%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU526^1 : 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 : n012.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 08:26:35 AM UTC 2026
% Result : Theorem 0.08s 0.16s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU526^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 13:47:48 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.14 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.0xWCuMYDt7/E---3.1_128370.p
% 0.08/0.16 % Version: 3.5.1-ho
% 0.08/0.16 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.16 % Starting sh5l with 300s (1) cores
% 0.08/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.16 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.16 % new_bool_2 with pid 128386 completed with status 0
% 0.08/0.16 % Result found by new_bool_2
% 0.08/0.16 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.16 % Starting sh5l with 300s (1) cores
% 0.08/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.16 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.16 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.16 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.16 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.08/0.16 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.16 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.16 % SubtermCWHack with pid 128387 completed with status 0
% 0.08/0.16 % Result found by SubtermCWHack
% 0.08/0.16 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.16 % Starting sh5l with 300s (1) cores
% 0.08/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.16 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.16 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.16 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.16 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.08/0.16 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.16 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.16 % Preprocessing time : 0.002 s
% 0.08/0.16
% 0.08/0.16 % Proof found!
% 0.08/0.16 % SZS status Theorem
% 0.08/0.16 % SZS output start CNFRefutation
% 0.08/0.16 thf(decl_23, type, in: $i > $i > $o).
% 0.08/0.16 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.08/0.16 thf(decl_25, type, setextAx: $o).
% 0.08/0.16 thf(decl_26, type, emptyset: $i).
% 0.08/0.16 thf(decl_27, type, emptysetAx: $o).
% 0.08/0.16 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.08/0.16 thf(decl_29, type, setadjoinAx: $o).
% 0.08/0.16 thf(decl_30, type, powerset: $i > $i).
% 0.08/0.16 thf(decl_31, type, powersetAx: $o).
% 0.08/0.16 thf(decl_32, type, setunion: $i > $i).
% 0.08/0.16 thf(decl_33, type, setunionAx: $o).
% 0.08/0.16 thf(decl_34, type, omega: $i).
% 0.08/0.16 thf(decl_35, type, omega0Ax: $o).
% 0.08/0.16 thf(decl_36, type, omegaSAx: $o).
% 0.08/0.16 thf(decl_37, type, omegaIndAx: $o).
% 0.08/0.16 thf(decl_38, type, replAx: $o).
% 0.08/0.16 thf(decl_39, type, foundationAx: $o).
% 0.08/0.16 thf(decl_40, type, wellorderingAx: $o).
% 0.08/0.16 thf(decl_42, type, descrp: $o).
% 0.08/0.16 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.08/0.16 thf(decl_44, type, dsetconstrI: $o).
% 0.08/0.16 thf(decl_45, type, dsetconstrEL: $o).
% 0.08/0.16 thf(decl_46, type, dsetconstrER: $o).
% 0.08/0.16 thf(decl_47, type, exuE1: $o).
% 0.08/0.16 thf(decl_48, type, prop2set: $o > $i).
% 0.08/0.16 thf(decl_49, type, prop2setE: $o).
% 0.08/0.16 thf(decl_50, type, emptysetE: $o).
% 0.08/0.16 thf(decl_51, type, emptysetimpfalse: $o).
% 0.08/0.16 thf(decl_52, type, notinemptyset: $o).
% 0.08/0.16 thf(decl_53, type, exuE3e: $o).
% 0.08/0.16 thf(decl_54, type, setext: $o).
% 0.08/0.16 thf(decl_55, type, emptyI: $o).
% 0.08/0.16 thf(decl_56, type, noeltsimpempty: $o).
% 0.08/0.16 thf(decl_57, type, setbeta: $o).
% 0.08/0.16 thf(decl_58, type, nonempty: $i > $o).
% 0.08/0.16 thf(decl_59, type, nonemptyE1: $o).
% 0.08/0.16 thf(decl_60, type, nonemptyI: $o).
% 0.08/0.16 thf(decl_61, type, nonemptyI1: $o).
% 0.08/0.16 thf(decl_62, type, setadjoinIL: $o).
% 0.08/0.16 thf(decl_63, type, emptyinunitempty: $o).
% 0.08/0.16 thf(decl_64, type, setadjoinIR: $o).
% 0.08/0.16 thf(decl_65, type, setadjoinE: $o).
% 0.08/0.16 thf(decl_66, type, setadjoinOr: $o).
% 0.08/0.16 thf(decl_67, type, setoftrueEq: $o).
% 0.08/0.16 thf(decl_68, type, powersetI: $o).
% 0.08/0.16 thf(decl_69, type, emptyinPowerset: $o).
% 0.08/0.16 thf(decl_70, type, emptyInPowerset: $o).
% 0.08/0.16 thf(decl_71, type, powersetE: $o).
