in @ X383 @ (esk20_3 @ X382 @ X383 @ X384))|(X384)|~(in @ X383 @ (setunion @ X382)))&(((in @ (esk20_3 @ X382 @ X383 @ X384) @ X382)|(X384)|~(in @ X383 @ (setunion @ X382)))&(~(X384)|(X384)|~(in @ X383 @ (setunion @ X382)))))&((~(in @ X387 @ X386)|(in @ X387 @ (powerset @ (setunion @ X386))))&((((~(X388 @ X392)|((X392)=(esk22_1 @ X388))|((X388 @ (esk21_2 @ X388 @ X389))|~(X388 @ X389)))&(((X393)!=(esk22_1 @ X388))|(X388 @ X393)|((X388 @ (esk21_2 @ X388 @ X389))|~(X388 @ X389))))&((~(X388 @ X392)|((X392)=(esk22_1 @ X388))|(((X389)!=(esk21_2 @ X388 @ X389))|~(X388 @ X389)))&(((X393)!=(esk22_1 @ X388))|(X388 @ X393)|(((X389)!=(esk21_2 @ X388 @ X389))|~(X388 @ X389)))))&((((in @ (esk23_1 @ X394) @ X394)|((X394)=(emptyset)))&(($true)|((X394)=(emptyset))))&((~(in @ X396 @ (setadjoin @ X397 @ emptyset))|((X396)=(X397)))&((((X398)=(X399))|~(in @ X399 @ (setadjoin @ X398 @ emptyset)))&(((esk24_0)=(esk25_0))&~(in @ esk24_0 @ (setadjoin @ esk25_0 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])])])])])])])).
% 0.22/0.28 thf(c_0_74, negated_conjecture, ~((in @ esk24_0 @ (setadjoin @ esk25_0 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_73])).
% 0.22/0.28 thf(c_0_75, negated_conjecture, ((esk24_0)=(esk25_0)), inference(split_conjunct,[status(thm)],[c_0_73])).
% 0.22/0.28 thf(c_0_76, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_73])).
% 0.22/0.28 thf(c_0_77, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74, c_0_75]), c_0_76])]), ['proof']).
% 0.22/0.28 % SZS output end CNFRefutation
% 0.22/0.28 % Parsed axioms : 105
% 0.22/0.28 % Removed by relevancy pruning/SinE : 57
% 0.22/0.28 % Initial clauses : 96
% 0.22/0.28 % Removed in clause preprocessing : 5
% 0.22/0.28 % Initial clauses in saturation : 91
% 0.22/0.28 % Processed clauses : 15
% 0.22/0.28 % ...of these trivial : 1
% 0.22/0.28 % ...subsumed : 3
% 0.22/0.28 % ...remaining for further processing : 10
% 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 : 1
% 0.22/0.28 % Generated clauses : 0
% 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 : 0
% 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 : 4
% 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 : 9
% 0.22/0.28 % Positive orientable unit clauses : 7
% 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: 76
% 0.22/0.28 % ...number of literals in the above : 251
% 0.22/0.28 % Current number of archived formulas : 0
% 0.22/0.28 % Current number of archived clauses : 1
% 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 : 2
% 0.22/0.28 % Rewrite failures with RHS unbound : 0
% 0.22/0.28 % BW rewrite match attempts : 1
% 0.22/0.28 % BW rewrite match successes : 1
% 0.22/0.28 % Condensation attempts : 0
% 0.22/0.28 % Condensation successes : 0
% 0.22/0.28 % Termbank termtop insertions : 11784
% 0.22/0.28 % Search garbage collected termcells : 4689
% 0.22/0.28
% 0.22/0.28 % -------------------------------------------------
% 0.22/0.28 % User time : 0.007 s
% 0.22/0.28 % System time : 0.008 s
% 0.22/0.28 % Total time : 0.015 s
% 0.22/0.28 % Maximum resident set size: 4764 pages
% 0.22/0.28
% 0.22/0.28 % -------------------------------------------------
% 0.22/0.28 % User time : 0.011 s
% 0.22/0.28 % System time : 0.014 s
% 0.22/0.28 % Total time : 0.024 s
% 0.22/0.28 % Maximum resident set size: 4864 pages
% 0.22/0.28 % E exiting
%------------------------------------------------------------------------------