%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU521^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:26:34 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU521^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n026.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:50:42 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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.DfZkwBunqR/E---3.1_619285.p
% 0.20/0.27 % Version: 3.5.1-ho
% 0.20/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.27 % Starting sh5l with 300s (1) cores
% 0.20/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.20/0.27 % new_bool_2 with pid 619328 completed with status 0
% 0.20/0.27 % Result found by new_bool_2
% 0.20/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.27 % Starting sh5l with 300s (1) cores
% 0.20/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.20/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.27 % Search class: HGHSM-FFMM31-SHFSMSBN
% 0.20/0.27 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.20/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.27 % SubtermCWHack with pid 619336 completed with status 0
% 0.20/0.27 % Result found by SubtermCWHack
% 0.20/0.27 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.20/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.27 % Starting sh5l with 300s (1) cores
% 0.20/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.20/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.27 % Search class: HGHSM-FFMM31-SHFSMSBN
% 0.20/0.27 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.20/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.27 % Preprocessing time : 0.002 s
% 0.20/0.27
% 0.20/0.27 % Proof found!
% 0.20/0.27 % SZS status Theorem
% 0.20/0.27 % SZS output start CNFRefutation
% 0.20/0.27 thf(decl_23, type, in: $i > $i > $o).
% 0.20/0.27 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.20/0.27 thf(decl_25, type, setextAx: $o).
% 0.20/0.27 thf(decl_26, type, emptyset: $i).
% 0.20/0.27 thf(decl_27, type, emptysetAx: $o).
% 0.20/0.27 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.20/0.27 thf(decl_29, type, setadjoinAx: $o).
% 0.20/0.27 thf(decl_30, type, powerset: $i > $i).
% 0.20/0.27 thf(decl_31, type, powersetAx: $o).
% 0.20/0.27 thf(decl_33, type, setunionAx: $o).
% 0.20/0.27 thf(decl_34, type, omega: $i).
% 0.20/0.27 thf(decl_35, type, omega0Ax: $o).
% 0.20/0.27 thf(decl_36, type, omegaSAx: $o).
% 0.20/0.27 thf(decl_37, type, omegaIndAx: $o).
% 0.20/0.27 thf(decl_38, type, replAx: $o).
% 0.20/0.27 thf(decl_39, type, foundationAx: $o).
% 0.20/0.27 thf(decl_40, type, wellorderingAx: $o).
% 0.20/0.27 thf(decl_42, type, descrp: $o).
% 0.20/0.27 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.20/0.27 thf(decl_44, type, dsetconstrI: $o).
% 0.20/0.27 thf(decl_45, type, dsetconstrEL: $o).
% 0.20/0.27 thf(decl_46, type, dsetconstrER: $o).
% 0.20/0.27 thf(decl_47, type, exuE1: $o).
% 0.20/0.27 thf(decl_48, type, prop2set: $o > $i).
% 0.20/0.27 thf(decl_49, type, prop2setE: $o).
% 0.20/0.27 thf(decl_50, type, emptysetE: $o).
% 0.20/0.27 thf(decl_51, type, emptysetimpfalse: $o).
% 0.20/0.27 thf(decl_52, type, notinemptyset: $o).
% 0.20/0.27 thf(decl_53, type, exuE3e: $o).
% 0.20/0.27 thf(decl_54, type, setext: $o).
% 0.20/0.27 thf(decl_55, type, emptyI: $o).
% 0.20/0.27 thf(decl_56, type, noeltsimpempty: $o).
% 0.20/0.27 thf(decl_57, type, setbeta: $o).
% 0.20/0.27 thf(decl_58, type, nonempty: $i > $o).
% 0.20/0.27 thf(decl_59, type, nonemptyE1: $o).
% 0.20/0.27 thf(decl_60, type, nonemptyI: $o).
% 0.20/0.27 thf(decl_61, type, nonemptyI1: $o).
% 0.20/0.27 thf(decl_62, type, setadjoinIL: $o).
% 0.20/0.27 thf(decl_63, type, emptyinunitempty: $o).
% 0.20/0.27 thf(decl_64, type, setadjoinIR: $o).
% 0.20/0.27 thf(decl_65, type, setadjoinE: $o).
% 0.20/0.27 thf(decl_66, type, setadjoinOr: $o).
