%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU520^1 : 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:21 AM UTC 2026
% Result : Theorem 0.10s 0.28s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU520^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n016.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 13:52:49 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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.3PPYI6L2kY/E---3.1_380719.p
% 0.10/0.28 % Version: 3.5.1-ho
% 0.10/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.10/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.28 % Starting sh5l with 300s (1) cores
% 0.10/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.10/0.28 % new_bool_1 with pid 380750 completed with status 0
% 0.10/0.28 % Result found by new_bool_1
% 0.10/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.10/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.28 % Starting sh5l with 300s (1) cores
% 0.10/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.28 % Search class: HGHSS-FFMS31-SHFSMSBN
% 0.10/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.28 % SubtermCWHack with pid 380755 completed with status 0
% 0.10/0.28 % Result found by SubtermCWHack
% 0.10/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.10/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.28 % Starting sh5l with 300s (1) cores
% 0.10/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.28 % Search class: HGHSS-FFMS31-SHFSMSBN
% 0.10/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.28 % Preprocessing time : 0.003 s
% 0.10/0.28
% 0.10/0.28 % Proof found!
% 0.10/0.28 % SZS status Theorem
% 0.10/0.28 % SZS output start CNFRefutation
% 0.10/0.28 thf(decl_23, type, in: $i > $i > $o).
% 0.10/0.28 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.10/0.28 thf(decl_25, type, setextAx: $o).
% 0.10/0.28 thf(decl_26, type, emptyset: $i).
% 0.10/0.28 thf(decl_27, type, emptysetAx: $o).
% 0.10/0.28 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.10/0.28 thf(decl_29, type, setadjoinAx: $o).
% 0.10/0.28 thf(decl_30, type, powerset: $i > $i).
% 0.10/0.28 thf(decl_31, type, powersetAx: $o).
% 0.10/0.28 thf(decl_33, type, setunionAx: $o).
% 0.10/0.28 thf(decl_34, type, omega: $i).
% 0.10/0.28 thf(decl_35, type, omega0Ax: $o).
% 0.10/0.28 thf(decl_36, type, omegaSAx: $o).
% 0.10/0.28 thf(decl_37, type, omegaIndAx: $o).
% 0.10/0.28 thf(decl_38, type, replAx: $o).
% 0.10/0.28 thf(decl_39, type, foundationAx: $o).
% 0.10/0.28 thf(decl_40, type, wellorderingAx: $o).
% 0.10/0.28 thf(decl_42, type, descrp: $o).
% 0.10/0.28 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.10/0.28 thf(decl_44, type, dsetconstrI: $o).
% 0.10/0.28 thf(decl_45, type, dsetconstrEL: $o).
% 0.10/0.28 thf(decl_46, type, dsetconstrER: $o).
% 0.10/0.28 thf(decl_47, type, exuE1: $o).
% 0.10/0.28 thf(decl_48, type, prop2set: $o > $i).
% 0.10/0.28 thf(decl_49, type, prop2setE: $o).
% 0.10/0.28 thf(decl_50, type, emptysetE: $o).
% 0.10/0.28 thf(decl_51, type, emptysetimpfalse: $o).
% 0.10/0.28 thf(decl_52, type, notinemptyset: $o).
% 0.10/0.28 thf(decl_53, type, exuE3e: $o).
% 0.10/0.28 thf(decl_54, type, setext: $o).
% 0.10/0.28 thf(decl_55, type, emptyI: $o).
% 0.10/0.28 thf(decl_56, type, noeltsimpempty: $o).
% 0.10/0.28 thf(decl_57, type, setbeta: $o).
% 0.10/0.28 thf(decl_58, type, nonempty: $i > $o).
% 0.10/0.28 thf(decl_59, type, nonemptyE1: $o).
% 0.10/0.28 thf(decl_60, type, nonemptyI: $o).
% 0.10/0.28 thf(decl_61, type, nonemptyI1: $o).
% 0.10/0.28 thf(decl_62, type, setadjoinIL: $o).
% 0.10/0.28 thf(decl_63, type, emptyinunitempty: $o).