% 0.08/0.16 thf(decl_72, type, setunionI: $o).
% 0.08/0.16 thf(decl_73, type, setunionE: $o).
% 0.08/0.16 thf(decl_74, type, subPowSU: $o).
% 0.08/0.16 thf(decl_75, type, exuE2: $o).
% 0.08/0.16 thf(decl_76, type, epred1_0: $o).
% 0.08/0.16 thf(decl_77, type, esk1_2: $i > $i > $i).
% 0.08/0.16 thf(decl_78, type, esk2_2: $i > $i > $i).
% 0.08/0.16 thf(decl_79, type, esk3_2: $i > $i > $i).
% 0.08/0.16 thf(decl_80, type, esk4_1: $i > $i).
% 0.08/0.16 thf(decl_81, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.08/0.16 thf(decl_82, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.16 thf(decl_83, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.08/0.16 thf(decl_84, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.16 thf(decl_85, type, esk9_1: $i > $i).
% 0.08/0.16 thf(decl_86, type, esk10_2: ($i > $o) > $i > $i).
% 0.08/0.16 thf(decl_87, type, esk11_1: ($i > $o) > $i).
% 0.08/0.16 thf(decl_88, type, esk12_2: ($i > $o) > $i > $i).
% 0.08/0.16 thf(decl_89, type, esk13_1: ($i > $o) > $i).
% 0.08/0.16 thf(decl_90, type, esk14_2: $i > $i > $i).
% 0.08/0.16 thf(decl_91, type, esk15_2: $i > $i > $i).
% 0.08/0.16 thf(decl_92, type, esk16_1: $i > $i).
% 0.08/0.16 thf(decl_93, type, esk17_1: $i > $i).
% 0.08/0.16 thf(decl_94, type, esk18_1: $i > $i).
% 0.08/0.16 thf(decl_95, type, esk19_2: $i > $i > $i).
% 0.08/0.16 thf(decl_96, type, esk20_3: $i > $i > $o > $i).
% 0.08/0.16 thf(decl_97, type, esk21_2: ($i > $o) > $i > $i).
% 0.08/0.16 thf(decl_98, type, esk22_1: ($i > $o) > $i).
% 0.08/0.16 thf(decl_99, type, esk23_0: $i).
% 0.08/0.16 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', replAx)).
% 0.08/0.16 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', exu)).
% 0.08/0.16 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', exuE2)).
% 0.08/0.16 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', prop2set)).
% 0.08/0.16 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.0xWCuMYDt7/E---3.1_128370.p', exuE1)).
% 0.08/0.16 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', exuE3e)).
% 0.08/0.16 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', nonempty)).
% 0.08/0.16 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', nonemptyI)).
% 0.08/0.16 thf(nonemptyImpWitness, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', nonemptyImpWitness)).
% 0.08/0.16 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', setoftrueEq)).
% 0.08/0.16 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', dsetconstrI)).
% 0.08/0.16 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', prop2setE)).
% 0.08/0.16 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', dsetconstrER)).
% 0.08/0.16 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', dsetconstrEL)).
% 0.08/0.16 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', nonemptyI1)).
% 0.08/0.16 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', nonemptyE1)).
% 0.08/0.16 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', setbeta)).
% 0.08/0.16 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', powersetI)).
% 0.08/0.16 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', emptyinPowerset)).
% 0.08/0.16 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', powersetAx)).
% 0.08/0.16 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', emptyInPowerset)).
% 0.08/0.16 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', powersetE)).
% 0.08/0.16 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', setunionI)).
% 0.08/0.16 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14)))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', setunionE)).
% 0.08/0.16 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', subPowSU)).
% 0.08/0.16 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', setadjoinAx)).
% 0.08/0.16 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', wellorderingAx)).
% 0.08/0.16 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', foundationAx)).
% 0.08/0.16 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.0xWCuMYDt7/E---3.1_128370.p', omegaIndAx)).
% 0.08/0.16 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', omegaSAx)).
% 0.08/0.16 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', omega0Ax)).
% 0.08/0.16 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', setunionAx)).
% 0.08/0.16 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', notinemptyset)).
% 0.08/0.16 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', emptysetimpfalse)).
% 0.08/0.16 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', emptysetE)).
% 0.08/0.16 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', noeltsimpempty)).
% 0.08/0.16 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', emptyI)).
% 0.08/0.16 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', setext)).
% 0.08/0.16 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', emptyinunitempty)).
% 0.08/0.16 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', setadjoinIR)).
% 0.08/0.16 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.0xWCuMYDt7/E---3.1_128370.p', setadjoinE)).
% 0.08/0.16 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', setadjoinOr)).
% 0.08/0.16 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', setadjoinIL)).
% 0.08/0.16 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', emptysetAx)).
