%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU527^1 : 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 : n014.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 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU527^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n014.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 13:48:00 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.22 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.vrJvBOc15A/E---3.1_2687406.p
% 0.09/0.26 % Version: 3.5.1-ho
% 0.09/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.26 % Starting sh5l with 300s (1) cores
% 0.09/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.09/0.26 % new_ho_10 with pid 2687439 completed with status 0
% 0.09/0.26 % Result found by new_ho_10
% 0.09/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.09/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.09/0.26 % Starting new_ho_10 with 901s (1) cores
% 0.09/0.26 % Starting sh5l with 151s (1) cores
% 0.09/0.26 % Starting new_bool_1 with 151s (1) cores
% 0.09/0.26 % Starting new_bool_2 with 146s (1) cores
% 0.09/0.26 % SubtermCWHack with pid 2687449 completed with status 0
% 0.09/0.26 % Result found by SubtermCWHack
% 0.09/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.09/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.09/0.26 % Preprocessing time : 0.002 s
% 0.09/0.26
% 0.09/0.26 % Proof found!
% 0.09/0.26 % SZS status Theorem
% 0.09/0.26 % SZS output start CNFRefutation
% 0.09/0.26 thf(decl_23, type, in: $i > $i > $o).
% 0.09/0.26 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.09/0.26 thf(decl_25, type, setextAx: $o).
% 0.09/0.26 thf(decl_26, type, emptyset: $i).
% 0.09/0.26 thf(decl_27, type, emptysetAx: $o).
% 0.09/0.26 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.09/0.26 thf(decl_29, type, setadjoinAx: $o).
% 0.09/0.26 thf(decl_30, type, powerset: $i > $i).
% 0.09/0.26 thf(decl_31, type, powersetAx: $o).
% 0.09/0.26 thf(decl_32, type, setunion: $i > $i).
% 0.09/0.26 thf(decl_33, type, setunionAx: $o).
% 0.09/0.26 thf(decl_34, type, omega: $i).
% 0.09/0.26 thf(decl_35, type, omega0Ax: $o).
% 0.09/0.26 thf(decl_36, type, omegaSAx: $o).
% 0.09/0.26 thf(decl_37, type, omegaIndAx: $o).
% 0.09/0.26 thf(decl_38, type, replAx: $o).
% 0.09/0.26 thf(decl_39, type, foundationAx: $o).
% 0.09/0.26 thf(decl_40, type, wellorderingAx: $o).
% 0.09/0.26 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.09/0.26 thf(decl_42, type, descrp: $o).
% 0.09/0.26 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.09/0.26 thf(decl_44, type, dsetconstrI: $o).
% 0.09/0.26 thf(decl_45, type, dsetconstrEL: $o).
% 0.09/0.26 thf(decl_46, type, dsetconstrER: $o).
% 0.09/0.26 thf(decl_47, type, exuE1: $o).
% 0.09/0.26 thf(decl_48, type, prop2set: $o > $i).
% 0.09/0.26 thf(decl_49, type, prop2setE: $o).
% 0.09/0.26 thf(decl_50, type, emptysetE: $o).
% 0.09/0.26 thf(decl_51, type, emptysetimpfalse: $o).
% 0.09/0.26 thf(decl_52, type, notinemptyset: $o).
% 0.09/0.26 thf(decl_53, type, exuE3e: $o).
% 0.09/0.26 thf(decl_54, type, setext: $o).
% 0.09/0.26 thf(decl_55, type, emptyI: $o).
% 0.09/0.26 thf(decl_56, type, noeltsimpempty: $o).
% 0.09/0.26 thf(decl_57, type, setbeta: $o).
% 0.09/0.26 thf(decl_58, type, nonempty: $i > $o).
% 0.09/0.26 thf(decl_59, type, nonemptyE1: $o).
% 0.09/0.26 thf(decl_60, type, nonemptyI: $o).
% 0.09/0.26 thf(decl_61, type, nonemptyI1: $o).
% 0.09/0.26 thf(decl_62, type, setadjoinIL: $o).
% 0.09/0.26 thf(decl_63, type, emptyinunitempty: $o).
% 0.09/0.26 thf(decl_64, type, setadjoinIR: $o).
% 0.09/0.26 thf(decl_65, type, setadjoinE: $o).
% 0.09/0.26 thf(decl_66, type, setadjoinOr: $o).
% 0.09/0.26 thf(decl_67, type, setoftrueEq: $o).
% 0.09/0.26 thf(decl_68, type, powersetI: $o).
% 0.09/0.26 thf(decl_69, type, emptyinPowerset: $o).
% 0.09/0.26 thf(decl_70, type, emptyInPowerset: $o).
% 0.09/0.26 thf(decl_71, type, powersetE: $o).
% 0.09/0.26 thf(decl_72, type, setunionI: $o).
