%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU520^1 : 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 : 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 08:26:33 AM UTC 2026
% Result : Theorem 0.08s 0.29s
% Output : CNFRefutation 0.08s
% 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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n016.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 13:52:49 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.26 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.KIFoMXqTQa/E---3.1_380717.p
% 0.08/0.28 % Version: 3.5.1-ho
% 0.08/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.28 % Starting sh5l with 300s (1) cores
% 0.08/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.28 % sh5l with pid 380745 completed with status 0
% 0.08/0.28 % Result found by sh5l
% 0.08/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.28 % Starting sh5l with 300s (1) cores
% 0.08/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.08/0.28 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.08/0.28 % Search class: HGHSS-FFMS31-SHFSMSBN
% 0.08/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.28 % SubtermCWHack with pid 380752 completed with status 0
% 0.08/0.28 % Result found by SubtermCWHack
% 0.08/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.29 % Starting sh5l with 300s (1) cores
% 0.08/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.08/0.29 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.08/0.29 % Search class: HGHSS-FFMS31-SHFSMSBN
% 0.08/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.29 % Preprocessing time : 0.002 s
% 0.08/0.29
% 0.08/0.29 % Proof found!
% 0.08/0.29 % SZS status Theorem
% 0.08/0.29 % SZS output start CNFRefutation
% 0.08/0.29 thf(decl_23, type, in: $i > $i > $o).
% 0.08/0.29 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.08/0.29 thf(decl_25, type, setextAx: $o).
% 0.08/0.29 thf(decl_26, type, emptyset: $i).
% 0.08/0.29 thf(decl_27, type, emptysetAx: $o).
% 0.08/0.29 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.08/0.29 thf(decl_29, type, setadjoinAx: $o).
% 0.08/0.29 thf(decl_30, type, powerset: $i > $i).
% 0.08/0.29 thf(decl_31, type, powersetAx: $o).
% 0.08/0.29 thf(decl_32, type, setunion: $i > $i).
% 0.08/0.29 thf(decl_33, type, setunionAx: $o).
% 0.08/0.29 thf(decl_34, type, omega: $i).
% 0.08/0.29 thf(decl_35, type, omega0Ax: $o).
% 0.08/0.29 thf(decl_36, type, omegaSAx: $o).
% 0.08/0.29 thf(decl_37, type, omegaIndAx: $o).
% 0.08/0.29 thf(decl_38, type, replAx: $o).
% 0.08/0.29 thf(decl_39, type, foundationAx: $o).
% 0.08/0.29 thf(decl_40, type, wellorderingAx: $o).
% 0.08/0.29 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.08/0.29 thf(decl_42, type, descrp: $o).
% 0.08/0.29 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.08/0.29 thf(decl_44, type, dsetconstrI: $o).
% 0.08/0.29 thf(decl_45, type, dsetconstrEL: $o).
% 0.08/0.29 thf(decl_46, type, dsetconstrER: $o).
% 0.08/0.29 thf(decl_47, type, exuE1: $o).
% 0.08/0.29 thf(decl_48, type, prop2set: $o > $i).
% 0.08/0.29 thf(decl_49, type, prop2setE: $o).
% 0.08/0.29 thf(decl_50, type, emptysetE: $o).
% 0.08/0.29 thf(decl_51, type, emptysetimpfalse: $o).
% 0.08/0.29 thf(decl_52, type, notinemptyset: $o).
% 0.08/0.29 thf(decl_53, type, exuE3e: $o).
% 0.08/0.29 thf(decl_54, type, setext: $o).
% 0.08/0.29 thf(decl_55, type, emptyI: $o).
% 0.08/0.29 thf(decl_56, type, noeltsimpempty: $o).
% 0.08/0.29 thf(decl_57, type, setbeta: $o).
% 0.08/0.29 thf(decl_58, type, nonempty: $i > $o).
% 0.08/0.29 thf(decl_59, type, nonemptyE1: $o).
% 0.08/0.29 thf(decl_60, type, nonemptyI: $o).
% 0.08/0.29 thf(decl_61, type, nonemptyI1: $o).
% 0.08/0.29 thf(decl_62, type, setadjoinIL: $o).
% 0.08/0.29 thf(decl_63, type, emptyinunitempty: $o).
% 0.08/0.29 thf(decl_64, type, setadjoinIR: $o).