% 0.08/0.16 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.0xWCuMYDt7/E---3.1_128370.p', setextAx)).
% 0.08/0.16 thf(c_0_45, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.08/0.16 thf(c_0_46, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.08/0.16 thf(c_0_47, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.08/0.16 thf(c_0_48, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.08/0.16 thf(c_0_49, 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])).
% 0.08/0.16 thf(c_0_50, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.08/0.16 thf(c_0_51, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.08/0.16 thf(c_0_52, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.08/0.16 thf(c_0_53, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[nonemptyImpWitness])).
% 0.08/0.16 thf(c_0_54, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X134:$i]:(((((X6 @ X2 @ X134)))&(![X135:$i]:(((((X6 @ X2 @ X135)))=>(((X134)=(X135)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_45, c_0_46])).
% 0.08/0.16 thf(c_0_55, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.08/0.16 thf(c_0_56, plain, ((exuE2)=(![X1:$i > $o]:((((?[X140:$i]:(((((X1 @ X140)))&(![X141:$i]:(((((X1 @ X141)))=>(((X140)=(X141))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_47, c_0_46])).
% 0.08/0.16 thf(c_0_57, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.08/0.16 thf(c_0_58, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_48])).
% 0.08/0.16 thf(c_0_59, plain, ((exuE1)=(![X1:$i > $o]:((((?[X136:$i]:(((((X1 @ X136)))&(![X137:$i]:(((((X1 @ X137)))=>(((X136)=(X137))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_49, c_0_46])).
% 0.08/0.16 thf(c_0_60, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.08/0.16 thf(c_0_61, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.08/0.16 thf(c_0_62, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X138:$i]:(((((X1 @ X138)))&(![X139:$i]:(((((X1 @ X139)))=>(((X138)=(X139))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_50, c_0_46])).
% 0.08/0.16 thf(c_0_63, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_51])).
% 0.08/0.16 thf(c_0_64, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_52, c_0_51])).
% 0.08/0.16 thf(c_0_65, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_51])).
% 0.08/0.16 thf(c_0_66, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.08/0.16 thf(c_0_67, plain, ((epred1_0)<=>![X171:$i]:(?[X172:$i]:((((![X173:$i]:(((in @ X173 @ X172)=>![X174:$i]:(((in @ X174 @ X173)=>(in @ X174 @ X171)))))&![X175:$i, X176:$i]:((((in @ X175 @ X171)&(in @ X176 @ X171))=>(![X177:$i]:(((in @ X177 @ X172)=>((in @ X175 @ X177)<=>(in @ X176 @ X177))))=>((X175)=(X176))))))&![X178:$i, X179:$i]:((((in @ X178 @ X172)&(in @ X179 @ X172))=>(![X180:$i]:(((in @ X180 @ X178)=>(in @ X180 @ X179)))|![X181:$i]:(((in @ X181 @ X179)=>(in @ X181 @ X178)))))))&![X182:$i]:(((![X183:$i]:(((in @ X183 @ X182)=>(in @ X183 @ X171)))&?[X184:$i]:((in @ X184 @ X182)))=>?[X185:$i, X186:$i]:(((((in @ X185 @ X172)&(in @ X186 @ X182))&~(?[X187:$i]:(((in @ X187 @ X185)&(in @ X187 @ X182)))))&![X188:$i]:(((in @ X188 @ X172)=>(![X189:$i]:(((in @ X189 @ X188)=>(in @ X189 @ X185)))|(in @ X186 @ X188)))))))))))), introduced(definition)).