% 0.20/0.27 thf(decl_67, type, setoftrueEq: $o).
% 0.20/0.27 thf(decl_68, type, powersetI: $o).
% 0.20/0.27 thf(decl_69, type, emptyinPowerset: $o).
% 0.20/0.27 thf(decl_70, type, emptyInPowerset: $o).
% 0.20/0.27 thf(decl_71, type, epred1_0: $o).
% 0.20/0.27 thf(decl_72, type, esk1_2: $i > $i > $i).
% 0.20/0.27 thf(decl_73, type, esk2_2: $i > $i > $i).
% 0.20/0.27 thf(decl_74, type, esk3_1: $i > $i).
% 0.20/0.27 thf(decl_75, type, esk4_2: ($i > $i > $o) > $i > $i).
% 0.20/0.27 thf(decl_76, type, esk5_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.27 thf(decl_77, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.20/0.27 thf(decl_78, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.27 thf(decl_79, type, esk8_1: $i > $i).
% 0.20/0.27 thf(decl_80, type, esk9_2: ($i > $o) > $i > $i).
% 0.20/0.27 thf(decl_81, type, esk10_1: ($i > $o) > $i).
% 0.20/0.27 thf(decl_82, type, esk11_2: ($i > $o) > $i > $i).
% 0.20/0.27 thf(decl_83, type, esk12_1: ($i > $o) > $i).
% 0.20/0.27 thf(decl_84, type, esk13_2: $i > $i > $i).
% 0.20/0.27 thf(decl_85, type, esk14_2: $i > $i > $i).
% 0.20/0.27 thf(decl_86, type, esk15_1: $i > $i).
% 0.20/0.27 thf(decl_87, type, esk16_1: $i > $i).
% 0.20/0.27 thf(decl_88, type, esk17_1: $i > $i).
% 0.20/0.27 thf(decl_89, type, esk18_2: $i > $i > $i).
% 0.20/0.27 thf(decl_90, type, esk19_0: $i).
% 0.20/0.27 thf(decl_91, type, esk20_0: $i).
% 0.20/0.27 thf(decl_92, type, esk21_0: $i).
% 0.20/0.27 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', nonempty)).
% 0.20/0.27 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', nonemptyI)).
% 0.20/0.27 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', replAx)).
% 0.20/0.27 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', exu)).
% 0.20/0.27 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', prop2set)).
% 0.20/0.27 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', exuE1)).
% 0.20/0.27 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', exuE3e)).
% 0.20/0.27 thf(powersetE, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', powersetE)).
% 0.20/0.27 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', nonemptyE1)).
% 0.20/0.27 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', nonemptyI1)).
% 0.20/0.27 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', setoftrueEq)).
% 0.20/0.27 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', dsetconstrI)).
% 0.20/0.27 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', prop2setE)).
% 0.20/0.27 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', dsetconstrER)).
% 0.20/0.27 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', dsetconstrEL)).
% 0.20/0.27 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', setbeta)).
% 0.20/0.27 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', setadjoinIL)).
% 0.20/0.27 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', emptyinunitempty)).
% 0.20/0.27 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', setadjoinIR)).
% 0.20/0.27 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.DfZkwBunqR/E---3.1_619285.p', setadjoinE)).
% 0.20/0.27 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', setadjoinOr)).
% 0.20/0.27 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', emptysetAx)).
% 0.20/0.27 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', powersetI)).
% 0.20/0.27 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', setextAx)).
% 0.20/0.27 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', emptyinPowerset)).
% 0.20/0.27 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', emptyInPowerset)).
% 0.20/0.27 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', setadjoinAx)).
% 0.20/0.27 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', wellorderingAx)).
% 0.20/0.27 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', foundationAx)).
% 0.20/0.27 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', omegaIndAx)).
% 0.20/0.27 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', omegaSAx)).
% 0.20/0.27 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', omega0Ax)).
% 0.20/0.27 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', powersetAx)).
% 0.20/0.27 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', notinemptyset)).
% 0.20/0.27 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', emptysetimpfalse)).
% 0.20/0.27 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', emptysetE)).
% 0.20/0.27 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', setext)).
% 0.20/0.27 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', emptyI)).