% 0.10/0.28 thf(decl_64, type, setadjoinIR: $o).
% 0.10/0.28 thf(decl_65, type, setadjoinE: $o).
% 0.10/0.28 thf(decl_66, type, setadjoinOr: $o).
% 0.10/0.28 thf(decl_67, type, setoftrueEq: $o).
% 0.10/0.28 thf(decl_68, type, powersetI: $o).
% 0.10/0.28 thf(decl_69, type, emptyinPowerset: $o).
% 0.10/0.28 thf(decl_70, type, epred1_0: $o).
% 0.10/0.28 thf(decl_71, type, esk1_2: $i > $i > $i).
% 0.10/0.28 thf(decl_72, type, esk2_2: $i > $i > $i).
% 0.10/0.28 thf(decl_73, type, esk3_1: $i > $i).
% 0.10/0.28 thf(decl_74, type, esk4_2: ($i > $i > $o) > $i > $i).
% 0.10/0.28 thf(decl_75, type, esk5_3: ($i > $i > $o) > $i > $i > $i).
% 0.10/0.28 thf(decl_76, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.10/0.28 thf(decl_77, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.10/0.28 thf(decl_78, type, esk8_1: $i > $i).
% 0.10/0.28 thf(decl_79, type, esk9_2: ($i > $o) > $i > $i).
% 0.10/0.28 thf(decl_80, type, esk10_1: ($i > $o) > $i).
% 0.10/0.28 thf(decl_81, type, esk11_2: ($i > $o) > $i > $i).
% 0.10/0.28 thf(decl_82, type, esk12_1: ($i > $o) > $i).
% 0.10/0.28 thf(decl_83, type, esk13_2: $i > $i > $i).
% 0.10/0.28 thf(decl_84, type, esk14_2: $i > $i > $i).
% 0.10/0.28 thf(decl_85, type, esk15_1: $i > $i).
% 0.10/0.28 thf(decl_86, type, esk16_1: $i > $i).
% 0.10/0.28 thf(decl_87, type, esk17_1: $i > $i).
% 0.10/0.28 thf(decl_88, type, esk18_2: $i > $i > $i).
% 0.10/0.28 thf(decl_89, type, esk19_0: $i).
% 0.10/0.28 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', nonempty)).
% 0.10/0.28 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', nonemptyI)).
% 0.10/0.28 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', replAx)).
% 0.10/0.28 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', exu)).
% 0.10/0.28 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', prop2set)).
% 0.10/0.28 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', exuE1)).
% 0.10/0.28 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', exuE3e)).
% 0.10/0.28 thf(emptyInPowerset, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>![X4:$i]:((in @ emptyset @ (powerset @ X4))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', emptyInPowerset)).
% 0.10/0.28 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', setbeta)).
% 0.10/0.28 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', nonemptyE1)).
% 0.10/0.28 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', nonemptyI1)).
% 0.10/0.28 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', setoftrueEq)).
% 0.10/0.28 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', prop2setE)).
% 0.10/0.28 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', dsetconstrER)).
% 0.10/0.28 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', dsetconstrEL)).
% 0.10/0.28 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', dsetconstrI)).
% 0.10/0.28 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', setadjoinIL)).
% 0.10/0.28 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', emptyinunitempty)).
% 0.10/0.28 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', setadjoinIR)).
% 0.10/0.28 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.3PPYI6L2kY/E---3.1_380719.p', setadjoinE)).
% 0.10/0.28 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', setextAx)).
% 0.10/0.28 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', setadjoinOr)).
% 0.10/0.28 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', powersetI)).
% 0.10/0.28 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', emptyinPowerset)).
% 0.10/0.28 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', emptysetAx)).
% 0.10/0.28 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', foundationAx)).
% 0.10/0.28 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.3PPYI6L2kY/E---3.1_380719.p', omegaIndAx)).
% 0.10/0.28 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', omegaSAx)).
% 0.10/0.28 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', omega0Ax)).
% 0.10/0.28 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', powersetAx)).
% 0.10/0.28 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', setadjoinAx)).
% 0.10/0.28 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.3PPYI6L2kY/E---3.1_380719.p', wellorderingAx)).