% 0.08/0.29 thf(decl_65, type, setadjoinE: $o).
% 0.08/0.29 thf(decl_66, type, setadjoinOr: $o).
% 0.08/0.29 thf(decl_67, type, setoftrueEq: $o).
% 0.08/0.29 thf(decl_68, type, powersetI: $o).
% 0.08/0.29 thf(decl_69, type, emptyinPowerset: $o).
% 0.08/0.29 thf(decl_70, type, epred1_0: $o).
% 0.08/0.29 thf(decl_71, type, esk1_2: $i > $i > $i).
% 0.08/0.29 thf(decl_72, type, esk2_2: $i > $i > $i).
% 0.08/0.29 thf(decl_73, type, esk3_2: $i > $i > $i).
% 0.08/0.29 thf(decl_74, type, esk4_1: $i > $i).
% 0.08/0.29 thf(decl_75, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.08/0.29 thf(decl_76, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.29 thf(decl_77, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.08/0.29 thf(decl_78, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.29 thf(decl_79, type, esk9_1: $i > $i).
% 0.08/0.29 thf(decl_80, type, esk10_2: ($i > $o) > $i > $i).
% 0.08/0.29 thf(decl_81, type, esk11_2: ($i > $o) > $i > $i).
% 0.08/0.29 thf(decl_82, type, esk12_1: ($i > $o) > $i).
% 0.08/0.29 thf(decl_83, type, esk13_2: ($i > $o) > $i > $i).
% 0.08/0.29 thf(decl_84, type, esk14_1: ($i > $o) > $i).
% 0.08/0.29 thf(decl_85, type, esk15_2: $i > $i > $i).
% 0.08/0.29 thf(decl_86, type, esk16_2: $i > $i > $i).
% 0.08/0.29 thf(decl_87, type, esk17_1: $i > $i).
% 0.08/0.29 thf(decl_88, type, esk18_1: $i > $i).
% 0.08/0.29 thf(decl_89, type, esk19_1: $i > $i).
% 0.08/0.29 thf(decl_90, type, esk20_2: $i > $i > $i).
% 0.08/0.29 thf(decl_91, type, esk21_0: $i).
% 0.08/0.29 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', nonempty)).
% 0.08/0.29 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', replAx)).
% 0.08/0.29 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', exu)).
% 0.08/0.29 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', prop2set)).
% 0.08/0.29 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', exuE1)).
% 0.08/0.29 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', descrp)).
% 0.08/0.29 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', exuE3e)).
% 0.08/0.29 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', nonemptyI)).
% 0.08/0.29 thf(emptyInPowerset, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>![X4:$i]:((in @ emptyset @ (powerset @ X4))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', emptyInPowerset)).
% 0.08/0.29 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', nonemptyI1)).
% 0.08/0.29 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', setoftrueEq)).
% 0.08/0.29 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', prop2setE)).
% 0.08/0.29 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', dsetconstrER)).
% 0.08/0.29 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', dsetconstrEL)).
% 0.08/0.29 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', dsetconstrI)).
% 0.08/0.29 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', nonemptyE1)).
% 0.08/0.29 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', setbeta)).
% 0.08/0.29 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', setadjoinE)).
% 0.08/0.29 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', setadjoinIL)).
% 0.08/0.29 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', emptyinunitempty)).
% 0.08/0.29 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', setadjoinOr)).
% 0.08/0.29 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', emptyinPowerset)).
% 0.08/0.29 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', powersetI)).
% 0.08/0.29 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', powersetAx)).
% 0.08/0.29 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', foundationAx)).
% 0.08/0.29 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.KIFoMXqTQa/E---3.1_380717.p', omegaIndAx)).
% 0.08/0.29 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', omegaSAx)).
% 0.08/0.29 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', omega0Ax)).
% 0.08/0.29 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', setunionAx)).
% 0.08/0.29 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', setadjoinAx)).
% 0.08/0.29 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.KIFoMXqTQa/E---3.1_380717.p', wellorderingAx)).
% 0.08/0.29 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', emptysetE)).
% 0.08/0.29 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', emptysetimpfalse)).
% 0.08/0.29 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', noeltsimpempty)).
% 0.08/0.29 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', emptyI)).
% 0.08/0.29 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.KIFoMXqTQa/E---3.1_380717.p', setext)).