% 0.09/0.26 thf(decl_73, type, setunionE: $o).
% 0.09/0.26 thf(decl_74, type, subPowSU: $o).
% 0.09/0.26 thf(decl_75, type, exuE2: $o).
% 0.09/0.26 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.09/0.26 thf(decl_77, type, epred1_0: $o).
% 0.09/0.26 thf(decl_78, type, esk1_2: $i > $i > $i).
% 0.09/0.26 thf(decl_79, type, esk2_2: $i > $i > $i).
% 0.09/0.26 thf(decl_80, type, esk3_2: $i > $i > $i).
% 0.09/0.26 thf(decl_81, type, esk4_1: $i > $i).
% 0.09/0.26 thf(decl_82, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.09/0.26 thf(decl_83, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.09/0.26 thf(decl_84, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.09/0.26 thf(decl_85, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.09/0.26 thf(decl_86, type, esk9_1: $i > $i).
% 0.09/0.26 thf(decl_87, type, esk10_2: ($i > $o) > $i > $i).
% 0.09/0.26 thf(decl_88, type, esk11_2: ($i > $o) > $i > $i).
% 0.09/0.26 thf(decl_89, type, esk12_1: ($i > $o) > $i).
% 0.09/0.26 thf(decl_90, type, esk13_2: ($i > $o) > $i > $i).
% 0.09/0.26 thf(decl_91, type, esk14_1: ($i > $o) > $i).
% 0.09/0.26 thf(decl_92, type, esk15_2: $i > $i > $i).
% 0.09/0.26 thf(decl_93, type, esk16_2: $i > $i > $i).
% 0.09/0.26 thf(decl_94, type, esk17_1: $i > $i).
% 0.09/0.26 thf(decl_95, type, esk18_1: $i > $i).
% 0.09/0.26 thf(decl_96, type, esk19_1: $i > $i).
% 0.09/0.26 thf(decl_97, type, esk20_2: $i > $i > $i).
% 0.09/0.26 thf(decl_98, type, esk21_3: $i > $i > $o > $i).
% 0.09/0.26 thf(decl_99, type, esk22_2: ($i > $o) > $i > $i).
% 0.09/0.26 thf(decl_100, type, esk23_1: ($i > $o) > $i).
% 0.09/0.26 thf(decl_101, type, esk24_1: $i > $i).
% 0.09/0.26 thf(decl_102, type, esk25_0: $i).
% 0.09/0.26 thf(decl_103, type, esk26_0: $i).
% 0.09/0.26 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', replAx)).
% 0.09/0.26 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', exu)).
% 0.09/0.26 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', descrp)).
% 0.09/0.26 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', exuE1)).
% 0.09/0.26 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', exuE3e)).
% 0.09/0.26 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', nonempty)).
% 0.09/0.26 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', nonemptyI)).
% 0.09/0.26 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', exuE2)).
% 0.09/0.26 thf(uniqinunit, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', uniqinunit)).
% 0.09/0.26 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', dsetconstrI)).
% 0.09/0.26 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', dsetconstrEL)).
% 0.09/0.26 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', dsetconstrER)).
% 0.09/0.26 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', setbeta)).
% 0.09/0.26 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', nonemptyE1)).
% 0.09/0.26 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', nonemptyI1)).
% 0.09/0.26 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', setoftrueEq)).
% 0.09/0.26 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', nonemptyImpWitness)).
% 0.09/0.26 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', setextAx)).
% 0.09/0.26 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', emptysetAx)).
% 0.09/0.26 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', setadjoinAx)).
% 0.09/0.26 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', powersetAx)).
% 0.09/0.26 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', setunionAx)).
% 0.09/0.26 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', omega0Ax)).
% 0.09/0.26 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', omegaSAx)).
% 0.09/0.26 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.vrJvBOc15A/E---3.1_2687406.p', omegaIndAx)).
% 0.09/0.26 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.vrJvBOc15A/E---3.1_2687406.p', foundationAx)).
% 0.09/0.26 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', wellorderingAx)).
% 0.09/0.26 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', prop2setE)).
% 0.09/0.26 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', emptysetE)).
% 0.09/0.26 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', emptysetimpfalse)).
% 0.09/0.26 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', notinemptyset)).
% 0.09/0.26 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.vrJvBOc15A/E---3.1_2687406.p', setext)).
% 0.09/0.26 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', emptyI)).
% 0.09/0.26 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', noeltsimpempty)).
% 0.09/0.26 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', setadjoinIL)).
% 0.09/0.26 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', emptyinunitempty)).
% 0.09/0.26 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', setadjoinIR)).
% 0.09/0.26 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', setadjoinE)).
% 0.09/0.26 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', setadjoinOr)).
% 0.09/0.26 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', powersetI)).
% 0.09/0.26 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', emptyinPowerset)).
% 0.09/0.26 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', emptyInPowerset)).
