%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU532^1 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:24 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU532^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n020.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 13:49:19 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 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.dVY1Udg5m9/E---3.1_1080264.p
% 0.10/0.26 % Version: 3.5.1-ho
% 0.10/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.10/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.26 % Starting sh5l with 300s (1) cores
% 0.10/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.10/0.26 % new_ho_10 with pid 1080294 completed with status 0
% 0.10/0.26 % Result found by new_ho_10
% 0.10/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.10/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.26 % No SInE strategy applied
% 0.10/0.26 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.10/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.10/0.26 % Starting new_ho_10 with 901s (1) cores
% 0.10/0.26 % Starting sh5l with 151s (1) cores
% 0.10/0.26 % Starting new_bool_1 with 151s (1) cores
% 0.10/0.26 % Starting new_bool_2 with 146s (1) cores
% 0.10/0.26 % SubtermCWHack with pid 1080300 completed with status 0
% 0.10/0.26 % Result found by SubtermCWHack
% 0.10/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.10/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.26 % No SInE strategy applied
% 0.10/0.26 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.10/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.10/0.26 % Preprocessing time : 0.003 s
% 0.10/0.26
% 0.10/0.26 % Proof found!
% 0.10/0.26 % SZS status Theorem
% 0.10/0.26 % SZS output start CNFRefutation
% 0.10/0.26 thf(decl_23, type, in: $i > $i > $o).
% 0.10/0.26 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.10/0.26 thf(decl_25, type, setextAx: $o).
% 0.10/0.26 thf(decl_26, type, emptyset: $i).
% 0.10/0.26 thf(decl_27, type, emptysetAx: $o).
% 0.10/0.26 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.10/0.26 thf(decl_29, type, setadjoinAx: $o).
% 0.10/0.26 thf(decl_30, type, powerset: $i > $i).
% 0.10/0.26 thf(decl_31, type, powersetAx: $o).
% 0.10/0.26 thf(decl_32, type, setunion: $i > $i).
% 0.10/0.26 thf(decl_33, type, setunionAx: $o).
% 0.10/0.26 thf(decl_34, type, omega: $i).
% 0.10/0.26 thf(decl_35, type, omega0Ax: $o).
% 0.10/0.26 thf(decl_36, type, omegaSAx: $o).
% 0.10/0.26 thf(decl_37, type, omegaIndAx: $o).
% 0.10/0.26 thf(decl_38, type, replAx: $o).
% 0.10/0.26 thf(decl_39, type, foundationAx: $o).
% 0.10/0.26 thf(decl_40, type, wellorderingAx: $o).
% 0.10/0.26 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.10/0.26 thf(decl_42, type, descrp: $o).
% 0.10/0.26 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.10/0.26 thf(decl_44, type, dsetconstrI: $o).
% 0.10/0.26 thf(decl_45, type, dsetconstrEL: $o).
% 0.10/0.26 thf(decl_46, type, dsetconstrER: $o).
% 0.10/0.26 thf(decl_47, type, exuE1: $o).
% 0.10/0.26 thf(decl_48, type, prop2set: $o > $i).
% 0.10/0.26 thf(decl_49, type, prop2setE: $o).
% 0.10/0.26 thf(decl_50, type, emptysetE: $o).
% 0.10/0.26 thf(decl_51, type, emptysetimpfalse: $o).
% 0.10/0.26 thf(decl_52, type, notinemptyset: $o).
% 0.10/0.26 thf(decl_53, type, exuE3e: $o).
% 0.10/0.26 thf(decl_54, type, setext: $o).
% 0.10/0.26 thf(decl_55, type, emptyI: $o).
% 0.10/0.26 thf(decl_56, type, noeltsimpempty: $o).
% 0.10/0.26 thf(decl_57, type, setbeta: $o).
% 0.10/0.26 thf(decl_58, type, nonempty: $i > $o).
% 0.10/0.26 thf(decl_59, type, nonemptyE1: $o).
% 0.10/0.26 thf(decl_60, type, nonemptyI: $o).