% 0.08/0.16 thf(c_0_68, negated_conjecture, ~((![X142:$i, X143:$i]:((![X144:$i]:(((in @ X144 @ X142)<=>(in @ X144 @ X143)))=>((X142)=(X143))))=>(![X145:$i]:(~(in @ X145 @ emptyset))=>(![X146:$i, X147:$i, X148:$i]:(((in @ X148 @ (setadjoin @ X146 @ X147))<=>(((X148)=(X146))|(in @ X148 @ X147))))=>(![X149:$i, X150:$i]:(((in @ X150 @ (powerset @ X149))<=>![X151:$i]:(((in @ X151 @ X150)=>(in @ X151 @ X149)))))=>(![X152:$i, X153:$i]:(((in @ X153 @ (setunion @ X152))<=>?[X154:$i]:(((in @ X153 @ X154)&(in @ X154 @ X152)))))=>((in @ emptyset @ omega)=>(![X155:$i]:(((in @ X155 @ omega)=>(in @ (setadjoin @ X155 @ X155) @ omega)))=>(![X156:$i]:((((in @ emptyset @ X156)&![X157:$i]:((((in @ X157 @ omega)&(in @ X157 @ X156))=>(in @ (setadjoin @ X157 @ X157) @ X156))))=>![X158:$i]:(((in @ X158 @ omega)=>(in @ X158 @ X156)))))=>(![X159:$i > $i > $o, X160:$i]:((![X161:$i]:(((in @ X161 @ X160)=>?[X162:$i]:(((X159 @ X161 @ X162)&![X163:$i]:(((X159 @ X161 @ X163)=>((X162)=(X163))))))))=>?[X164:$i]:(![X165:$i]:(((in @ X165 @ X164)<=>?[X166:$i]:(((in @ X166 @ X160)&(X159 @ X166 @ X165))))))))=>(![X167:$i]:((?[X168:$i]:((in @ X168 @ X167))=>?[X169:$i]:(((in @ X169 @ X167)&~(?[X170:$i]:(((in @ X170 @ X169)&(in @ X170 @ X167))))))))=>((epred1_0)=>((descrp)=>(![X190:$i, X191:$i > $o, X192:$i]:(((in @ X192 @ X190)=>((X191 @ X192)=>(in @ X192 @ (dsetconstr @ X190 @ (^[Z0:$i]:((X191 @ Z0))))))))=>(![X193:$i, X194:$i > $o, X195:$i]:(((in @ X195 @ (dsetconstr @ X193 @ (^[Z0:$i]:((X194 @ Z0)))))=>(in @ X195 @ X193)))=>(![X196:$i, X197:$i > $o, X198:$i]:(((in @ X198 @ (dsetconstr @ X196 @ (^[Z0:$i]:((X197 @ Z0)))))=>(X197 @ X198)))=>(![X199:$i > $o]:((?[X200:$i]:(((X199 @ X200)&![X201:$i]:(((X199 @ X201)=>((X200)=(X201))))))=>?[X202:$i]:(((X199 @ X202)&![X203:$i]:(((X199 @ X203)=>((X202)=(X203))))))))=>(![X204:$o, X205:$i]:(((in @ X205 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X204)))))=>(X204)))=>(![X206:$i]:(((in @ X206 @ emptyset)=>![X207:$o]:((X207))))=>(![X208:$i]:(~(in @ X208 @ emptyset))=>(![X209:$i]:(~(in @ X209 @ emptyset))=>(![X210:$i > $o]:((?[X211:$i]:(((X210 @ X211)&![X212:$i]:(((X210 @ X212)=>((X211)=(X212))))))=>?[X213:$i]:((X210 @ X213))))=>(![X214:$i, X215:$i]:((![X216:$i]:(((in @ X216 @ X214)=>(in @ X216 @ X215)))=>(![X217:$i]:(((in @ X217 @ X215)=>(in @ X217 @ X214)))=>((X214)=(X215)))))=>(![X218:$i]:((![X219:$i]:(~(in @ X219 @ X218))=>((X218)=(emptyset))))=>(![X220:$i]:((![X221:$i]:(~(in @ X221 @ X220))=>((X220)=(emptyset))))=>(![X222:$i, X223:$i > $o, X224:$i]:(((in @ X224 @ X222)=>((in @ X224 @ (dsetconstr @ X222 @ (^[Z0:$i]:((X223 @ Z0)))))<=>(X223 @ X224))))=>(![X225:$i]:((((X225)!=(emptyset))=>?[X226:$i]:((in @ X226 @ X225))))=>(![X227:$i, X228:$i > $o, X229:$i]:(((in @ X229 @ X227)=>((X228 @ X229)=>((dsetconstr @ X227 @ (^[Z0:$i]:((X228 @ Z0))))!=(emptyset)))))=>(![X230:$i]:((?[X231:$i]:((in @ X231 @ X230))=>((X230)!