% 0.10/0.28 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', emptysetimpfalse)).
% 0.10/0.28 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', emptysetE)).
% 0.10/0.28 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.3PPYI6L2kY/E---3.1_380719.p', setext)).
% 0.10/0.28 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', emptyI)).
% 0.10/0.28 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', noeltsimpempty)).
% 0.10/0.28 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.3PPYI6L2kY/E---3.1_380719.p', notinemptyset)).
% 0.10/0.28 thf(c_0_38, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.10/0.28 thf(c_0_39, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.10/0.28 thf(c_0_40, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.10/0.28 thf(c_0_41, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.10/0.28 thf(c_0_42, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.10/0.28 thf(c_0_43, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.10/0.28 thf(c_0_44, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.10/0.28 thf(c_0_45, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[emptyInPowerset])).
% 0.10/0.28 thf(c_0_46, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.10/0.28 thf(c_0_47, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_38])).
% 0.10/0.28 thf(c_0_48, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_39, c_0_38])).
% 0.10/0.28 thf(c_0_49, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_38])).
% 0.10/0.28 thf(c_0_50, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.10/0.28 thf(c_0_51, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X113:$i]:(((((X6 @ X2 @ X113)))&(![X114:$i]:(((((X6 @ X2 @ X114)))=>(((X113)=(X114)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_40, c_0_41])).
% 0.10/0.28 thf(c_0_52, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_42])).
% 0.10/0.28 thf(c_0_53, plain, ((exuE1)=(![X1:$i > $o]:((((?[X115:$i]:(((((X1 @ X115)))&(![X116:$i]:(((((X1 @ X116)))=>(((X115)=(X116))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_43, c_0_41])).
% 0.10/0.28 thf(c_0_54, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.10/0.28 thf(c_0_55, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.10/0.28 thf(c_0_56, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.10/0.28 thf(c_0_57, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X117:$i]:(((((X1 @ X117)))&(![X118:$i]:(((((X1 @ X118)))=>(((X117)=(X118))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_44, c_0_41])).
% 0.10/0.28 thf(c_0_58, plain, ((epred1_0)<=>![X145:$i]:(?[X146:$i]:((((![X147:$i]:(((in @ X147 @ X146)=>![X148:$i]:(((in @ X148 @ X147)=>(in @ X148 @ X145)))))&![X149:$i, X150:$i]:((((in @ X149 @ X145)&(in @ X150 @ X145))=>(![X151:$i]:(((in @ X151 @ X146)=>((in @ X149 @ X151)<=>(in @ X150 @ X151))))=>((X149)=(X150))))))&![X152:$i, X153:$i]:((((in @ X152 @ X146)&(in @ X153 @ X146))=>(![X154:$i]:(((in @ X154 @ X152)=>(in @ X154 @ X153)))|![X155:$i]:(((in @ X155 @ X153)=>(in @ X155 @ X152)))))))&![X156:$i]:(((![X157:$i]:(((in @ X157 @ X156)=>(in @ X157 @ X145)))&?[X158:$i]:((in @ X158 @ X156)))=>?[X159:$i, X160:$i]:(((((in @ X159 @ X146)&(in @ X160 @ X156))&~(?[X161:$i]:(((in @ X161 @ X159)&(in @ X161 @ X156)))))&![X162:$i]:(((in @ X162 @ X146)=>(![X163:$i]:(((in @ X163 @ X162)=>(in @ X163 @ X159)))|(in @ X160 @ X162)))))))))))), introduced(definition)).