% 0.10/0.26 thf(decl_61, type, nonemptyI1: $o).
% 0.10/0.26 thf(decl_62, type, setadjoinIL: $o).
% 0.10/0.26 thf(decl_63, type, emptyinunitempty: $o).
% 0.10/0.26 thf(decl_64, type, setadjoinIR: $o).
% 0.10/0.26 thf(decl_65, type, setadjoinE: $o).
% 0.10/0.26 thf(decl_66, type, setadjoinOr: $o).
% 0.10/0.26 thf(decl_67, type, setoftrueEq: $o).
% 0.10/0.26 thf(decl_68, type, powersetI: $o).
% 0.10/0.26 thf(decl_69, type, emptyinPowerset: $o).
% 0.10/0.26 thf(decl_70, type, emptyInPowerset: $o).
% 0.10/0.26 thf(decl_71, type, powersetE: $o).
% 0.10/0.26 thf(decl_72, type, setunionI: $o).
% 0.10/0.26 thf(decl_73, type, setunionE: $o).
% 0.10/0.26 thf(decl_74, type, subPowSU: $o).
% 0.10/0.26 thf(decl_75, type, exuE2: $o).
% 0.10/0.26 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.10/0.26 thf(decl_77, type, uniqinunit: $o).
% 0.10/0.26 thf(decl_78, type, notinsingleton: $o).
% 0.10/0.26 thf(decl_79, type, eqinunit: $o).
% 0.10/0.26 thf(decl_80, type, singletonsswitch: $o).
% 0.10/0.26 thf(decl_81, type, upairsetE: $o).
% 0.10/0.26 thf(decl_82, type, epred1_0: $o).
% 0.10/0.26 thf(decl_83, type, esk1_2: $i > $i > $i).
% 0.10/0.26 thf(decl_84, type, esk2_2: $i > $i > $i).
% 0.10/0.26 thf(decl_85, type, esk3_2: $i > $i > $i).
% 0.10/0.26 thf(decl_86, type, esk4_1: $i > $i).
% 0.10/0.26 thf(decl_87, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.10/0.26 thf(decl_88, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.10/0.26 thf(decl_89, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.10/0.26 thf(decl_90, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.10/0.26 thf(decl_91, type, esk9_1: $i > $i).
% 0.10/0.26 thf(decl_92, type, esk10_2: ($i > $o) > $i > $i).
% 0.10/0.26 thf(decl_93, type, esk11_2: ($i > $o) > $i > $i).
% 0.10/0.26 thf(decl_94, type, esk12_1: ($i > $o) > $i).
% 0.10/0.26 thf(decl_95, type, esk13_2: ($i > $o) > $i > $i).
% 0.10/0.26 thf(decl_96, type, esk14_1: ($i > $o) > $i).
% 0.10/0.26 thf(decl_97, type, esk15_2: $i > $i > $i).
% 0.10/0.26 thf(decl_98, type, esk16_2: $i > $i > $i).
% 0.10/0.26 thf(decl_99, type, esk17_1: $i > $i).
% 0.10/0.26 thf(decl_100, type, esk18_1: $i > $i).
% 0.10/0.26 thf(decl_101, type, esk19_1: $i > $i).
% 0.10/0.26 thf(decl_102, type, esk20_2: $i > $i > $i).
% 0.10/0.26 thf(decl_103, type, esk21_3: $i > $i > $o > $i).
% 0.10/0.26 thf(decl_104, type, esk22_2: ($i > $o) > $i > $i).
% 0.10/0.26 thf(decl_105, type, esk23_1: ($i > $o) > $i).
% 0.10/0.26 thf(decl_106, type, esk24_1: $i > $i).
% 0.10/0.26 thf(decl_107, type, esk25_0: $i).
% 0.10/0.26 thf(decl_108, type, esk26_0: $i).
% 0.10/0.26 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', replAx)).
% 0.10/0.26 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', exu)).
% 0.10/0.26 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', descrp)).