% 0.09/0.26 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', powersetE)).
% 0.09/0.26 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', setunionI)).
% 0.09/0.26 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14)))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', setunionE)).
% 0.09/0.26 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.vrJvBOc15A/E---3.1_2687406.p', subPowSU)).
% 0.09/0.26 thf(c_0_46, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.09/0.26 thf(c_0_47, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.09/0.26 thf(c_0_48, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.09/0.26 thf(c_0_49, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.09/0.26 thf(c_0_50, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.09/0.26 thf(c_0_51, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.09/0.26 thf(c_0_52, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.09/0.26 thf(c_0_53, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.09/0.26 thf(c_0_54, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3)))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[uniqinunit])).
% 0.09/0.26 thf(c_0_55, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X137:$i]:(((((X6 @ X2 @ X137)))&(![X138:$i]:(((((X6 @ X2 @ X138)))=>(((X137)=(X138)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_46, c_0_47])).
% 0.09/0.26 thf(c_0_56, plain, ((descrp)=(![X1:$i > $o]:((((?[X139:$i]:(((((X1 @ X139)))&(![X140:$i]:(((((X1 @ X140)))=>(((X139)=(X140))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_48, c_0_47])).
% 0.09/0.26 thf(c_0_57, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.09/0.26 thf(c_0_58, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.09/0.26 thf(c_0_59, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.09/0.26 thf(c_0_60, plain, ((exuE1)=(![X1:$i > $o]:((((?[X141:$i]:(((((X1 @ X141)))&(![X142:$i]:(((((X1 @ X142)))=>(((X141)=(X142))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_49, c_0_47])).
% 0.09/0.26 thf(c_0_61, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X143:$i]:(((((X1 @ X143)))&(![X144:$i]:(((((X1 @ X144)))=>(((X143)=(X144))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_50, c_0_47])).
% 0.09/0.26 thf(c_0_62, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.09/0.26 thf(c_0_63, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_51])).
% 0.09/0.26 thf(c_0_64, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_52, c_0_51])).
% 0.09/0.26 thf(c_0_65, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_51])).
% 0.09/0.26 thf(c_0_66, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.09/0.26 thf(c_0_67, plain, ((exuE2)=(![X1:$i > $o]:((((?[X145:$i]:(((((X1 @ X145)))&(![X146:$i]:(((((X1 @ X146)))=>(((X145)=(X146))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_53, c_0_47])).
% 0.09/0.26 thf(c_0_68, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_51])).
% 0.09/0.26 thf(c_0_69, plain, ((epred1_0)<=>![X176:$i]:(?[X177:$i]:((((![X178:$i]:(((in @ X178 @ X177)=>![X179:$i]:(((in @ X179 @ X178)=>(in @ X179 @ X176)))))&![X180:$i, X181:$i]:((((in @ X180 @ X176)&(in @ X181 @ X176))=>(![X182:$i]:(((in @ X182 @ X177)=>((in @ X180 @ X182)<=>(in @ X181 @ X182))))=>((X180)=(X181))))))&![X183:$i, X184:$i]:((((in @ X183 @ X177)&(in @ X184 @ X177))=>(![X185:$i]:(((in @ X185 @ X183)=>(in @ X185 @ X184)))|![X186:$i]:(((in @ X186 @ X184)=>(in @ X186 @ X183)))))))&![X187:$i]:(((![X188:$i]:(((in @ X188 @ X187)=>(in @ X188 @ X176)))&?[X189:$i]:((in @ X189 @ X187)))=>?[X190:$i, X191:$i]:(((((in @ X190 @ X177)&(in @ X191 @ X187))&~(?[X192:$i]:(((in @ X192 @ X190)&(in @ X192 @ X187)))))&![X193:$i]:(((in @ X193 @ X177)=>(![X194:$i]:(((in @ X194 @ X193)=>(in @ X194 @ X190)))|(in @ X191 @ X193)))))))))))), introduced(definition)).