% 0.08/0.29 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', notinemptyset)).
% 0.08/0.29 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', setadjoinIR)).
% 0.08/0.29 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', emptysetAx)).
% 0.08/0.29 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.KIFoMXqTQa/E---3.1_380717.p', setextAx)).
% 0.08/0.29 thf(c_0_40, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.08/0.29 thf(c_0_41, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.08/0.29 thf(c_0_42, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.08/0.29 thf(c_0_43, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.08/0.29 thf(c_0_44, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.08/0.29 thf(c_0_45, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.08/0.29 thf(c_0_46, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.08/0.29 thf(c_0_47, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.08/0.29 thf(c_0_48, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[emptyInPowerset])).
% 0.08/0.29 thf(c_0_49, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_40])).
% 0.08/0.29 thf(c_0_50, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.08/0.29 thf(c_0_51, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X117:$i]:(((((X6 @ X2 @ X117)))&(![X118:$i]:(((((X6 @ X2 @ X118)))=>(((X117)=(X118)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_41, c_0_42])).
% 0.08/0.29 thf(c_0_52, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_43])).
% 0.08/0.29 thf(c_0_53, plain, ((exuE1)=(![X1:$i > $o]:((((?[X121:$i]:(((((X1 @ X121)))&(![X122:$i]:(((((X1 @ X122)))=>(((X121)=(X122))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_44, c_0_42])).
% 0.08/0.29 thf(c_0_54, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.08/0.29 thf(c_0_55, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.08/0.29 thf(c_0_56, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.08/0.29 thf(c_0_57, plain, ((descrp)=(![X1:$i > $o]:((((?[X119:$i]:(((((X1 @ X119)))&(![X120:$i]:(((((X1 @ X120)))=>(((X119)=(X120))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_45, c_0_42])).
% 0.08/0.29 thf(c_0_58, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_40])).
% 0.08/0.29 thf(c_0_59, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.08/0.29 thf(c_0_60, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X123:$i]:(((((X1 @ X123)))&(![X124:$i]:(((((X1 @ X124)))=>(((X123)=(X124))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_46, c_0_42])).
% 0.08/0.29 thf(c_0_61, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_47, c_0_40])).
% 0.08/0.29 thf(c_0_62, plain, ((epred1_0)<=>![X154:$i]:(?[X155:$i]:((((![X156:$i]:(((in @ X156 @ X155)=>![X157:$i]:(((in @ X157 @ X156)=>(in @ X157 @ X154)))))&![X158:$i, X159:$i]:((((in @ X158 @ X154)&(in @ X159 @ X154))=>(![X160:$i]:(((in @ X160 @ X155)=>((in @ X158 @ X160)<=>(in @ X159 @ X160))))=>((X158)=(X159))))))&![X161:$i, X162:$i]:((((in @ X161 @ X155)&(in @ X162 @ X155))=>(![X163:$i]:(((in @ X163 @ X161)=>(in @ X163 @ X162)))|![X164:$i]:(((in @ X164 @ X162)=>(in @ X164 @ X161)))))))&![X165:$i]:(((![X166:$i]:(((in @ X166 @ X165)=>(in @ X166 @ X154)))&?[X167:$i]:((in @ X167 @ X165)))=>?[X168:$i, X169:$i]:(((((in @ X168 @ X155)&(in @ X169 @ X165))&~(?[X170:$i]:(((in @ X170 @ X168)&(in @ X170 @ X165)))))&![X171:$i]:(((in @ X171 @ X155)=>(![X172:$i]:(((in @ X172 @ X171)=>(in @ X172 @ X168)))|(in @ X169 @ X171)))))))))))), introduced(definition)).