% 0.20/0.27 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.DfZkwBunqR/E---3.1_619285.p', noeltsimpempty)).
% 0.20/0.27 thf(c_0_39, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.20/0.27 thf(c_0_40, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.20/0.27 thf(c_0_41, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.20/0.27 thf(c_0_42, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.20/0.27 thf(c_0_43, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.20/0.27 thf(c_0_44, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.20/0.27 thf(c_0_45, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.20/0.27 thf(c_0_46, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4)))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[powersetE])).
% 0.20/0.27 thf(c_0_47, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_39])).
% 0.20/0.27 thf(c_0_48, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_40, c_0_39])).
% 0.20/0.27 thf(c_0_49, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_39])).
% 0.20/0.27 thf(c_0_50, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.20/0.27 thf(c_0_51, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X116:$i]:(((((X6 @ X2 @ X116)))&(![X117:$i]:(((((X6 @ X2 @ X117)))=>(((X116)=(X117)))))))))))))=>(?[X5:$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])).
% 0.20/0.27 thf(c_0_52, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.20/0.27 thf(c_0_53, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_43])).
% 0.20/0.27 thf(c_0_54, plain, ((exuE1)=(![X1:$i > $o]:((((?[X118:$i]:(((((X1 @ X118)))&(![X119:$i]:(((((X1 @ X119)))=>(((X118)=(X119))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_44, c_0_42])).
% 0.20/0.27 thf(c_0_55, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.20/0.27 thf(c_0_56, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.20/0.27 thf(c_0_57, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.20/0.27 thf(c_0_58, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X120:$i]:(((((X1 @ X120)))&(![X121:$i]:(((((X1 @ X121)))=>(((X120)=(X121))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_45, c_0_42])).
% 0.20/0.27 thf(c_0_59, plain, ((epred1_0)<=>![X148:$i]:(?[X149:$i]:((((![X150:$i]:(((in @ X150 @ X149)=>![X151:$i]:(((in @ X151 @ X150)=>(in @ X151 @ X148)))))&![X152:$i, X153:$i]:((((in @ X152 @ X148)&(in @ X153 @ X148))=>(![X154:$i]:(((in @ X154 @ X149)=>((in @ X152 @ X154)<=>(in @ X153 @ X154))))=>((X152)=(X153))))))&![X155:$i, X156:$i]:((((in @ X155 @ X149)&(in @ X156 @ X149))=>(![X157:$i]:(((in @ X157 @ X155)=>(in @ X157 @ X156)))|![X158:$i]:(((in @ X158 @ X156)=>(in @ X158 @ X155)))))))&![X159:$i]:(((![X160:$i]:(((in @ X160 @ X159)=>(in @ X160 @ X148)))&?[X161:$i]:((in @ X161 @ X159)))=>?[X162:$i, X163:$i]:(((((in @ X162 @ X149)&(in @ X163 @ X159))&~(?[X164:$i]:(((in @ X164 @ X162)&(in @ X164 @ X159)))))&![X165:$i]:(((in @ X165 @ X149)=>(![X166:$i]:(((in @ X166 @ X165)=>(in @ X166 @ X162)))|(in @ X163 @ X165)))))))))))), introduced(definition)).