=(emptyset))))=>(![X232:$i, X233:$i]:((in @ X232 @ (setadjoin @ X232 @ X233)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X234:$i, X235:$i, X236:$i]:(((in @ X236 @ X235)=>(in @ X236 @ (setadjoin @ X234 @ X235))))=>(![X237:$i, X238:$i, X239:$i]:(((in @ X239 @ (setadjoin @ X237 @ X238))=>![X240:$o]:(((((X239)=(X237))=>(X240))=>(((in @ X239 @ X238)=>(X240))=>(X240))))))=>(![X241:$i, X242:$i, X243:$i]:(((in @ X243 @ (setadjoin @ X241 @ X242))=>(((X243)=(X241))|(in @ X243 @ X242))))=>(![X244:$i]:(((dsetconstr @ X244 @ (^[Z0:$i]:(($true))))=(X244)))=>(![X245:$i, X246:$i]:((![X247:$i]:(((in @ X247 @ X246)=>(in @ X247 @ X245)))=>(in @ X246 @ (powerset @ X245))))=>(![X248:$i]:((in @ emptyset @ (powerset @ X248)))=>(![X249:$i]:((in @ emptyset @ (powerset @ X249)))=>(![X250:$i, X251:$i, X252:$i]:(((in @ X251 @ (powerset @ X250))=>((in @ X252 @ X251)=>(in @ X252 @ X250))))=>(![X253:$i, X254:$i, X255:$i]:(((in @ X254 @ X255)=>((in @ X255 @ X253)=>(in @ X254 @ (setunion @ X253)))))=>(![X256:$i, X257:$i]:(((in @ X257 @ (setunion @ X256))=>![X258:$o]:((![X259:$i]:(((in @ X257 @ X259)=>((in @ X259 @ X256)=>(X258))))=>(X258)))))=>(![X260:$i, X261:$i]:(((in @ X261 @ X260)=>(in @ X261 @ (powerset @ (setunion @ X260)))))=>(![X262:$i > $o]:((?[X263:$i]:(((X262 @ X263)&![X264:$i]:(((X262 @ X264)=>((X263)=(X264))))))=>?[X265:$i]:(![X266:$i]:(((X262 @ X266)<=>((X266)=(X265)))))))=>![X4:$i]:((((X4)!=(emptyset))=>?[X2:$i]:((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)],[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_53, c_0_54]), c_0_55]), powersetI]), emptyinPowerset]), powersetAx]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_56]), c_0_51]), setadjoinAx]), wellorderingAx]), foundationAx]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), c_0_57]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_58]), c_0_59]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66]), noeltsimpempty]), emptyI]), setext]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), setadjoinIL]), emptysetAx]), setextAx])]), c_0_67])).
% 0.08/0.16 thf(c_0_69, negated_conjecture, ![X267:$i, X268:$i, X270:$i, X271:$i, X272:$i, X273:$i, X274:$i, X275:$i, X276:$i, X277:$i, X278:$i, X280:$i, X281:$i, X283:$i, X284:$i, X285:$i, X286:$i, X287:$i, X289:$i, X290:$i > $i > $o, X291:$i, X293:$i, X296:$i, X298:$i, X299:$i, X300:$i, X301:$i, X303:$i, X304:$i, X305:$i > $o, X306:$i, X307:$i, X308:$i > $o, X309:$i, X310:$i, X311:$i > $o, X312:$i, X313:$i > $o, X314:$i, X317:$i, X318:$o, X319:$i, X320:$i, X321:$o, X322:$i, X323:$i, X324:$i > $o, X325:$i, X328:$i, X329:$i, X332:$i, X334:$i, X336:$i, X337:$i > $o, X338:$i, X339:$i, X341:$i, X342:$i > $o, X343:$i, X344:$i, X345:$i, X346:$i, X347:$i, X348:$i, X349:$i, X350:$i, X351:$i, X352:$i, X353:$i, X354:$o, X355:$i, X356:$i, X357:$i, X358:$i, X359:$i, X360:$i, X362:$i, X363:$i, X364:$i, X365:$i, X366:$i, X367:$i, X368:$i, X369:$i, X370:$i, X371:$i, X372:$o, X374:$i, X375:$i, X376:$i > $o, X377:$i, X380:$i, X381:$i, X383:$i]:((((~(in @ (esk1_2 @ X267 @ X268) @ X267)|~(in @ (esk1_2 @ X267 @ X268) @ X268)|((X267)=(X268)))&((in @ (esk1_2 @ X267 @ X268) @ X267)|(in @ (esk1_2 @ X267 @ X268) @ X268)|((X267)=(X268))))&(~(in @ X270 @ emptyset)&(((~(in @ X273 @ (setadjoin @ X271 @ X272))|(((X273)=(X271))|(in @ X273 @ X272)))&((((X273)!