% 0.10/0.28 thf(c_0_59, negated_conjecture, ~((![X119:$i, X120:$i]:((![X121:$i]:(((in @ X121 @ X119)<=>(in @ X121 @ X120)))=>((X119)=(X120))))=>(![X122:$i]:(~(in @ X122 @ emptyset))=>(![X123:$i, X124:$i, X125:$i]:(((in @ X125 @ (setadjoin @ X123 @ X124))<=>(((X125)=(X123))|(in @ X125 @ X124))))=>(![X126:$i, X127:$i]:(((in @ X127 @ (powerset @ X126))<=>![X128:$i]:(((in @ X128 @ X127)=>(in @ X128 @ X126)))))=>((setunionAx)=>((in @ emptyset @ omega)=>(![X129:$i]:(((in @ X129 @ omega)=>(in @ (setadjoin @ X129 @ X129) @ omega)))=>(![X130:$i]:((((in @ emptyset @ X130)&![X131:$i]:((((in @ X131 @ omega)&(in @ X131 @ X130))=>(in @ (setadjoin @ X131 @ X131) @ X130))))=>![X132:$i]:(((in @ X132 @ omega)=>(in @ X132 @ X130)))))=>(![X133:$i > $i > $o, X134:$i]:((![X135:$i]:(((in @ X135 @ X134)=>?[X136:$i]:(((X133 @ X135 @ X136)&![X137:$i]:(((X133 @ X135 @ X137)=>((X136)=(X137))))))))=>?[X138:$i]:(![X139:$i]:(((in @ X139 @ X138)<=>?[X140:$i]:(((in @ X140 @ X134)&(X133 @ X140 @ X139))))))))=>(![X141:$i]:((?[X142:$i]:((in @ X142 @ X141))=>?[X143:$i]:(((in @ X143 @ X141)&~(?[X144:$i]:(((in @ X144 @ X143)&(in @ X144 @ X141))))))))=>((epred1_0)=>((descrp)=>(![X164:$i, X165:$i > $o, X166:$i]:(((in @ X166 @ X164)=>((X165 @ X166)=>(in @ X166 @ (dsetconstr @ X164 @ X165)))))=>(![X167:$i, X168:$i > $o, X169:$i]:(((in @ X169 @ (dsetconstr @ X167 @ X168))=>(in @ X169 @ X167)))=>(![X170:$i, X171:$i > $o, X172:$i]:(((in @ X172 @ (dsetconstr @ X170 @ X171))=>(X171 @ X172)))=>(![X173:$i > $o]:((?[X174:$i]:(((X173 @ X174)&![X175:$i]:(((X173 @ X175)=>((X174)=(X175))))))=>?[X176:$i]:(((X173 @ X176)&![X177:$i]:(((X173 @ X177)=>((X176)=(X177))))))))=>(![X178:$o, X179:$i]:(((in @ X179 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X178)))))=>(X178)))=>(![X180:$i]:(((in @ X180 @ emptyset)=>![X181:$o]:((X181))))=>(![X182:$i]:(((in @ X182 @ emptyset)=>~($true)))=>(![X183:$i]:(~(in @ X183 @ emptyset))=>(![X184:$i > $o]:((?[X185:$i]:(((X184 @ X185)&![X186:$i]:(((X184 @ X186)=>((X185)=(X186))))))=>?[X187:$i]:((X184 @ X187))))=>(![X188:$i, X189:$i]:((![X190:$i]:(((in @ X190 @ X188)=>(in @ X190 @ X189)))=>(![X191:$i]:(((in @ X191 @ X189)=>(in @ X191 @ X188)))=>((X188)=(X189)))))=>(![X192:$i]:((![X193:$i]:(~(in @ X193 @ X192))=>((X192)=(emptyset))))=>(![X194:$i]:((![X195:$i]:(~(in @ X195 @ X194))=>((X194)=(emptyset))))=>(![X196:$i, X197:$i > $o, X198:$i]:(((in @ X198 @ X196)=>((in @ X198 @ (dsetconstr @ X196 @ X197))<=>(X197 @ X198))))=>(![X199:$i]:((((X199)!=(emptyset))=>?[X200:$i]:((in @ X200 @ X199))))=>(![X201:$i, X202:$i > $o, X203:$i]:(((in @ X203 @ X201)=>((X202 @ X203)=>((dsetconstr @ X201 @ X202)!