% 0.20/0.27 thf(c_0_60, negated_conjecture, ~((![X122:$i, X123:$i]:((![X124:$i]:(((in @ X124 @ X122)<=>(in @ X124 @ X123)))=>((X122)=(X123))))=>(![X125:$i]:(~(in @ X125 @ emptyset))=>(![X126:$i, X127:$i, X128:$i]:(((in @ X128 @ (setadjoin @ X126 @ X127))<=>(((X128)=(X126))|(in @ X128 @ X127))))=>(![X129:$i, X130:$i]:(((in @ X130 @ (powerset @ X129))<=>![X131:$i]:(((in @ X131 @ X130)=>(in @ X131 @ X129)))))=>((setunionAx)=>((in @ emptyset @ omega)=>(![X132:$i]:(((in @ X132 @ omega)=>(in @ (setadjoin @ X132 @ X132) @ omega)))=>(![X133:$i]:((((in @ emptyset @ X133)&![X134:$i]:((((in @ X134 @ omega)&(in @ X134 @ X133))=>(in @ (setadjoin @ X134 @ X134) @ X133))))=>![X135:$i]:(((in @ X135 @ omega)=>(in @ X135 @ X133)))))=>(![X136:$i > $i > $o, X137:$i]:((![X138:$i]:(((in @ X138 @ X137)=>?[X139:$i]:(((X136 @ X138 @ X139)&![X140:$i]:(((X136 @ X138 @ X140)=>((X139)=(X140))))))))=>?[X141:$i]:(![X142:$i]:(((in @ X142 @ X141)<=>?[X143:$i]:(((in @ X143 @ X137)&(X136 @ X143 @ X142))))))))=>(![X144:$i]:((?[X145:$i]:((in @ X145 @ X144))=>?[X146:$i]:(((in @ X146 @ X144)&~(?[X147:$i]:(((in @ X147 @ X146)&(in @ X147 @ X144))))))))=>((epred1_0)=>((descrp)=>(![X167:$i, X168:$i > $o, X169:$i]:(((in @ X169 @ X167)=>((X168 @ X169)=>(in @ X169 @ (dsetconstr @ X167 @ (^[Z0:$i]:((X168 @ Z0))))))))=>(![X170:$i, X171:$i > $o, X172:$i]:(((in @ X172 @ (dsetconstr @ X170 @ (^[Z0:$i]:((X171 @ Z0)))))=>(in @ X172 @ X170)))=>(![X173:$i, X174:$i > $o, X175:$i]:(((in @ X175 @ (dsetconstr @ X173 @ (^[Z0:$i]:((X174 @ Z0)))))=>(X174 @ X175)))=>(![X176:$i > $o]:((?[X177:$i]:(((X176 @ X177)&![X178:$i]:(((X176 @ X178)=>((X177)=(X178))))))=>?[X179:$i]:(((X176 @ X179)&![X180:$i]:(((X176 @ X180)=>((X179)=(X180))))))))=>(![X181:$o, X182:$i]:(((in @ X182 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X181)))))=>(X181)))=>(![X183:$i]:(((in @ X183 @ emptyset)=>![X184:$o]:((X184))))=>(![X185:$i]:(~(in @ X185 @ emptyset))=>(![X186:$i]:(~(in @ X186 @ emptyset))=>(![X187:$i > $o]:((?[X188:$i]:(((X187 @ X188)&![X189:$i]:(((X187 @ X189)=>((X188)=(X189))))))=>?[X190:$i]:((X187 @ X190))))=>(![X191:$i, X192:$i]:((![X193:$i]:(((in @ X193 @ X191)=>(in @ X193 @ X192)))=>(![X194:$i]:(((in @ X194 @ X192)=>(in @ X194 @ X191)))=>((X191)=(X192)))))=>(![X195:$i]:((![X196:$i]:(~(in @ X196 @ X195))=>((X195)=(emptyset))))=>(![X197:$i]:((![X198:$i]:(~(in @ X198 @ X197))=>((X197)=(emptyset))))=>(![X199:$i, X200:$i > $o, X201:$i]:(((in @ X201 @ X199)=>((in @ X201 @ (dsetconstr @ X199 @ (^[Z0:$i]:((X200 @ Z0)))))<=>(X200 @ X201))))=>(![X202:$i]:((((X202)!=(emptyset))=>?[X203:$i]:((in @ X203 @ X202))))=>(![X204:$i, X205:$i > $o, X206:$i]:(((in @ X206 @ X204)=>((X205 @ X206)=>((dsetconstr @ X204 @ (^[Z0:$i]:((X205 @ Z0))))!=(emptyset)))))=>(![X207:$i]:((?[X208:$i]:((in @ X208 @ X207))=>((X207)!=(emptyset))))=>(![X209:$i, X210:$i]:((in @ X209 @ (setadjoin @ X209 @ X210)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X211:$i, X212:$i, X213:$i]:(((in @ X213 @ X212)=>(in @ X213 @ (setadjoin @ X211 @ X212))))=>(![X214:$i, X215:$i, X216:$i]:(((in @ X216 @ (setadjoin @ X214 @ X215))=>![X217:$o]:(((((X216)=(X214))=>(X217))=>(((in @ X216 @ X215)=>(X217))=>(X217))))))=>(![X218:$i, X219:$i, X220:$i]:(((in @ X220 @ (setadjoin @ X218 @ X219))=>(((X220)=(X218))|(in @ X220 @ X219))))=>(![X221:$i]:(((dsetconstr @ X221 @ (^[Z0:$i]:(($true))))=(X221)))=>(![X222:$i, X223:$i]:((![X224:$i]:(((in @ X224 @ X223)=>(in @ X224 @ X222)))=>(in @ X223 @ (powerset @ X222))))=>(![X225:$i]:((in @ emptyset @ (powerset @ X225)))=>(![X226:$i]:((in @ emptyset @ (powerset @ X226)))=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4)))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_46, c_0_47]), c_0_48]), c_0_49]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_50]), emptysetAx]), powersetI]), setextAx]), emptyinPowerset]), emptyInPowerset]), setadjoinAx]), wellorderingAx]), foundationAx]), c_0_51]), omegaIndAx]), omegaSAx]), omega0Ax]), powersetAx]), c_0_52]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_53]), c_0_54]), c_0_55]), c_0_56]), setext]), emptyI]), noeltsimpempty]), c_0_57]), c_0_58])]), c_0_59])).