% 0.08/0.29 thf(c_0_63, negated_conjecture, ~((![X125:$i, X126:$i]:((![X127:$i]:(((in @ X127 @ X125)<=>(in @ X127 @ X126)))=>((X125)=(X126))))=>(![X128:$i]:(~(in @ X128 @ emptyset))=>(![X129:$i, X130:$i, X131:$i]:(((in @ X131 @ (setadjoin @ X129 @ X130))<=>(((X131)=(X129))|(in @ X131 @ X130))))=>(![X132:$i, X133:$i]:(((in @ X133 @ (powerset @ X132))<=>![X134:$i]:(((in @ X134 @ X133)=>(in @ X134 @ X132)))))=>(![X135:$i, X136:$i]:(((in @ X136 @ (setunion @ X135))<=>?[X137:$i]:(((in @ X136 @ X137)&(in @ X137 @ X135)))))=>((in @ emptyset @ omega)=>(![X138:$i]:(((in @ X138 @ omega)=>(in @ (setadjoin @ X138 @ X138) @ omega)))=>(![X139:$i]:((((in @ emptyset @ X139)&![X140:$i]:((((in @ X140 @ omega)&(in @ X140 @ X139))=>(in @ (setadjoin @ X140 @ X140) @ X139))))=>![X141:$i]:(((in @ X141 @ omega)=>(in @ X141 @ X139)))))=>(![X142:$i > $i > $o, X143:$i]:((![X144:$i]:(((in @ X144 @ X143)=>?[X145:$i]:(((X142 @ X144 @ X145)&![X146:$i]:(((X142 @ X144 @ X146)=>((X145)=(X146))))))))=>?[X147:$i]:(![X148:$i]:(((in @ X148 @ X147)<=>?[X149:$i]:(((in @ X149 @ X143)&(X142 @ X149 @ X148))))))))=>(![X150:$i]:((?[X151:$i]:((in @ X151 @ X150))=>?[X152:$i]:(((in @ X152 @ X150)&~(?[X153:$i]:(((in @ X153 @ X152)&(in @ X153 @ X150))))))))=>((epred1_0)=>(![X173:$i > $o]:((?[X174:$i]:(((X173 @ X174)&![X175:$i]:(((X173 @ X175)=>((X174)=(X175))))))=>(X173 @ (descr @ (^[Z0:$i]:(X173 @ Z0))))))=>(![X176:$i, X177:$i > $o, X178:$i]:(((in @ X178 @ X176)=>((X177 @ X178)=>(in @ X178 @ (dsetconstr @ X176 @ X177)))))=>(![X179:$i, X180:$i > $o, X181:$i]:(((in @ X181 @ (dsetconstr @ X179 @ X180))=>(in @ X181 @ X179)))=>(![X182:$i, X183:$i > $o, X184:$i]:(((in @ X184 @ (dsetconstr @ X182 @ X183))=>(X183 @ X184)))=>(![X185:$i > $o]:((?[X186:$i]:(((X185 @ X186)&![X187:$i]:(((X185 @ X187)=>((X186)=(X187))))))=>?[X188:$i]:(((X185 @ X188)&![X189:$i]:(((X185 @ X189)=>((X188)=(X189))))))))=>(![X190:$o, X191:$i]:(((in @ X191 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X190)))))=>(X190)))=>(![X192:$i]:(((in @ X192 @ emptyset)=>![X193:$o]:((X193))))=>(![X194:$i]:(((in @ X194 @ emptyset)=>~($true)))=>(![X195:$i]:(~(in @ X195 @ emptyset))=>(![X196:$i > $o]:((?[X197:$i]:(((X196 @ X197)&![X198:$i]:(((X196 @ X198)=>((X197)=(X198))))))=>?[X199:$i]:((X196 @ X199))))=>(![X200:$i, X201:$i]:((![X202:$i]:(((in @ X202 @ X200)=>(in @ X202 @ X201)))=>(![X203:$i]:(((in @ X203 @ X201)=>(in @ X203 @ X200)))=>((X200)=(X201)))))=>(![X204:$i]:((![X205:$i]:(~(in @ X205 @ X204))=>((X204)=(emptyset))))=>(![X206:$i]:((![X207:$i]:(~(in @ X207 @ X206))=>((X206)=(emptyset))))=>(![X208:$i, X209:$i > $o, X210:$i]:(((in @ X210 @ X208)=>((in @ X210 @ (dsetconstr @ X208 @ X209))<=>(X209 @ X210))))=>(![X211:$i]:((((X211)!=(emptyset))=>?