% 0.09/0.26 thf(c_0_70, negated_conjecture, ~((![X147:$i, X148:$i]:((![X149:$i]:(((in @ X149 @ X147)<=>(in @ X149 @ X148)))=>((X147)=(X148))))=>(![X150:$i]:(~(in @ X150 @ emptyset))=>(![X151:$i, X152:$i, X153:$i]:(((in @ X153 @ (setadjoin @ X151 @ X152))<=>(((X153)=(X151))|(in @ X153 @ X152))))=>(![X154:$i, X155:$i]:(((in @ X155 @ (powerset @ X154))<=>![X156:$i]:(((in @ X156 @ X155)=>(in @ X156 @ X154)))))=>(![X157:$i, X158:$i]:(((in @ X158 @ (setunion @ X157))<=>?[X159:$i]:(((in @ X158 @ X159)&(in @ X159 @ X157)))))=>((in @ emptyset @ omega)=>(![X160:$i]:(((in @ X160 @ omega)=>(in @ (setadjoin @ X160 @ X160) @ omega)))=>(![X161:$i]:((((in @ emptyset @ X161)&![X162:$i]:((((in @ X162 @ omega)&(in @ X162 @ X161))=>(in @ (setadjoin @ X162 @ X162) @ X161))))=>![X163:$i]:(((in @ X163 @ omega)=>(in @ X163 @ X161)))))=>(![X164:$i > $i > $o, X165:$i]:((![X166:$i]:(((in @ X166 @ X165)=>?[X167:$i]:(((X164 @ X166 @ X167)&![X168:$i]:(((X164 @ X166 @ X168)=>((X167)=(X168))))))))=>?[X169:$i]:(![X170:$i]:(((in @ X170 @ X169)<=>?[X171:$i]:(((in @ X171 @ X165)&(X164 @ X171 @ X170))))))))=>(![X172:$i]:((?[X173:$i]:((in @ X173 @ X172))=>?[X174:$i]:(((in @ X174 @ X172)&~(?[X175:$i]:(((in @ X175 @ X174)&(in @ X175 @ X172))))))))=>((epred1_0)=>(![X195:$i > $o]:((?[X196:$i]:(((X195 @ X196)&![X197:$i]:(((X195 @ X197)=>((X196)=(X197))))))=>(X195 @ (descr @ (^[Z0:$i]:(X195 @ Z0))))))=>(![X198:$i, X199:$i > $o, X200:$i]:(((in @ X200 @ X198)=>((X199 @ X200)=>(in @ X200 @ (dsetconstr @ X198 @ X199)))))=>(![X201:$i, X202:$i > $o, X203:$i]:(((in @ X203 @ (dsetconstr @ X201 @ X202))=>(in @ X203 @ X201)))=>(![X204:$i, X205:$i > $o, X206:$i]:(((in @ X206 @ (dsetconstr @ X204 @ X205))=>(X205 @ X206)))=>(![X207:$i > $o]:((?[X208:$i]:(((X207 @ X208)&![X209:$i]:(((X207 @ X209)=>((X208)=(X209))))))=>?[X210:$i]:(((X207 @ X210)&![X211:$i]:(((X207 @ X211)=>((X210)=(X211))))))))=>(![X212:$o, X213:$i]:(((in @ X213 @ (prop2set @ ((X212))))=>(X212)))=>(![X214:$i]:(((in @ X214 @ emptyset)=>![X215:$o]:((X215))))=>(![X216:$i]:(((in @ X216 @ emptyset)=>~($true)))=>(![X217:$i]:(~(in @ X217 @ emptyset))=>(![X218:$i > $o]:((?[X219:$i]:(((X218 @ X219)&![X220:$i]:(((X218 @ X220)=>((X219)=(X220))))))=>?[X221:$i]:((X218 @ X221))))=>(![X222:$i, X223:$i]:((![X224:$i]:(((in @ X224 @ X222)=>(in @ X224 @ X223)))=>(![X225:$i]:(((in @ X225 @ X223)=>(in @ X225 @ X222)))=>((X222)=(X223)))))=>(![X226:$i]:((![X227:$i]:(~(in @ X227 @ X226))=>((X226)=(emptyset))))=>(![X228:$i]:((![X229:$i]:(~(in @ X229 @ X228))=>((X228)=(emptyset))))=>(![X230:$i, X231:$i > $o, X232:$i]:(((in @ X232 @ X230)=>((in @ X232 @ (dsetconstr @ X230 @ X231))<=>(X231 @ X232))))=>(![X233:$i]:((((X233)!=(emptyset))=>?[X234:$i]:((in @ X234 @ X233))))=>(![X235:$i, X236:$i > $o, X237:$i]:(((in @ X237 @ X235)=>((X236 @ X237)=>((dsetconstr @ X235 @ X236)!=(emptyset)))))=>(![X238:$i]:((?[X239:$i]:((in @ X239 @ X238))=>((X238)!