=(emptyset)))))=>(![X204:$i]:((?[X205:$i]:((in @ X205 @ X204))=>((X204)!=(emptyset))))=>(![X206:$i, X207:$i]:((in @ X206 @ (setadjoin @ X206 @ X207)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X208:$i, X209:$i, X210:$i]:(((in @ X210 @ X209)=>(in @ X210 @ (setadjoin @ X208 @ X209))))=>(![X211:$i, X212:$i, X213:$i]:(((in @ X213 @ (setadjoin @ X211 @ X212))=>![X214:$o]:(((((X213)=(X211))=>(X214))=>(((in @ X213 @ X212)=>(X214))=>(X214))))))=>(![X215:$i, X216:$i, X217:$i]:(((in @ X217 @ (setadjoin @ X215 @ X216))=>(((X217)=(X215))|(in @ X217 @ X216))))=>(![X218:$i]:(((dsetconstr @ X218 @ (^[Z0:$i]:($true)))=(X218)))=>(![X219:$i, X220:$i]:((![X221:$i]:(((in @ X221 @ X220)=>(in @ X221 @ X219)))=>(in @ X220 @ (powerset @ X219))))=>(![X222:$i]:((in @ emptyset @ (powerset @ X222)))=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))))))))))))))))))))))))))))))))))))))), 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)],[c_0_45, c_0_46]), c_0_47]), c_0_48]), c_0_49]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setextAx]), setadjoinOr]), c_0_50]), powersetI]), emptyinPowerset]), emptysetAx]), foundationAx]), c_0_51]), omegaIndAx]), omegaSAx]), omega0Ax]), powersetAx]), setadjoinAx]), wellorderingAx]), emptysetimpfalse]), emptysetE]), c_0_52]), c_0_53]), c_0_54]), c_0_55]), c_0_56]), c_0_57]), setext]), emptyI]), noeltsimpempty]), notinemptyset])])]), c_0_58])).
% 0.10/0.28 thf(c_0_60, negated_conjecture, ![X223:$i, X224:$i, X226:$i, X227:$i, X228:$i, X229:$i, X230:$i, X231:$i, X232:$i, X233:$i, X234:$i, X236:$i, X237:$i, X239:$i, X240:$i > $i > $o, X241:$i, X243:$i, X246:$i, X248:$i, X249:$i, X250:$i, X251:$i, X253:$i, X254:$i, X255:$i > $o, X256:$i, X257:$i, X258:$i > $o, X259:$i, X260:$i, X261:$i > $o, X262:$i, X263:$i > $o, X264:$i, X267:$i, X268:$o, X269:$i, X270:$i, X271:$o, X272:$i, X273:$i, X274:$i > $o, X275:$i, X278:$i, X279:$i, X282:$i, X284:$i, X286:$i, X287:$i > $o, X288:$i, X289:$i, X291:$i, X292:$i > $o, X293:$i, X294:$i, X295:$i, X296:$i, X297:$i, X298:$i, X299:$i, X300:$i, X301:$i, X302:$i, X303:$i, X304:$o, X305:$i, X306:$i, X307:$i, X308:$i, X309:$i, X310:$i, X312:$i]:((((~(in @ (esk1_2 @ X223 @ X224) @ X223)|~(in @ (esk1_2 @ X223 @ X224) @ X224)|((X223)=(X224)))&((in @ (esk1_2 @ X223 @ X224) @ X223)|(in @ (esk1_2 @ X223 @ X224) @ X224)|((X223)=(X224))))&(~(in @ X226 @ emptyset)&(((~(in @ X229 @ (setadjoin @ X227 @ X228))|(((X229)=(X227))|(in @ X229 @ X228)))&((((X229)!