[X212:$i]:((in @ X212 @ X211))))=>(![X213:$i, X214:$i > $o, X215:$i]:(((in @ X215 @ X213)=>((X214 @ X215)=>((dsetconstr @ X213 @ X214)!=(emptyset)))))=>(![X216:$i]:((?[X217:$i]:((in @ X217 @ X216))=>((X216)!=(emptyset))))=>(![X218:$i, X219:$i]:((in @ X218 @ (setadjoin @ X218 @ X219)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X220:$i, X221:$i, X222:$i]:(((in @ X222 @ X221)=>(in @ X222 @ (setadjoin @ X220 @ X221))))=>(![X223:$i, X224:$i, X225:$i]:(((in @ X225 @ (setadjoin @ X223 @ X224))=>![X226:$o]:(((((X225)=(X223))=>(X226))=>(((in @ X225 @ X224)=>(X226))=>(X226))))))=>(![X227:$i, X228:$i, X229:$i]:(((in @ X229 @ (setadjoin @ X227 @ X228))=>(((X229)=(X227))|(in @ X229 @ X228))))=>(![X230:$i]:(((dsetconstr @ X230 @ (^[Z0:$i]:($true)))=(X230)))=>(![X231:$i, X232:$i]:((![X233:$i]:(((in @ X233 @ X232)=>(in @ X233 @ X231)))=>(in @ X232 @ (powerset @ X231))))=>(![X234:$i]:((in @ emptyset @ (powerset @ X234)))=>![X4:$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)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_48, setadjoinE]), c_0_49]), setadjoinIL]), emptyinunitempty]), setadjoinOr]), c_0_50]), emptyinPowerset]), powersetI]), powersetAx]), foundationAx]), c_0_51]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), setadjoinAx]), wellorderingAx]), emptysetE]), c_0_52]), c_0_53]), c_0_54]), c_0_55]), c_0_56]), c_0_57]), emptysetimpfalse]), c_0_58]), c_0_59]), noeltsimpempty]), emptyI]), setext]), c_0_60]), notinemptyset]), setadjoinIR]), c_0_61]), emptysetAx]), setextAx])])]), c_0_62])).
% 0.08/0.29 thf(c_0_64, negated_conjecture, ![X235:$i, X236:$i, X238:$i, X239:$i, X240:$i, X241:$i, X242:$i, X243:$i, X244:$i, X245:$i, X246:$i, X248:$i, X249:$i, X251:$i, X252:$i, X253:$i, X254:$i, X255:$i, X257:$i, X258:$i > $i > $o, X259:$i, X261:$i, X264:$i, X266:$i, X267:$i, X268:$i, X269:$i, X271:$i, X272:$i > $o, X273:$i, X275:$i, X276:$i > $o, X277:$i, X278:$i, X279:$i > $o, X280:$i, X281:$i, X282:$i > $o, X283:$i, X284:$i > $o, X285:$i, X288:$i, X289:$o, X290:$i, X291:$i, X292:$o, X293:$i, X294:$i, X295:$i > $o, X296:$i, X299:$i, X300:$i, X303:$i, X305:$i, X307:$i, X308:$i > $o, X309:$i, X310:$i, X312:$i, X313:$i > $o, X314:$i, X315:$i, X316:$i, X317:$i, X318:$i, X319:$i, X320:$i, X321:$i, X322:$i, X323:$i, X324:$i, X325:$o, X326:$i, X327:$i, X328:$i, X329:$i, X330:$i, X331:$i, X333:$i]:((((~(in @ (esk1_2 @ X235 @ X236) @ X235)|~(in @ (esk1_2 @ X235 @ X236) @ X236)|((X235)=(X236)))&((in @ (esk1_2 @ X235 @ X236) @ X235)|(in @ (esk1_2 @ X235 @ X236) @ X236)|((X235)=(X236))))&(~(in @ X238 @ emptyset)&(((~(in @ X241 @ (setadjoin @ X239 @ X240))|(((X241)=(X239))|(in @ X241 @ X240)))&((((X241)!