% 0.20/0.27 thf(c_0_61, negated_conjecture, ![X227:$i, X228:$i, X230:$i, X231:$i, X232:$i, X233:$i, X234:$i, X235:$i, X236:$i, X237:$i, X238:$i, X240:$i, X241:$i, X243:$i, X244:$i > $i > $o, X245:$i, X247:$i, X250:$i, X252:$i, X253:$i, X254:$i, X255:$i, X257:$i, X258:$i, X259:$i > $o, X260:$i, X261:$i, X262:$i > $o, X263:$i, X264:$i, X265:$i > $o, X266:$i, X267:$i > $o, X268:$i, X271:$i, X272:$o, X273:$i, X274:$i, X275:$o, X276:$i, X277:$i, X278:$i > $o, X279:$i, X282:$i, X283:$i, X286:$i, X288:$i, X290:$i, X291:$i > $o, X292:$i, X293:$i, X295:$i, X296:$i > $o, X297:$i, X298:$i, X299:$i, X300:$i, X301:$i, X302:$i, X303:$i, X304:$i, X305:$i, X306:$i, X307:$i, X308:$o, X309:$i, X310:$i, X311:$i, X312:$i, X313:$i, X314:$i, X316:$i, X317:$i]:((((~(in @ (esk1_2 @ X227 @ X228) @ X227)|~(in @ (esk1_2 @ X227 @ X228) @ X228)|((X227)=(X228)))&((in @ (esk1_2 @ X227 @ X228) @ X227)|(in @ (esk1_2 @ X227 @ X228) @ X228)|((X227)=(X228))))&(~(in @ X230 @ emptyset)&(((~(in @ X233 @ (setadjoin @ X231 @ X232))|(((X233)=(X231))|(in @ X233 @ X232)))&((((X233)!=(X231))|(in @ X233 @ (setadjoin @ X231 @ X232)))&(~(in @ X233 @ X232)|(in @ X233 @ (setadjoin @ X231 @ X232)))))&(((~(in @ X235 @ (powerset @ X234))|(~(in @ X236 @ X235)|(in @ X236 @ X234)))&(((in @ (esk2_2 @ X237 @ X238) @ X238)|(in @ X238 @ (powerset @ X237)))&(~(in @ (esk2_2 @ X237 @ X238) @ X237)|(in @ X238 @ (powerset @ X237)))))&((setunionAx)&((in @ emptyset @ omega)&((~(in @ X240 @ omega)|(in @ (setadjoin @ X240 @ X240) @ omega))&(((((in @ (esk3_1 @ X241) @ omega)|~(in @ emptyset @ X241)|(~(in @ X243 @ omega)|(in @ X243 @ X241)))&((in @ (esk3_1 @ X241) @ X241)|~(in @ emptyset @ X241)|(~(in @ X243 @ omega)|(in @ X243 @ X241))))&(~(in @ (setadjoin @ (esk3_1 @ X241) @ (esk3_1 @ X241)) @ X241)|~(in @ emptyset @ X241)|(~(in @ X243 @ omega)|(in @ X243 @ X241))))&((((((in @ (esk7_3 @ X244 @ X245 @ X250) @ X245)|~(in @ X250 @ (esk6_2 @ X244 @ X245))|(in @ (esk4_2 @ X244 @ X245) @ X245))&((X244 @ (esk7_3 @ X244 @ X245 @ X250) @ X250)|~(in @ X250 @ (esk6_2 @ X244 @ X245))|(in @ (esk4_2 @ X244 @ X245) @ X245)))&(~(in @ X253 @ X245)|~(X244 @ X253 @ X252)|(in @ X252 @ (esk6_2 @ X244 @ X245))|(in @ (esk4_2 @ X244 @ X245) @ X245)))&(((((in @ (esk7_3 @ X244 @ X245 @ X250) @ X245)|~(in @ X250 @ (esk6_2 @ X244 @ X245))|((X244 @ (esk4_2 @ X244 @ X245) @ (esk5_3 @ X244 @ X245 @ X247))|~(X244 @ (esk4_2 @ X244 @ X245) @ X247)))&((X244 @ (esk7_3 @ X244 @ X245 @ X250) @ X250)|~(in @ X250 @ (esk6_2 @ X244 @ X245))|((X244 @ (esk4_2 @ X244 @ X245) @ (esk5_3 @ X244 @ X245 @ X247))|~(X244 @ (esk4_2 @ X244 @ X245) @ X247))))&(~(in @ X253 @ X245)|~(X244 @ X253 @ X252)|(in @ X252 @ (esk6_2 @ X244 @ X245))|((X244 @ (esk4_2 @ X244 @ X245) @ (esk5_3 @ X244 @ X245 @ X247))|~(X244 @ (esk4_2 @ X244 @ X245) @ X247))))&((((in @ (esk7_3 @ X244 @ X245 @ X250) @ X245)|~(in @ X250 @ (esk6_2 @ X244 @ X245))|(((X247)!=(esk5_3 @ X244 @ X245 @ X247))|~(X244 @ (esk4_2 @ X244 @ X245) @ X247)))&((X244 @ (esk7_3 @ X244 @ X245 @ X250) @ X250)|~(in @ X250 @ (esk6_2 @ X244 @ X245))|(((X247)!=(esk5_3 @ X244 @ X245 @ X247))|~(X244 @ (esk4_2 @ X244 @ X245) @ X247))))&(~(in @ X253 @ X245)|~(X244 @ X253 @ X252)|(in @ X252 @ (esk6_2 @ X244 @ X245))|(((X247)!=(esk5_3 @ X244 @ X245 @ X247))|~(X244 @ (esk4_2 @ X244 @ X245) @ X247))))))&((((in @ (esk8_1 @ X254) @ X254)|~(in @ X255 @ X254))&(~(in @ X257 @ (esk8_1 @ X254))|~(in @ X257 @ X254)|~(in @ X255 @ X254)))&((epred1_0)&((descrp)&((~(in @ X260 @ X258)|(~(X259 @ X260)|(in @ X260 @ (dsetconstr @ X258 @ (^[Z0:$i]:((X259 @ Z0)))))))&((~(in @ X263 @ (dsetconstr @ X261 @ (^[Z0:$i]:((X262 @ Z0)))))|(in @ X263 @ X261))&((~(in @ X266 @ (dsetconstr @ X264 @ (^[Z0:$i]:((X265 @ Z0)))))|(X265 @ X266))&(((((X267 @ (esk10_1 @ X267))|((X267 @ (esk9_2 @ X267 @ X268))|~(X267 @ X268)))&(~(X267 @ X271)|((esk10_1 @ X267)=(X271))|((X267 @ (esk9_2 @ X267 @ X268))|~(X267 @ X268))))&(((X267 @ (esk10_1 @ X267))|(((X268)!=(esk9_2 @ X267 @ X268))|~(X267 @ X268)))&(~(X267 @ X271)|((esk10_1 @ X267)=(X271))|(((X268)!=(esk9_2 @ X267 @ X268))|~(X267 @ X268)))))&((~(in @ X273 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X272)))))|(X272))&((~(in @ X274 @ emptyset)|(X275))&(~(in @ X276 @ emptyset)&(~(in @ X277 @ emptyset)&((((X278 @ (esk11_2 @ X278 @ X279))|~(X278 @ X279)|(X278 @ (esk12_1 @ X278)))&(((X279)!=(esk11_2 @ X278 @ X279))|~(X278 @ X279)|(X278 @ (esk12_1 @ X278))))&(((((in @ (esk14_2 @ X282 @ X283) @ X283)|((X282)=(X283))|(in @ (esk13_2 @ X282 @ X283) @ X282))&(~(in @ (esk14_2 @ X282 @ X283) @ X282)|((X282)=(X283))|(in @ (esk13_2 @ X282 @ X283) @ X282)))&(((in @ (esk14_2 @ X282 @ X283) @ X283)|((X282)=(X283))|~(in @ (esk13_2 @ X282 @ X283) @ X283))&(~(in @ (esk14_2 @ X282 @ X283) @ X282)|((X282)=(X283))|~(in @ (esk13_2 @ X282 @ X283) @ X283))))&(((in @ (esk15_1 @ X286) @ X286)|((X286)=(emptyset)))&(((in @ (esk16_1 @ X288) @ X288)|((X288)=(emptyset)))&(((~(in @ X292 @ (dsetconstr @ X290 @ (^[Z0:$i]:((X291 @ Z0)))))|(X291 @ X292)|~(in @ X292 @ X290))&(~(X291 @ X292)|(in @ X292 @ (dsetconstr @ X290 @ (^[Z0:$i]:((X291 @ Z0)))))|~(in @ X292 @ X290)))&((((X293)=(emptyset))|(in @ (esk17_1 @ X293) @ X293))&((~(in @ X297 @ X295)|(~(X296 @ X297)|((dsetconstr @ X295 @ (^[Z0:$i]:((X296 @ Z0))))!=(emptyset))))&((~(in @ X299 @ X298)|((X298)!=(emptyset)))&((in @ X300 @ (setadjoin @ X300 @ X301))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X304 @ X303)|(in @ X304 @ (setadjoin @ X302 @ X303)))&(((((in @ X307 @ X306)|(X308)|((X307)=(X305))|~(in @ X307 @ (setadjoin @ X305 @ X306)))&(~(X308)|(X308)|((X307)=(X305))|~(in @ X307 @ (setadjoin @ X305 @ X306))))&(((in @ X307 @ X306)|(X308)|~(X308)|~(in @ X307 @ (setadjoin @ X305 @ X306)))&(~(X308)|(X308)|~(X308)|~(in @ X307 @ (setadjoin @ X305 @ X306)))))&((~(in @ X311 @ (setadjoin @ X309 @ X310))|(((X311)=(X309))|(in @ X311 @ X310)))&(((dsetconstr @ X312 @ (^[Z0:$i]:(($true))))=(X312))&((((in @ (esk18_2 @ X313 @ X314) @ X314)|(in @ X314 @ (powerset @ X313)))&(~(in @ (esk18_2 @ X313 @ X314) @ X313)|(in @ X314 @ (powerset @ X313))))&((in @ emptyset @ (powerset @ X316))&((in @ emptyset @ (powerset @ X317))&((in @ esk20_0 @ (powerset @ esk19_0))&((in @ esk21_0 @ esk20_0)&~(in @ esk21_0 @ esk19_0))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])])])])])).
% 0.20/0.27 thf(c_0_62, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((in @ X2 @ (powerset @ X3)))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_61])).
% 0.20/0.27 thf(c_0_63, negated_conjecture, (in @ esk20_0 @ (powerset @ esk19_0)), inference(split_conjunct,[status(thm)],[c_0_61])).
% 0.20/0.27 thf(c_0_64, negated_conjecture, ~((in @ esk21_0 @ esk19_0)), inference(split_conjunct,[status(thm)],[c_0_61])).
% 0.20/0.27 thf(c_0_65, negated_conjecture, ![X2:$i]:(((in @ X2 @ esk19_0)|~((in @ X2 @ esk20_0)))), inference(spm,[status(thm)],[c_0_62, c_0_63])).
% 0.20/0.27 thf(c_0_66, negated_conjecture, (in @ esk21_0 @ esk20_0), inference(split_conjunct,[status(thm)],[c_0_61])).
% 0.20/0.27 thf(c_0_67, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65]), c_0_66])]), ['proof']).