=(X271))|(in @ X273 @ (setadjoin @ X271 @ X272)))&(~(in @ X273 @ X272)|(in @ X273 @ (setadjoin @ X271 @ X272)))))&(((~(in @ X275 @ (powerset @ X274))|(~(in @ X276 @ X275)|(in @ X276 @ X274)))&(((in @ (esk2_2 @ X277 @ X278) @ X278)|(in @ X278 @ (powerset @ X277)))&(~(in @ (esk2_2 @ X277 @ X278) @ X277)|(in @ X278 @ (powerset @ X277)))))&(((((in @ X281 @ (esk3_2 @ X280 @ X281))|~(in @ X281 @ (setunion @ X280)))&((in @ (esk3_2 @ X280 @ X281) @ X280)|~(in @ X281 @ (setunion @ X280))))&(~(in @ X284 @ X285)|~(in @ X285 @ X283)|(in @ X284 @ (setunion @ X283))))&((in @ emptyset @ omega)&((~(in @ X286 @ omega)|(in @ (setadjoin @ X286 @ X286) @ omega))&(((((in @ (esk4_1 @ X287) @ omega)|~(in @ emptyset @ X287)|(~(in @ X289 @ omega)|(in @ X289 @ X287)))&((in @ (esk4_1 @ X287) @ X287)|~(in @ emptyset @ X287)|(~(in @ X289 @ omega)|(in @ X289 @ X287))))&(~(in @ (setadjoin @ (esk4_1 @ X287) @ (esk4_1 @ X287)) @ X287)|~(in @ emptyset @ X287)|(~(in @ X289 @ omega)|(in @ X289 @ X287))))&((((((in @ (esk8_3 @ X290 @ X291 @ X296) @ X291)|~(in @ X296 @ (esk7_2 @ X290 @ X291))|(in @ (esk5_2 @ X290 @ X291) @ X291))&((X290 @ (esk8_3 @ X290 @ X291 @ X296) @ X296)|~(in @ X296 @ (esk7_2 @ X290 @ X291))|(in @ (esk5_2 @ X290 @ X291) @ X291)))&(~(in @ X299 @ X291)|~(X290 @ X299 @ X298)|(in @ X298 @ (esk7_2 @ X290 @ X291))|(in @ (esk5_2 @ X290 @ X291) @ X291)))&(((((in @ (esk8_3 @ X290 @ X291 @ X296) @ X291)|~(in @ X296 @ (esk7_2 @ X290 @ X291))|((X290 @ (esk5_2 @ X290 @ X291) @ (esk6_3 @ X290 @ X291 @ X293))|~(X290 @ (esk5_2 @ X290 @ X291) @ X293)))&((X290 @ (esk8_3 @ X290 @ X291 @ X296) @ X296)|~(in @ X296 @ (esk7_2 @ X290 @ X291))|((X290 @ (esk5_2 @ X290 @ X291) @ (esk6_3 @ X290 @ X291 @ X293))|~(X290 @ (esk5_2 @ X290 @ X291) @ X293))))&(~(in @ X299 @ X291)|~(X290 @ X299 @ X298)|(in @ X298 @ (esk7_2 @ X290 @ X291))|((X290 @ (esk5_2 @ X290 @ X291) @ (esk6_3 @ X290 @ X291 @ X293))|~(X290 @ (esk5_2 @ X290 @ X291) @ X293))))&((((in @ (esk8_3 @ X290 @ X291 @ X296) @ X291)|~(in @ X296 @ (esk7_2 @ X290 @ X291))|(((X293)!=(esk6_3 @ X290 @ X291 @ X293))|~(X290 @ (esk5_2 @ X290 @ X291) @ X293)))&((X290 @ (esk8_3 @ X290 @ X291 @ X296) @ X296)|~(in @ X296 @ (esk7_2 @ X290 @ X291))|(((X293)!=(esk6_3 @ X290 @ X291 @ X293))|~(X290 @ (esk5_2 @ X290 @ X291) @ X293))))&(~(in @ X299 @ X291)|~(X290 @ X299 @ X298)|(in @ X298 @ (esk7_2 @ X290 @ X291))|(((X293)!=(esk6_3 @ X290 @ X291 @ X293))|~(X290 @ (esk5_2 @ X290 @ X291) @ X293))))))&((((in @ (esk9_1 @ X300) @ X300)|~(in @ X301 @ X300))&(~(in @ X303 @ (esk9_1 @ X300))|~(in @ X303 @ X300)|~(in @ X301 @ X300)))&((epred1_0)&((descrp)&((~(in @ X306 @ X304)|(~(X305 @ X306)|(in @ X306 @ (dsetconstr @ X304 @ (^[Z0:$i]:((X305 @ Z0)))))))&((~(in @ X309 @ (dsetconstr @ X307 @ (^[Z0:$i]:((X308 @ Z0)))))|(in @ X309 @ X307))&((~(in @ X312 @ (dsetconstr @ X310 @ (^[Z0:$i]:((X311 @ Z0)))))|(X311 @ X312))&(((((X313 @ (esk11_1 @ X313))|((X313 @ (esk10_2 @ X313 @ X314))|~(X313 @ X314)))&(~(X313 @ X317)|((esk11_1 @ X313)=(X317))|((X313 @ (esk10_2 @ X313 @ X314))|~(X313 @ X314))))&(((X313 @ (esk11_1 @ X313))|(((X314)!