=(emptyset))))=>(![X240:$i, X241:$i]:((in @ X240 @ (setadjoin @ X240 @ X241)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X242:$i, X243:$i, X244:$i]:(((in @ X244 @ X243)=>(in @ X244 @ (setadjoin @ X242 @ X243))))=>(![X245:$i, X246:$i, X247:$i]:(((in @ X247 @ (setadjoin @ X245 @ X246))=>![X248:$o]:(((((X247)=(X245))=>(X248))=>(((in @ X247 @ X246)=>(X248))=>(X248))))))=>(![X249:$i, X250:$i, X251:$i]:(((in @ X251 @ (setadjoin @ X249 @ X250))=>(((X251)=(X249))|(in @ X251 @ X250))))=>(![X252:$i]:(((dsetconstr @ X252 @ (^[Z0:$i]:($true)))=(X252)))=>(![X253:$i, X254:$i]:((![X255:$i]:(((in @ X255 @ X254)=>(in @ X255 @ X253)))=>(in @ X254 @ (powerset @ X253))))=>(![X256:$i]:((in @ emptyset @ (powerset @ X256)))=>(![X257:$i]:((in @ emptyset @ (powerset @ X257)))=>(![X258:$i, X259:$i, X260:$i]:(((in @ X259 @ (powerset @ X258))=>((in @ X260 @ X259)=>(in @ X260 @ X258))))=>(![X261:$i, X262:$i, X263:$i]:(((in @ X262 @ X263)=>((in @ X263 @ X261)=>(in @ X262 @ (setunion @ X261)))))=>(![X264:$i, X265:$i]:(((in @ X265 @ (setunion @ X264))=>![X266:$o]:((![X267:$i]:(((in @ X265 @ X267)=>((in @ X267 @ X264)=>(X266))))=>(X266)))))=>(![X268:$i, X269:$i]:(((in @ X269 @ X268)=>(in @ X269 @ (powerset @ (setunion @ X268)))))=>(![X270:$i > $o]:((?[X271:$i]:(((X270 @ X271)&![X272:$i]:(((X270 @ X272)=>((X271)=(X272))))))=>?[X273:$i]:(![X274:$i]:(((X270 @ X274)<=>((X274)=(X273)))))))=>(![X275:$i]:((((X275)!=(emptyset))=>?[X276:$i]:(((in @ X276 @ X275)&$true))))=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3)))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_54, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_55]), foundationAx]), wellorderingAx]), c_0_56]), c_0_57]), c_0_58]), c_0_59]), c_0_60]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_61]), setext]), emptyI]), noeltsimpempty]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_66]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_67]), c_0_68])])]), c_0_69])).
% 0.09/0.26 thf(c_0_71, negated_conjecture, ![X279:$i, X280:$i, X282:$i, X283:$i, X284:$i, X285:$i, X286:$i, X287:$i, X288:$i, X289:$i, X290:$i, X292:$i, X293:$i, X295:$i, X296:$i, X297:$i, X298:$i, X299:$i, X301:$i, X302:$i > $i > $o, X303:$i, X305:$i, X308:$i, X310:$i, X311:$i, X312:$i, X313:$i, X315:$i, X316:$i > $o, X317:$i, X319:$i, X320:$i > $o, X321:$i, X322:$i, X323:$i > $o, X324:$i, X325:$i, X326:$i > $o, X327:$i, X328:$i > $o, X329:$i, X332:$i, X333:$o, X334:$i, X335:$i, X336:$o, X337:$i, X338:$i, X339:$i > $o, X340:$i, X343:$i, X344:$i, X347:$i, X349:$i, X351:$i, X352:$i > $o, X353:$i, X354:$i, X356:$i, X357:$i > $o, X358:$i, X359:$i, X360:$i, X361:$i, X362:$i, X363:$i, X364:$i, X365:$i, X366:$i, X367:$i, X368:$i, X369:$o, X370:$i, X371:$i, X372:$i, X373:$i, X374:$i, X375:$i, X377:$i, X378:$i, X379:$i, X380:$i, X381:$i, X382:$i, X383:$i, X384:$i, X385:$i, X386:$i, X387:$o, X389:$i, X390:$i, X391:$i > $o, X392:$i, X395:$i, X396:$i, X397:$i]:((((~(in @ (esk1_2 @ X279 @ X280) @ X279)|~(in @ (esk1_2 @ X279 @ X280) @ X280)|((X279)=(X280)))&((in @ (esk1_2 @ X279 @ X280) @ X279)|(in @ (esk1_2 @ X279 @ X280) @ X280)|((X279)=(X280))))&(~(in @ X282 @ emptyset)&(((~(in @ X285 @ (setadjoin @ X283 @ X284))|(((X285)=(X283))|(in @ X285 @ X284)))&((((X285)!