=(X239))|(in @ X241 @ (setadjoin @ X239 @ X240)))&(~(in @ X241 @ X240)|(in @ X241 @ (setadjoin @ X239 @ X240)))))&(((~(in @ X243 @ (powerset @ X242))|(~(in @ X244 @ X243)|(in @ X244 @ X242)))&(((in @ (esk2_2 @ X245 @ X246) @ X246)|(in @ X246 @ (powerset @ X245)))&(~(in @ (esk2_2 @ X245 @ X246) @ X245)|(in @ X246 @ (powerset @ X245)))))&(((((in @ X249 @ (esk3_2 @ X248 @ X249))|~(in @ X249 @ (setunion @ X248)))&((in @ (esk3_2 @ X248 @ X249) @ X248)|~(in @ X249 @ (setunion @ X248))))&(~(in @ X252 @ X253)|~(in @ X253 @ X251)|(in @ X252 @ (setunion @ X251))))&((in @ emptyset @ omega)&((~(in @ X254 @ omega)|(in @ (setadjoin @ X254 @ X254) @ omega))&(((((in @ (esk4_1 @ X255) @ omega)|~(in @ emptyset @ X255)|(~(in @ X257 @ omega)|(in @ X257 @ X255)))&((in @ (esk4_1 @ X255) @ X255)|~(in @ emptyset @ X255)|(~(in @ X257 @ omega)|(in @ X257 @ X255))))&(~(in @ (setadjoin @ (esk4_1 @ X255) @ (esk4_1 @ X255)) @ X255)|~(in @ emptyset @ X255)|(~(in @ X257 @ omega)|(in @ X257 @ X255))))&((((((in @ (esk8_3 @ X258 @ X259 @ X264) @ X259)|~(in @ X264 @ (esk7_2 @ X258 @ X259))|(in @ (esk5_2 @ X258 @ X259) @ X259))&((X258 @ (esk8_3 @ X258 @ X259 @ X264) @ X264)|~(in @ X264 @ (esk7_2 @ X258 @ X259))|(in @ (esk5_2 @ X258 @ X259) @ X259)))&(~(in @ X267 @ X259)|~(X258 @ X267 @ X266)|(in @ X266 @ (esk7_2 @ X258 @ X259))|(in @ (esk5_2 @ X258 @ X259) @ X259)))&(((((in @ (esk8_3 @ X258 @ X259 @ X264) @ X259)|~(in @ X264 @ (esk7_2 @ X258 @ X259))|((X258 @ (esk5_2 @ X258 @ X259) @ (esk6_3 @ X258 @ X259 @ X261))|~(X258 @ (esk5_2 @ X258 @ X259) @ X261)))&((X258 @ (esk8_3 @ X258 @ X259 @ X264) @ X264)|~(in @ X264 @ (esk7_2 @ X258 @ X259))|((X258 @ (esk5_2 @ X258 @ X259) @ (esk6_3 @ X258 @ X259 @ X261))|~(X258 @ (esk5_2 @ X258 @ X259) @ X261))))&(~(in @ X267 @ X259)|~(X258 @ X267 @ X266)|(in @ X266 @ (esk7_2 @ X258 @ X259))|((X258 @ (esk5_2 @ X258 @ X259) @ (esk6_3 @ X258 @ X259 @ X261))|~(X258 @ (esk5_2 @ X258 @ X259) @ X261))))&((((in @ (esk8_3 @ X258 @ X259 @ X264) @ X259)|~(in @ X264 @ (esk7_2 @ X258 @ X259))|(((X261)!=(esk6_3 @ X258 @ X259 @ X261))|~(X258 @ (esk5_2 @ X258 @ X259) @ X261)))&((X258 @ (esk8_3 @ X258 @ X259 @ X264) @ X264)|~(in @ X264 @ (esk7_2 @ X258 @ X259))|(((X261)!=(esk6_3 @ X258 @ X259 @ X261))|~(X258 @ (esk5_2 @ X258 @ X259) @ X261))))&(~(in @ X267 @ X259)|~(X258 @ X267 @ X266)|(in @ X266 @ (esk7_2 @ X258 @ X259))|(((X261)!=(esk6_3 @ X258 @ X259 @ X261))|~(X258 @ (esk5_2 @ X258 @ X259) @ X261))))))&((((in @ (esk9_1 @ X268) @ X268)|~(in @ X269 @ X268))&(~(in @ X271 @ (esk9_1 @ X268))|~(in @ X271 @ X268)|~(in @ X269 @ X268)))&((epred1_0)&((((X272 @ (esk10_2 @ X272 @ X273))|~(X272 @ X273)|(X272 @ (descr @ X272)))&(((X273)!