=(X227))|(in @ X229 @ (setadjoin @ X227 @ X228)))&(~(in @ X229 @ X228)|(in @ X229 @ (setadjoin @ X227 @ X228)))))&(((~(in @ X231 @ (powerset @ X230))|(~(in @ X232 @ X231)|(in @ X232 @ X230)))&(((in @ (esk2_2 @ X233 @ X234) @ X234)|(in @ X234 @ (powerset @ X233)))&(~(in @ (esk2_2 @ X233 @ X234) @ X233)|(in @ X234 @ (powerset @ X233)))))&((setunionAx)&((in @ emptyset @ omega)&((~(in @ X236 @ omega)|(in @ (setadjoin @ X236 @ X236) @ omega))&(((((in @ (esk3_1 @ X237) @ omega)|~(in @ emptyset @ X237)|(~(in @ X239 @ omega)|(in @ X239 @ X237)))&((in @ (esk3_1 @ X237) @ X237)|~(in @ emptyset @ X237)|(~(in @ X239 @ omega)|(in @ X239 @ X237))))&(~(in @ (setadjoin @ (esk3_1 @ X237) @ (esk3_1 @ X237)) @ X237)|~(in @ emptyset @ X237)|(~(in @ X239 @ omega)|(in @ X239 @ X237))))&((((((in @ (esk7_3 @ X240 @ X241 @ X246) @ X241)|~(in @ X246 @ (esk6_2 @ X240 @ X241))|(in @ (esk4_2 @ X240 @ X241) @ X241))&((X240 @ (esk7_3 @ X240 @ X241 @ X246) @ X246)|~(in @ X246 @ (esk6_2 @ X240 @ X241))|(in @ (esk4_2 @ X240 @ X241) @ X241)))&(~(in @ X249 @ X241)|~(X240 @ X249 @ X248)|(in @ X248 @ (esk6_2 @ X240 @ X241))|(in @ (esk4_2 @ X240 @ X241) @ X241)))&(((((in @ (esk7_3 @ X240 @ X241 @ X246) @ X241)|~(in @ X246 @ (esk6_2 @ X240 @ X241))|((X240 @ (esk4_2 @ X240 @ X241) @ (esk5_3 @ X240 @ X241 @ X243))|~(X240 @ (esk4_2 @ X240 @ X241) @ X243)))&((X240 @ (esk7_3 @ X240 @ X241 @ X246) @ X246)|~(in @ X246 @ (esk6_2 @ X240 @ X241))|((X240 @ (esk4_2 @ X240 @ X241) @ (esk5_3 @ X240 @ X241 @ X243))|~(X240 @ (esk4_2 @ X240 @ X241) @ X243))))&(~(in @ X249 @ X241)|~(X240 @ X249 @ X248)|(in @ X248 @ (esk6_2 @ X240 @ X241))|((X240 @ (esk4_2 @ X240 @ X241) @ (esk5_3 @ X240 @ X241 @ X243))|~(X240 @ (esk4_2 @ X240 @ X241) @ X243))))&((((in @ (esk7_3 @ X240 @ X241 @ X246) @ X241)|~(in @ X246 @ (esk6_2 @ X240 @ X241))|(((X243)!=(esk5_3 @ X240 @ X241 @ X243))|~(X240 @ (esk4_2 @ X240 @ X241) @ X243)))&((X240 @ (esk7_3 @ X240 @ X241 @ X246) @ X246)|~(in @ X246 @ (esk6_2 @ X240 @ X241))|(((X243)!=(esk5_3 @ X240 @ X241 @ X243))|~(X240 @ (esk4_2 @ X240 @ X241) @ X243))))&(~(in @ X249 @ X241)|~(X240 @ X249 @ X248)|(in @ X248 @ (esk6_2 @ X240 @ X241))|(((X243)!=(esk5_3 @ X240 @ X241 @ X243))|~(X240 @ (esk4_2 @ X240 @ X241) @ X243))))))&((((in @ (esk8_1 @ X250) @ X250)|~(in @ X251 @ X250))&(~(in @ X253 @ (esk8_1 @ X250))|~(in @ X253 @ X250)|~(in @ X251 @ X250)))&((epred1_0)&((descrp)&((~(in @ X256 @ X254)|(~(X255 @ X256)|(in @ X256 @ (dsetconstr @ X254 @ X255))))&((~(in @ X259 @ (dsetconstr @ X257 @ X258))|(in @ X259 @ X257))&((~(in @ X262 @ (dsetconstr @ X260 @ X261))|(X261 @ X262))&(((((X263 @ (esk10_1 @ X263))|((X263 @ (esk9_2 @ X263 @ X264))|~(X263 @ X264)))&(~(X263 @ X267)|((esk10_1 @ X263)=(X267))|((X263 @ (esk9_2 @ X263 @ X264))|~(X263 @ X264))))&(((X263 @ (esk10_1 @ X263))|(((X264)!