% 0.20/0.27 % SZS output end CNFRefutation
% 0.20/0.27 % Parsed axioms : 89
% 0.20/0.27 % Removed by relevancy pruning/SinE : 50
% 0.20/0.27 % Initial clauses : 81
% 0.20/0.27 % Removed in clause preprocessing : 3
% 0.20/0.27 % Initial clauses in saturation : 78
% 0.20/0.27 % Processed clauses : 58
% 0.20/0.27 % ...of these trivial : 1
% 0.20/0.27 % ...subsumed : 14
% 0.20/0.27 % ...remaining for further processing : 43
% 0.20/0.27 % Other redundant clauses eliminated : 3
% 0.20/0.27 % Clauses deleted for lack of memory : 0
% 0.20/0.27 % Backward-subsumed : 0
% 0.20/0.27 % Backward-rewritten : 3
% 0.20/0.27 % Generated clauses : 68
% 0.20/0.27 % ...of the previous two non-redundant : 49
% 0.20/0.27 % ...aggressively subsumed : 0
% 0.20/0.27 % Contextual simplify-reflections : 0
% 0.20/0.27 % Paramodulations : 65
% 0.20/0.27 % Factorizations : 0
% 0.20/0.27 % NegExts : 0
% 0.20/0.27 % Equation resolutions : 3
% 0.20/0.27 % Disequality decompositions : 0
% 0.20/0.27 % Total rewrite steps : 18
% 0.20/0.27 % ...of those cached : 6
% 0.20/0.27 % Propositional unsat checks : 0
% 0.20/0.27 % Propositional check models : 0
% 0.20/0.27 % Propositional check unsatisfiable : 0
% 0.20/0.27 % Propositional clauses : 0
% 0.20/0.27 % Propositional clauses after purity: 0
% 0.20/0.27 % Propositional unsat core size : 0
% 0.20/0.27 % Propositional preprocessing time : 0.000
% 0.20/0.27 % Propositional encoding time : 0.000
% 0.20/0.27 % Propositional solver time : 0.000
% 0.20/0.27 % Success case prop preproc time : 0.000
% 0.20/0.27 % Success case prop encoding time : 0.000
% 0.20/0.27 % Success case prop solver time : 0.000
% 0.20/0.27 % Current number of processed clauses : 38
% 0.20/0.27 % Positive orientable unit clauses : 15
% 0.20/0.27 % Positive unorientable unit clauses: 0
% 0.20/0.27 % Negative unit clauses : 2
% 0.20/0.27 % Non-unit-clauses : 21
% 0.20/0.27 % Current number of unprocessed clauses: 69
% 0.20/0.27 % ...number of literals in the above : 231
% 0.20/0.27 % Current number of archived formulas : 0
% 0.20/0.27 % Current number of archived clauses : 3
% 0.20/0.27 % Clause-clause subsumption calls (NU) : 54
% 0.20/0.27 % Rec. Clause-clause subsumption calls : 47
% 0.20/0.27 % Non-unit clause-clause subsumptions : 6
% 0.20/0.27 % Unit Clause-clause subsumption calls : 5
% 0.20/0.27 % Rewrite failures with RHS unbound : 0
% 0.20/0.27 % BW rewrite match attempts : 8
% 0.20/0.27 % BW rewrite match successes : 3
% 0.20/0.27 % Condensation attempts : 0
% 0.20/0.27 % Condensation successes : 0
% 0.20/0.27 % Termbank termtop insertions : 9198
% 0.20/0.27 % Search garbage collected termcells : 3144
% 0.20/0.27
% 0.20/0.27 % -------------------------------------------------
% 0.20/0.27 % User time : 0.012 s
% 0.20/0.27 % System time : 0.003 s
% 0.20/0.27 % Total time : 0.015 s
% 0.20/0.27 % Maximum resident set size: 4440 pages
% 0.20/0.27
% 0.20/0.27 % -------------------------------------------------
% 0.20/0.27 % User time : 0.013 s
% 0.20/0.27 % System time : 0.009 s
% 0.20/0.27 % Total time : 0.022 s
% 0.20/0.27 % Maximum resident set size: 4608 pages
% 0.20/0.27 % E exiting
%------------------------------------------------------------------------------