=(X283))|(in @ X285 @ (setadjoin @ X283 @ X284)))&(~(in @ X285 @ X284)|(in @ X285 @ (setadjoin @ X283 @ X284)))))&(((~(in @ X287 @ (powerset @ X286))|(~(in @ X288 @ X287)|(in @ X288 @ X286)))&(((in @ (esk2_2 @ X289 @ X290) @ X290)|(in @ X290 @ (powerset @ X289)))&(~(in @ (esk2_2 @ X289 @ X290) @ X289)|(in @ X290 @ (powerset @ X289)))))&(((((in @ X293 @ (esk3_2 @ X292 @ X293))|~(in @ X293 @ (setunion @ X292)))&((in @ (esk3_2 @ X292 @ X293) @ X292)|~(in @ X293 @ (setunion @ X292))))&(~(in @ X296 @ X297)|~(in @ X297 @ X295)|(in @ X296 @ (setunion @ X295))))&((in @ emptyset @ omega)&((~(in @ X298 @ omega)|(in @ (setadjoin @ X298 @ X298) @ omega))&(((((in @ (esk4_1 @ X299) @ omega)|~(in @ emptyset @ X299)|(~(in @ X301 @ omega)|(in @ X301 @ X299)))&((in @ (esk4_1 @ X299) @ X299)|~(in @ emptyset @ X299)|(~(in @ X301 @ omega)|(in @ X301 @ X299))))&(~(in @ (setadjoin @ (esk4_1 @ X299) @ (esk4_1 @ X299)) @ X299)|~(in @ emptyset @ X299)|(~(in @ X301 @ omega)|(in @ X301 @ X299))))&((((((in @ (esk8_3 @ X302 @ X303 @ X308) @ X303)|~(in @ X308 @ (esk7_2 @ X302 @ X303))|(in @ (esk5_2 @ X302 @ X303) @ X303))&((X302 @ (esk8_3 @ X302 @ X303 @ X308) @ X308)|~(in @ X308 @ (esk7_2 @ X302 @ X303))|(in @ (esk5_2 @ X302 @ X303) @ X303)))&(~(in @ X311 @ X303)|~(X302 @ X311 @ X310)|(in @ X310 @ (esk7_2 @ X302 @ X303))|(in @ (esk5_2 @ X302 @ X303) @ X303)))&(((((in @ (esk8_3 @ X302 @ X303 @ X308) @ X303)|~(in @ X308 @ (esk7_2 @ X302 @ X303))|((X302 @ (esk5_2 @ X302 @ X303) @ (esk6_3 @ X302 @ X303 @ X305))|~(X302 @ (esk5_2 @ X302 @ X303) @ X305)))&((X302 @ (esk8_3 @ X302 @ X303 @ X308) @ X308)|~(in @ X308 @ (esk7_2 @ X302 @ X303))|((X302 @ (esk5_2 @ X302 @ X303) @ (esk6_3 @ X302 @ X303 @ X305))|~(X302 @ (esk5_2 @ X302 @ X303) @ X305))))&(~(in @ X311 @ X303)|~(X302 @ X311 @ X310)|(in @ X310 @ (esk7_2 @ X302 @ X303))|((X302 @ (esk5_2 @ X302 @ X303) @ (esk6_3 @ X302 @ X303 @ X305))|~(X302 @ (esk5_2 @ X302 @ X303) @ X305))))&((((in @ (esk8_3 @ X302 @ X303 @ X308) @ X303)|~(in @ X308 @ (esk7_2 @ X302 @ X303))|(((X305)!=(esk6_3 @ X302 @ X303 @ X305))|~(X302 @ (esk5_2 @ X302 @ X303) @ X305)))&((X302 @ (esk8_3 @ X302 @ X303 @ X308) @ X308)|~(in @ X308 @ (esk7_2 @ X302 @ X303))|(((X305)!=(esk6_3 @ X302 @ X303 @ X305))|~(X302 @ (esk5_2 @ X302 @ X303) @ X305))))&(~(in @ X311 @ X303)|~(X302 @ X311 @ X310)|(in @ X310 @ (esk7_2 @ X302 @ X303))|(((X305)!=(esk6_3 @ X302 @ X303 @ X305))|~(X302 @ (esk5_2 @ X302 @ X303) @ X305))))))&((((in @ (esk9_1 @ X312) @ X312)|~(in @ X313 @ X312))&(~(in @ X315 @ (esk9_1 @ X312))|~(in @ X315 @ X312)|~(in @ X313 @ X312)))&((epred1_0)&((((X316 @ (esk10_2 @ X316 @ X317))|~(X316 @ X317)|(X316 @ (descr @ X316)))&(((X317)!=(esk10_2 @ X316 @ X317))|~(X316 @ X317)|(X316 @ (descr @ X316))))&((~(in @ X321 @ X319)|(~(X320 @ X321)|(in @ X321 @ (dsetconstr @ X319 @ X320))))&((~(in @ X324 @ (dsetconstr @ X322 @ X323))|(in @ X324 @ X322))&((~(in @ X327 @ (dsetconstr @ X325 @ X326))|(X326 @ X327))&(((((X328 @ (esk12_1 @ X328))|((X328 @ (esk11_2 @ X328 @ X329))|~(X328 @ X329)))&(~(X328 @ X332)|((esk12_1 @ X328)=(X332))|((X328 @ (esk11_2 @ X328 @ X329))|~(X328 @ X329))))&(((X328 @ (esk12_1 @ X328))|(((X329)!