=(esk9_2 @ X263 @ X264))|~(X263 @ X264)))&(~(X263 @ X267)|((esk10_1 @ X263)=(X267))|(((X264)!=(esk9_2 @ X263 @ X264))|~(X263 @ X264)))))&((~(in @ X269 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X268)))))|(X268))&((~(in @ X270 @ emptyset)|(X271))&((~(in @ X272 @ emptyset)|~($true))&(~(in @ X273 @ emptyset)&((((X274 @ (esk11_2 @ X274 @ X275))|~(X274 @ X275)|(X274 @ (esk12_1 @ X274)))&(((X275)!=(esk11_2 @ X274 @ X275))|~(X274 @ X275)|(X274 @ (esk12_1 @ X274))))&(((((in @ (esk14_2 @ X278 @ X279) @ X279)|((X278)=(X279))|(in @ (esk13_2 @ X278 @ X279) @ X278))&(~(in @ (esk14_2 @ X278 @ X279) @ X278)|((X278)=(X279))|(in @ (esk13_2 @ X278 @ X279) @ X278)))&(((in @ (esk14_2 @ X278 @ X279) @ X279)|((X278)=(X279))|~(in @ (esk13_2 @ X278 @ X279) @ X279))&(~(in @ (esk14_2 @ X278 @ X279) @ X278)|((X278)=(X279))|~(in @ (esk13_2 @ X278 @ X279) @ X279))))&(((in @ (esk15_1 @ X282) @ X282)|((X282)=(emptyset)))&(((in @ (esk16_1 @ X284) @ X284)|((X284)=(emptyset)))&(((~(in @ X288 @ (dsetconstr @ X286 @ X287))|(X287 @ X288)|~(in @ X288 @ X286))&(~(X287 @ X288)|(in @ X288 @ (dsetconstr @ X286 @ X287))|~(in @ X288 @ X286)))&((((X289)=(emptyset))|(in @ (esk17_1 @ X289) @ X289))&((~(in @ X293 @ X291)|(~(X292 @ X293)|((dsetconstr @ X291 @ X292)!=(emptyset))))&((~(in @ X295 @ X294)|((X294)!=(emptyset)))&((in @ X296 @ (setadjoin @ X296 @ X297))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X300 @ X299)|(in @ X300 @ (setadjoin @ X298 @ X299)))&(((((in @ X303 @ X302)|(X304)|((X303)=(X301))|~(in @ X303 @ (setadjoin @ X301 @ X302)))&(~(X304)|(X304)|((X303)=(X301))|~(in @ X303 @ (setadjoin @ X301 @ X302))))&(((in @ X303 @ X302)|(X304)|~(X304)|~(in @ X303 @ (setadjoin @ X301 @ X302)))&(~(X304)|(X304)|~(X304)|~(in @ X303 @ (setadjoin @ X301 @ X302)))))&((~(in @ X307 @ (setadjoin @ X305 @ X306))|(((X307)=(X305))|(in @ X307 @ X306)))&(((dsetconstr @ X308 @ (^[Z0:$i]:($true)))=(X308))&((((in @ (esk18_2 @ X309 @ X310) @ X310)|(in @ X310 @ (powerset @ X309)))&(~(in @ (esk18_2 @ X309 @ X310) @ X309)|(in @ X310 @ (powerset @ X309))))&((in @ emptyset @ (powerset @ X312))&~(in @ emptyset @ (powerset @ esk19_0))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])])])])])).
% 0.10/0.28 thf(c_0_61, negated_conjecture, ~((in @ emptyset @ (powerset @ esk19_0))), inference(split_conjunct,[status(thm)],[c_0_60])).
% 0.10/0.28 thf(c_0_62, negated_conjecture, ![X2:$i]:((in @ emptyset @ (powerset @ X2))), inference(split_conjunct,[status(thm)],[c_0_60])).
% 0.10/0.28 thf(c_0_63, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61, c_0_62])]), ['proof']).