=(esk10_2 @ X272 @ X273))|~(X272 @ X273)|(X272 @ (descr @ X272))))&((~(in @ X277 @ X275)|(~(X276 @ X277)|(in @ X277 @ (dsetconstr @ X275 @ X276))))&((~(in @ X280 @ (dsetconstr @ X278 @ X279))|(in @ X280 @ X278))&((~(in @ X283 @ (dsetconstr @ X281 @ X282))|(X282 @ X283))&(((((X284 @ (esk12_1 @ X284))|((X284 @ (esk11_2 @ X284 @ X285))|~(X284 @ X285)))&(~(X284 @ X288)|((esk12_1 @ X284)=(X288))|((X284 @ (esk11_2 @ X284 @ X285))|~(X284 @ X285))))&(((X284 @ (esk12_1 @ X284))|(((X285)!=(esk11_2 @ X284 @ X285))|~(X284 @ X285)))&(~(X284 @ X288)|((esk12_1 @ X284)=(X288))|(((X285)!=(esk11_2 @ X284 @ X285))|~(X284 @ X285)))))&((~(in @ X290 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X289)))))|(X289))&((~(in @ X291 @ emptyset)|(X292))&((~(in @ X293 @ emptyset)|~($true))&(~(in @ X294 @ emptyset)&((((X295 @ (esk13_2 @ X295 @ X296))|~(X295 @ X296)|(X295 @ (esk14_1 @ X295)))&(((X296)!=(esk13_2 @ X295 @ X296))|~(X295 @ X296)|(X295 @ (esk14_1 @ X295))))&(((((in @ (esk16_2 @ X299 @ X300) @ X300)|((X299)=(X300))|(in @ (esk15_2 @ X299 @ X300) @ X299))&(~(in @ (esk16_2 @ X299 @ X300) @ X299)|((X299)=(X300))|(in @ (esk15_2 @ X299 @ X300) @ X299)))&(((in @ (esk16_2 @ X299 @ X300) @ X300)|((X299)=(X300))|~(in @ (esk15_2 @ X299 @ X300) @ X300))&(~(in @ (esk16_2 @ X299 @ X300) @ X299)|((X299)=(X300))|~(in @ (esk15_2 @ X299 @ X300) @ X300))))&(((in @ (esk17_1 @ X303) @ X303)|((X303)=(emptyset)))&(((in @ (esk18_1 @ X305) @ X305)|((X305)=(emptyset)))&(((~(in @ X309 @ (dsetconstr @ X307 @ X308))|(X308 @ X309)|~(in @ X309 @ X307))&(~(X308 @ X309)|(in @ X309 @ (dsetconstr @ X307 @ X308))|~(in @ X309 @ X307)))&((((X310)=(emptyset))|(in @ (esk19_1 @ X310) @ X310))&((~(in @ X314 @ X312)|(~(X313 @ X314)|((dsetconstr @ X312 @ X313)!=(emptyset))))&((~(in @ X316 @ X315)|((X315)!=(emptyset)))&((in @ X317 @ (setadjoin @ X317 @ X318))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X321 @ X320)|(in @ X321 @ (setadjoin @ X319 @ X320)))&(((((in @ X324 @ X323)|(X325)|((X324)=(X322))|~(in @ X324 @ (setadjoin @ X322 @ X323)))&(~(X325)|(X325)|((X324)=(X322))|~(in @ X324 @ (setadjoin @ X322 @ X323))))&(((in @ X324 @ X323)|(X325)|~(X325)|~(in @ X324 @ (setadjoin @ X322 @ X323)))&(~(X325)|(X325)|~(X325)|~(in @ X324 @ (setadjoin @ X322 @ X323)))))&((~(in @ X328 @ (setadjoin @ X326 @ X327))|(((X328)=(X326))|(in @ X328 @ X327)))&(((dsetconstr @ X329 @ (^[Z0:$i]:($true)))=(X329))&((((in @ (esk20_2 @ X330 @ X331) @ X331)|(in @ X331 @ (powerset @ X330)))&(~(in @ (esk20_2 @ X330 @ X331) @ X330)|(in @ X331 @ (powerset @ X330))))&((in @ emptyset @ (powerset @ X333))&~(in @ emptyset @ (powerset @ esk21_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_63])])])])])])])).
% 0.08/0.29 thf(c_0_65, negated_conjecture, ~((in @ emptyset @ (powerset @ esk21_0))), inference(split_conjunct,[status(thm)],[c_0_64])).