=(esk11_2 @ X328 @ X329))|~(X328 @ X329)))&(~(X328 @ X332)|((esk12_1 @ X328)=(X332))|(((X329)!=(esk11_2 @ X328 @ X329))|~(X328 @ X329)))))&((~(in @ X334 @ (prop2set @ ((X333))))|(X333))&((~(in @ X335 @ emptyset)|(X336))&((~(in @ X337 @ emptyset)|~($true))&(~(in @ X338 @ emptyset)&((((X339 @ (esk13_2 @ X339 @ X340))|~(X339 @ X340)|(X339 @ (esk14_1 @ X339)))&(((X340)!=(esk13_2 @ X339 @ X340))|~(X339 @ X340)|(X339 @ (esk14_1 @ X339))))&(((((in @ (esk16_2 @ X343 @ X344) @ X344)|((X343)=(X344))|(in @ (esk15_2 @ X343 @ X344) @ X343))&(~(in @ (esk16_2 @ X343 @ X344) @ X343)|((X343)=(X344))|(in @ (esk15_2 @ X343 @ X344) @ X343)))&(((in @ (esk16_2 @ X343 @ X344) @ X344)|((X343)=(X344))|~(in @ (esk15_2 @ X343 @ X344) @ X344))&(~(in @ (esk16_2 @ X343 @ X344) @ X343)|((X343)=(X344))|~(in @ (esk15_2 @ X343 @ X344) @ X344))))&(((in @ (esk17_1 @ X347) @ X347)|((X347)=(emptyset)))&(((in @ (esk18_1 @ X349) @ X349)|((X349)=(emptyset)))&(((~(in @ X353 @ (dsetconstr @ X351 @ X352))|(X352 @ X353)|~(in @ X353 @ X351))&(~(X352 @ X353)|(in @ X353 @ (dsetconstr @ X351 @ X352))|~(in @ X353 @ X351)))&((((X354)=(emptyset))|(in @ (esk19_1 @ X354) @ X354))&((~(in @ X358 @ X356)|(~(X357 @ X358)|((dsetconstr @ X356 @ X357)!=(emptyset))))&((~(in @ X360 @ X359)|((X359)!=(emptyset)))&((in @ X361 @ (setadjoin @ X361 @ X362))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X365 @ X364)|(in @ X365 @ (setadjoin @ X363 @ X364)))&(((((in @ X368 @ X367)|(X369)|((X368)=(X366))|~(in @ X368 @ (setadjoin @ X366 @ X367)))&(~(X369)|(X369)|((X368)=(X366))|~(in @ X368 @ (setadjoin @ X366 @ X367))))&(((in @ X368 @ X367)|(X369)|~(X369)|~(in @ X368 @ (setadjoin @ X366 @ X367)))&(~(X369)|(X369)|~(X369)|~(in @ X368 @ (setadjoin @ X366 @ X367)))))&((~(in @ X372 @ (setadjoin @ X370 @ X371))|(((X372)=(X370))|(in @ X372 @ X371)))&(((dsetconstr @ X373 @ (^[Z0:$i]:($true)))=(X373))&((((in @ (esk20_2 @ X374 @ X375) @ X375)|(in @ X375 @ (powerset @ X374)))&(~(in @ (esk20_2 @ X374 @ X375) @ X374)|(in @ X375 @ (powerset @ X374))))&((in @ emptyset @ (powerset @ X377))&((in @ emptyset @ (powerset @ X378))&((~(in @ X380 @ (powerset @ X379))|(~(in @ X381 @ X380)|(in @ X381 @ X379)))&((~(in @ X383 @ X384)|(~(in @ X384 @ X382)|(in @ X383 @ (setunion @ X382))))&((((in @ X386 @ (esk21_3 @ X385 @ X386 @ X387))|(X387)|~(in @ X386 @ (setunion @ X385)))&(((in @ (esk21_3 @ X385 @ X386 @ X387) @ X385)|(X387)|~(in @ X386 @ (setunion @ X385)))&(~(X387)|(X387)|~(in @ X386 @ (setunion @ X385)))))&((~(in @ X390 @ X389)|(in @ X390 @ (powerset @ (setunion @ X389))))&((((~(X391 @ X395)|((X395)=(esk23_1 @ X391))|((X391 @ (esk22_2 @ X391 @ X392))|~(X391 @ X392)))&(((X396)!=(esk23_1 @ X391))|(X391 @ X396)|((X391 @ (esk22_2 @ X391 @ X392))|~(X391 @ X392))))&((~(X391 @ X395)|((X395)=(esk23_1 @ X391))|(((X392)!=(esk22_2 @ X391 @ X392))|~(X391 @ X392)))&(((X396)!=(esk23_1 @ X391))|(X391 @ X396)|(((X392)!=(esk22_2 @ X391 @ X392))|~(X391 @ X392)))))&((((in @ (esk24_1 @ X397) @ X397)|((X397)=(emptyset)))&(($true)|((X397)=(emptyset))))&((in @ esk25_0 @ (setadjoin @ esk26_0 @ emptyset))&((esk25_0)!=(esk26_0))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])])])])])])).