% 0.10/0.28 % SZS output end CNFRefutation
% 0.10/0.28 % Parsed axioms : 87
% 0.10/0.28 % Removed by relevancy pruning/SinE : 49
% 0.10/0.28 % Initial clauses : 78
% 0.10/0.28 % Removed in clause preprocessing : 3
% 0.10/0.28 % Initial clauses in saturation : 75
% 0.10/0.28 % Processed clauses : 10
% 0.10/0.28 % ...of these trivial : 0
% 0.10/0.28 % ...subsumed : 3
% 0.10/0.28 % ...remaining for further processing : 6
% 0.10/0.28 % Other redundant clauses eliminated : 0
% 0.10/0.28 % Clauses deleted for lack of memory : 0
% 0.10/0.28 % Backward-subsumed : 0
% 0.10/0.28 % Backward-rewritten : 0
% 0.10/0.28 % Generated clauses : 0
% 0.10/0.28 % ...of the previous two non-redundant : 0
% 0.10/0.28 % ...aggressively subsumed : 0
% 0.10/0.28 % Contextual simplify-reflections : 0
% 0.10/0.28 % Paramodulations : 0
% 0.10/0.28 % Factorizations : 0
% 0.10/0.28 % NegExts : 0
% 0.10/0.28 % Equation resolutions : 0
% 0.10/0.28 % Disequality decompositions : 0
% 0.10/0.28 % Total rewrite steps : 1
% 0.10/0.28 % ...of those cached : 0
% 0.10/0.28 % Propositional unsat checks : 0
% 0.10/0.28 % Propositional check models : 0
% 0.10/0.28 % Propositional check unsatisfiable : 0
% 0.10/0.28 % Propositional clauses : 0
% 0.10/0.28 % Propositional clauses after purity: 0
% 0.10/0.28 % Propositional unsat core size : 0
% 0.10/0.28 % Propositional preprocessing time : 0.000
% 0.10/0.28 % Propositional encoding time : 0.000
% 0.10/0.28 % Propositional solver time : 0.000
% 0.10/0.28 % Success case prop preproc time : 0.000
% 0.10/0.28 % Success case prop encoding time : 0.000
% 0.10/0.28 % Success case prop solver time : 0.000
% 0.10/0.28 % Current number of processed clauses : 6
% 0.10/0.28 % Positive orientable unit clauses : 5
% 0.10/0.28 % Positive unorientable unit clauses: 0
% 0.10/0.28 % Negative unit clauses : 1
% 0.10/0.28 % Non-unit-clauses : 0
% 0.10/0.28 % Current number of unprocessed clauses: 65
% 0.10/0.28 % ...number of literals in the above : 215
% 0.10/0.28 % Current number of archived formulas : 0
% 0.10/0.28 % Current number of archived clauses : 0
% 0.10/0.28 % Clause-clause subsumption calls (NU) : 0
% 0.10/0.28 % Rec. Clause-clause subsumption calls : 0
% 0.10/0.28 % Non-unit clause-clause subsumptions : 0
% 0.10/0.28 % Unit Clause-clause subsumption calls : 0
% 0.10/0.28 % Rewrite failures with RHS unbound : 0
% 0.10/0.28 % BW rewrite match attempts : 0
% 0.10/0.28 % BW rewrite match successes : 0
% 0.10/0.28 % Condensation attempts : 0
% 0.10/0.28 % Condensation successes : 0
% 0.10/0.28 % Termbank termtop insertions : 9419
% 0.10/0.28 % Search garbage collected termcells : 3683
% 0.10/0.28
% 0.10/0.28 % -------------------------------------------------
% 0.10/0.28 % User time : 0.010 s
% 0.10/0.28 % System time : 0.006 s
% 0.10/0.28 % Total time : 0.017 s
% 0.10/0.28 % Maximum resident set size: 4488 pages
% 0.10/0.28
% 0.10/0.28 % -------------------------------------------------
% 0.10/0.28 % User time : 0.013 s
% 0.10/0.28 % System time : 0.012 s
% 0.10/0.28 % Total time : 0.025 s
% 0.10/0.28 % Maximum resident set size: 4864 pages
% 0.10/0.28 % E exiting
%------------------------------------------------------------------------------