% 0.08/0.29 thf(c_0_66, negated_conjecture, ![X2:$i]:((in @ emptyset @ (powerset @ X2))), inference(split_conjunct,[status(thm)],[c_0_64])).
% 0.08/0.29 thf(c_0_67, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65, c_0_66])]), ['proof']).
% 0.08/0.29 % SZS output end CNFRefutation
% 0.08/0.29 % Parsed axioms : 87
% 0.08/0.29 % Removed by relevancy pruning/SinE : 47
% 0.08/0.29 % Initial clauses : 81
% 0.08/0.29 % Removed in clause preprocessing : 3
% 0.08/0.29 % Initial clauses in saturation : 78
% 0.08/0.29 % Processed clauses : 8
% 0.08/0.29 % ...of these trivial : 0
% 0.08/0.29 % ...subsumed : 3
% 0.08/0.29 % ...remaining for further processing : 4
% 0.08/0.29 % Other redundant clauses eliminated : 0
% 0.08/0.29 % Clauses deleted for lack of memory : 0
% 0.08/0.29 % Backward-subsumed : 0
% 0.08/0.29 % Backward-rewritten : 0
% 0.08/0.29 % Generated clauses : 0
% 0.08/0.29 % ...of the previous two non-redundant : 0
% 0.08/0.29 % ...aggressively subsumed : 0
% 0.08/0.29 % Contextual simplify-reflections : 0
% 0.08/0.29 % Paramodulations : 0
% 0.08/0.29 % Factorizations : 0
% 0.08/0.29 % NegExts : 0
% 0.08/0.29 % Equation resolutions : 0
% 0.08/0.29 % Disequality decompositions : 0
% 0.08/0.29 % Total rewrite steps : 1
% 0.08/0.29 % ...of those cached : 0
% 0.08/0.29 % Propositional unsat checks : 0
% 0.08/0.29 % Propositional check models : 0
% 0.08/0.29 % Propositional check unsatisfiable : 0
% 0.08/0.29 % Propositional clauses : 0
% 0.08/0.29 % Propositional clauses after purity: 0
% 0.08/0.29 % Propositional unsat core size : 0
% 0.08/0.29 % Propositional preprocessing time : 0.000
% 0.08/0.29 % Propositional encoding time : 0.000
% 0.08/0.29 % Propositional solver time : 0.000
% 0.08/0.29 % Success case prop preproc time : 0.000
% 0.08/0.29 % Success case prop encoding time : 0.000
% 0.08/0.29 % Success case prop solver time : 0.000
% 0.08/0.29 % Current number of processed clauses : 4
% 0.08/0.29 % Positive orientable unit clauses : 3
% 0.08/0.29 % Positive unorientable unit clauses: 0
% 0.08/0.29 % Negative unit clauses : 1
% 0.08/0.29 % Non-unit-clauses : 0
% 0.08/0.29 % Current number of unprocessed clauses: 70
% 0.08/0.29 % ...number of literals in the above : 228
% 0.08/0.29 % Current number of archived formulas : 0
% 0.08/0.29 % Current number of archived clauses : 0
% 0.08/0.29 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.29 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.29 % Non-unit clause-clause subsumptions : 0
% 0.08/0.29 % Unit Clause-clause subsumption calls : 0
% 0.08/0.29 % Rewrite failures with RHS unbound : 0
% 0.08/0.29 % BW rewrite match attempts : 0
% 0.08/0.29 % BW rewrite match successes : 0
% 0.08/0.29 % Condensation attempts : 0
% 0.08/0.29 % Condensation successes : 0
% 0.08/0.29 % Termbank termtop insertions : 10024
% 0.08/0.29 % Search garbage collected termcells : 3943
% 0.08/0.29
% 0.08/0.29 % -------------------------------------------------
% 0.08/0.29 % User time : 0.008 s
% 0.08/0.29 % System time : 0.003 s
% 0.08/0.29 % Total time : 0.010 s
% 0.08/0.29 % Maximum resident set size: 4488 pages
% 0.08/0.29
% 0.08/0.29 % -------------------------------------------------
% 0.08/0.29 % User time : 0.011 s
% 0.08/0.29 % System time : 0.007 s
% 0.08/0.29 % Total time : 0.018 s
% 0.08/0.29 % Maximum resident set size: 4864 pages
% 0.08/0.29 % E exiting
%------------------------------------------------------------------------------