=(esk10_2 @ X313 @ X314))|~(X313 @ X314)))&(~(X313 @ X317)|((esk11_1 @ X313)=(X317))|(((X314)!=(esk10_2 @ X313 @ X314))|~(X313 @ X314)))))&((~(in @ X319 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X318)))))|(X318))&((~(in @ X320 @ emptyset)|(X321))&(~(in @ X322 @ emptyset)&(~(in @ X323 @ emptyset)&((((X324 @ (esk12_2 @ X324 @ X325))|~(X324 @ X325)|(X324 @ (esk13_1 @ X324)))&(((X325)!=(esk12_2 @ X324 @ X325))|~(X324 @ X325)|(X324 @ (esk13_1 @ X324))))&(((((in @ (esk15_2 @ X328 @ X329) @ X329)|((X328)=(X329))|(in @ (esk14_2 @ X328 @ X329) @ X328))&(~(in @ (esk15_2 @ X328 @ X329) @ X328)|((X328)=(X329))|(in @ (esk14_2 @ X328 @ X329) @ X328)))&(((in @ (esk15_2 @ X328 @ X329) @ X329)|((X328)=(X329))|~(in @ (esk14_2 @ X328 @ X329) @ X329))&(~(in @ (esk15_2 @ X328 @ X329) @ X328)|((X328)=(X329))|~(in @ (esk14_2 @ X328 @ X329) @ X329))))&(((in @ (esk16_1 @ X332) @ X332)|((X332)=(emptyset)))&(((in @ (esk17_1 @ X334) @ X334)|((X334)=(emptyset)))&(((~(in @ X338 @ (dsetconstr @ X336 @ (^[Z0:$i]:((X337 @ Z0)))))|(X337 @ X338)|~(in @ X338 @ X336))&(~(X337 @ X338)|(in @ X338 @ (dsetconstr @ X336 @ (^[Z0:$i]:((X337 @ Z0)))))|~(in @ X338 @ X336)))&((((X339)=(emptyset))|(in @ (esk18_1 @ X339) @ X339))&((~(in @ X343 @ X341)|(~(X342 @ X343)|((dsetconstr @ X341 @ (^[Z0:$i]:((X342 @ Z0))))!=(emptyset))))&((~(in @ X345 @ X344)|((X344)!=(emptyset)))&((in @ X346 @ (setadjoin @ X346 @ X347))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X350 @ X349)|(in @ X350 @ (setadjoin @ X348 @ X349)))&(((((in @ X353 @ X352)|(X354)|((X353)=(X351))|~(in @ X353 @ (setadjoin @ X351 @ X352)))&(~(X354)|(X354)|((X353)=(X351))|~(in @ X353 @ (setadjoin @ X351 @ X352))))&(((in @ X353 @ X352)|(X354)|~(X354)|~(in @ X353 @ (setadjoin @ X351 @ X352)))&(~(X354)|(X354)|~(X354)|~(in @ X353 @ (setadjoin @ X351 @ X352)))))&((~(in @ X357 @ (setadjoin @ X355 @ X356))|(((X357)=(X355))|(in @ X357 @ X356)))&(((dsetconstr @ X358 @ (^[Z0:$i]:(($true))))=(X358))&((((in @ (esk19_2 @ X359 @ X360) @ X360)|(in @ X360 @ (powerset @ X359)))&(~(in @ (esk19_2 @ X359 @ X360) @ X359)|(in @ X360 @ (powerset @ X359))))&((in @ emptyset @ (powerset @ X362))&((in @ emptyset @ (powerset @ X363))&((~(in @ X365 @ (powerset @ X364))|(~(in @ X366 @ X365)|(in @ X366 @ X364)))&((~(in @ X368 @ X369)|(~(in @ X369 @ X367)|(in @ X368 @ (setunion @ X367))))&((((in @ X371 @ (esk20_3 @ X370 @ X371 @ X372))|(X372)|~(in @ X371 @ (setunion @ X370)))&(((in @ (esk20_3 @ X370 @ X371 @ X372) @ X370)|(X372)|~(in @ X371 @ (setunion @ X370)))&(~(X372)|(X372)|~(in @ X371 @ (setunion @ X370)))))&((~(in @ X375 @ X374)|(in @ X375 @ (powerset @ (setunion @ X374))))&((((~(X376 @ X380)|((X380)=(esk22_1 @ X376))|((X376 @ (esk21_2 @ X376 @ X377))|~(X376 @ X377)))&(((X381)!=(esk22_1 @ X376))|(X376 @ X381)|((X376 @ (esk21_2 @ X376 @ X377))|~(X376 @ X377))))&((~(X376 @ X380)|((X380)=(esk22_1 @ X376))|(((X377)!=(esk21_2 @ X376 @ X377))|~(X376 @ X377)))&(((X381)!=(esk22_1 @ X376))|(X376 @ X381)|(((X377)!=(esk21_2 @ X376 @ X377))|~(X376 @ X377)))))&(((esk23_0)!=(emptyset))&~(in @ X383 @ esk23_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_68])])])])])])).