% 0.09/0.26 thf(c_0_72, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ X3)|((X2)=(X4))|~((in @ X2 @ (setadjoin @ X4 @ X3))))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_71])])])).
% 0.09/0.26 thf(c_0_73, negated_conjecture, (in @ esk25_0 @ (setadjoin @ esk26_0 @ emptyset)), inference(split_conjunct,[status(thm)],[c_0_71])).
% 0.09/0.26 thf(c_0_74, negated_conjecture, ((esk25_0)!=(esk26_0)), inference(split_conjunct,[status(thm)],[c_0_71])).
% 0.09/0.26 thf(c_0_75, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_71])).
% 0.09/0.26 thf(c_0_76, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73]), c_0_74]), c_0_75]), ['proof']).
% 0.09/0.26 % SZS output end CNFRefutation
% 0.09/0.26 % Parsed axioms : 101
% 0.09/0.26 % Removed by relevancy pruning/SinE : 0
% 0.09/0.26 % Initial clauses : 152
% 0.09/0.26 % Removed in clause preprocessing : 59
% 0.09/0.26 % Initial clauses in saturation : 93
% 0.09/0.26 % Processed clauses : 187
% 0.09/0.26 % ...of these trivial : 1
% 0.09/0.26 % ...subsumed : 85
% 0.09/0.26 % ...remaining for further processing : 101
% 0.09/0.26 % Other redundant clauses eliminated : 4
% 0.09/0.26 % Clauses deleted for lack of memory : 0
% 0.09/0.26 % Backward-subsumed : 0
% 0.09/0.26 % Backward-rewritten : 4
% 0.09/0.26 % Generated clauses : 490
% 0.09/0.26 % ...of the previous two non-redundant : 413
% 0.09/0.26 % ...aggressively subsumed : 0
% 0.09/0.26 % Contextual simplify-reflections : 0
% 0.09/0.26 % Paramodulations : 486
% 0.09/0.26 % Factorizations : 0
% 0.09/0.26 % NegExts : 0
% 0.09/0.26 % Equation resolutions : 4
% 0.09/0.26 % Disequality decompositions : 0
% 0.09/0.26 % Total rewrite steps : 65
% 0.09/0.26 % ...of those cached : 35
% 0.09/0.26 % Propositional unsat checks : 0
% 0.09/0.26 % Propositional check models : 0
% 0.09/0.26 % Propositional check unsatisfiable : 0
% 0.09/0.26 % Propositional clauses : 0
% 0.09/0.26 % Propositional clauses after purity: 0
% 0.09/0.26 % Propositional unsat core size : 0
% 0.09/0.26 % Propositional preprocessing time : 0.000
% 0.09/0.26 % Propositional encoding time : 0.000
% 0.09/0.26 % Propositional solver time : 0.000
% 0.09/0.26 % Success case prop preproc time : 0.000
% 0.09/0.26 % Success case prop encoding time : 0.000
% 0.09/0.26 % Success case prop solver time : 0.000
% 0.09/0.26 % Current number of processed clauses : 94
% 0.09/0.26 % Positive orientable unit clauses : 16
% 0.09/0.26 % Positive unorientable unit clauses: 0
% 0.09/0.26 % Negative unit clauses : 3
% 0.09/0.26 % Non-unit-clauses : 75
% 0.09/0.26 % Current number of unprocessed clauses: 311
% 0.09/0.26 % ...number of literals in the above : 842
% 0.09/0.26 % Current number of archived formulas : 0
% 0.09/0.26 % Current number of archived clauses : 4
% 0.09/0.26 % Clause-clause subsumption calls (NU) : 781
% 0.09/0.26 % Rec. Clause-clause subsumption calls : 568
% 0.09/0.26 % Non-unit clause-clause subsumptions : 55
% 0.09/0.26 % Unit Clause-clause subsumption calls : 14
% 0.09/0.26 % Rewrite failures with RHS unbound : 0
% 0.09/0.26 % BW rewrite match attempts : 11
% 0.09/0.26 % BW rewrite match successes : 4
% 0.09/0.26 % Condensation attempts : 0
% 0.09/0.26 % Condensation successes : 0
% 0.09/0.26 % Termbank termtop insertions : 18012
% 0.09/0.26 % Search garbage collected termcells : 4754
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.020 s
% 0.09/0.26 % System time : 0.005 s
% 0.09/0.26 % Total time : 0.024 s
% 0.09/0.26 % Maximum resident set size: 4760 pages
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.049 s
% 0.09/0.26 % System time : 0.015 s
% 0.09/0.26 % Total time : 0.064 s
% 0.09/0.26 % Maximum resident set size: 4608 pages
% 0.09/0.26 % E exiting
%------------------------------------------------------------------------------