% 0.08/0.16 thf(c_0_70, negated_conjecture, ![X2:$i]:(~((in @ X2 @ esk23_0))), inference(split_conjunct,[status(thm)],[c_0_69])).
% 0.08/0.16 thf(c_0_71, negated_conjecture, ![X2:$i]:(((in @ (esk16_1 @ X2) @ X2)|((X2)=(emptyset)))), inference(split_conjunct,[status(thm)],[c_0_69])).
% 0.08/0.16 thf(c_0_72, negated_conjecture, ((esk23_0)!=(emptyset)), inference(split_conjunct,[status(thm)],[c_0_69])).
% 0.08/0.16 thf(c_0_73, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_72]), ['proof']).
% 0.08/0.16 % SZS output end CNFRefutation
% 0.08/0.16 % Parsed axioms : 99
% 0.08/0.16 % Removed by relevancy pruning/SinE : 54
% 0.08/0.16 % Initial clauses : 92
% 0.08/0.16 % Removed in clause preprocessing : 4
% 0.08/0.16 % Initial clauses in saturation : 88
% 0.08/0.16 % Processed clauses : 18
% 0.08/0.16 % ...of these trivial : 1
% 0.08/0.16 % ...subsumed : 4
% 0.08/0.16 % ...remaining for further processing : 13
% 0.08/0.16 % Other redundant clauses eliminated : 1
% 0.08/0.16 % Clauses deleted for lack of memory : 0
% 0.08/0.16 % Backward-subsumed : 0
% 0.08/0.16 % Backward-rewritten : 1
% 0.08/0.16 % Generated clauses : 3
% 0.08/0.16 % ...of the previous two non-redundant : 1
% 0.08/0.16 % ...aggressively subsumed : 0
% 0.08/0.16 % Contextual simplify-reflections : 0
% 0.08/0.16 % Paramodulations : 2
% 0.08/0.16 % Factorizations : 0
% 0.08/0.16 % NegExts : 0
% 0.08/0.16 % Equation resolutions : 1
% 0.08/0.16 % Disequality decompositions : 0
% 0.08/0.16 % Total rewrite steps : 2
% 0.08/0.16 % ...of those cached : 0
% 0.08/0.16 % Propositional unsat checks : 0
% 0.08/0.16 % Propositional check models : 0
% 0.08/0.16 % Propositional check unsatisfiable : 0
% 0.08/0.16 % Propositional clauses : 0
% 0.08/0.16 % Propositional clauses after purity: 0
% 0.08/0.16 % Propositional unsat core size : 0
% 0.08/0.16 % Propositional preprocessing time : 0.000
% 0.08/0.16 % Propositional encoding time : 0.000
% 0.08/0.16 % Propositional solver time : 0.000
% 0.08/0.16 % Success case prop preproc time : 0.000
% 0.08/0.16 % Success case prop encoding time : 0.000
% 0.08/0.16 % Success case prop solver time : 0.000
% 0.08/0.16 % Current number of processed clauses : 11
% 0.08/0.16 % Positive orientable unit clauses : 6
% 0.08/0.16 % Positive unorientable unit clauses: 0
% 0.08/0.16 % Negative unit clauses : 4
% 0.08/0.16 % Non-unit-clauses : 1
% 0.08/0.16 % Current number of unprocessed clauses: 71
% 0.08/0.16 % ...number of literals in the above : 242
% 0.08/0.16 % Current number of archived formulas : 0
% 0.08/0.16 % Current number of archived clauses : 1
% 0.08/0.16 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.16 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.16 % Non-unit clause-clause subsumptions : 0
% 0.08/0.16 % Unit Clause-clause subsumption calls : 1
% 0.08/0.16 % Rewrite failures with RHS unbound : 0
% 0.08/0.16 % BW rewrite match attempts : 1
% 0.08/0.16 % BW rewrite match successes : 1
% 0.08/0.16 % Condensation attempts : 0
% 0.08/0.16 % Condensation successes : 0
% 0.08/0.16 % Termbank termtop insertions : 9917
% 0.08/0.16 % Search garbage collected termcells : 3784
% 0.08/0.16
% 0.08/0.16 % -------------------------------------------------
% 0.08/0.16 % User time : 0.009 s
% 0.08/0.16 % System time : 0.001 s
% 0.08/0.16 % Total time : 0.010 s
% 0.08/0.16 % Maximum resident set size: 4712 pages
% 0.08/0.16
% 0.08/0.16 % -------------------------------------------------
% 0.08/0.16 % User time : 0.011 s
% 0.08/0.16 % System time : 0.004 s
% 0.08/0.16 % Total time : 0.014 s
% 0.08/0.16 % Maximum resident set size: 4864 pages
% 0.08/0.16 % E exiting
%------------------------------------------------------------------------------