% 0.10/0.26 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', exuE1)).
% 0.10/0.26 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', exuE3e)).
% 0.10/0.26 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', nonempty)).
% 0.10/0.26 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', nonemptyI)).
% 0.10/0.26 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', exuE2)).
% 0.10/0.26 thf(upairsetIL, 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)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', upairsetIL)).
% 0.10/0.26 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', dsetconstrI)).
% 0.10/0.26 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', dsetconstrEL)).
% 0.10/0.26 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', dsetconstrER)).
% 0.10/0.26 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', setbeta)).
% 0.10/0.26 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', nonemptyE1)).
% 0.10/0.26 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', nonemptyI1)).
% 0.10/0.26 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', setoftrueEq)).
% 0.10/0.26 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', nonemptyImpWitness)).
% 0.10/0.26 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', setextAx)).
% 0.10/0.26 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', emptysetAx)).
% 0.10/0.26 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', setadjoinAx)).
% 0.10/0.26 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', powersetAx)).
% 0.10/0.26 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', setunionAx)).
% 0.10/0.26 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', omega0Ax)).
% 0.10/0.26 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', omegaSAx)).
% 0.10/0.26 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', omegaIndAx)).
% 0.10/0.26 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/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', foundationAx)).
% 0.10/0.26 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', wellorderingAx)).
% 0.10/0.26 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', prop2setE)).
% 0.10/0.26 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', emptysetE)).
% 0.10/0.26 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', emptysetimpfalse)).
% 0.10/0.26 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', notinemptyset)).
% 0.10/0.26 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/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', setext)).
% 0.10/0.26 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', emptyI)).
% 0.10/0.26 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', noeltsimpempty)).
% 0.10/0.26 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', setadjoinIL)).
% 0.10/0.26 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', emptyinunitempty)).
% 0.10/0.26 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', setadjoinIR)).
% 0.10/0.26 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', setadjoinE)).
% 0.10/0.26 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', setadjoinOr)).
% 0.10/0.26 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', powersetI)).
% 0.10/0.26 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', emptyinPowerset)).
% 0.10/0.26 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', emptyInPowerset)).
% 0.10/0.26 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', powersetE)).
% 0.10/0.26 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', setunionI)).
% 0.10/0.26 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14)))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', setunionE)).
% 0.10/0.26 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', subPowSU)).
% 0.10/0.26 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', uniqinunit)).
% 0.10/0.26 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', notinsingleton)).
% 0.10/0.26 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', eqinunit)).
% 0.10/0.26 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', singletonsswitch)).
% 0.10/0.26 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X15:$i]:(((in @ X15 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X15)=(X2))|((X15)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.dVY1Udg5m9/E---3.1_1080264.p', upairsetE)).
% 0.10/0.26 thf(c_0_51, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.10/0.26 thf(c_0_52, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.10/0.26 thf(c_0_53, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.10/0.26 thf(c_0_54, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.10/0.26 thf(c_0_55, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.10/0.26 thf(c_0_56, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.10/0.26 thf(c_0_57, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.10/0.26 thf(c_0_58, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.10/0.26 thf(c_0_59, 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)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[upairsetIL])).
% 0.10/0.26 thf(c_0_60, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X149:$i]:(((((X6 @ X2 @ X149)))&(![X150:$i]:(((((X6 @ X2 @ X150)))=>(((X149)=(X150)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_51, c_0_52])).
% 0.10/0.26 thf(c_0_61, plain, ((descrp)=(![X1:$i > $o]:((((?[X151:$i]:(((((X1 @ X151)))&(![X152:$i]:(((((X1 @ X152)))=>(((X151)=(X152))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_53, c_0_52])).
% 0.10/0.26 thf(c_0_62, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.10/0.26 thf(c_0_63, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.10/0.26 thf(c_0_64, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.10/0.26 thf(c_0_65, plain, ((exuE1)=(![X1:$i > $o]:((((?[X153:$i]:(((((X1 @ X153)))&(![X154:$i]:(((((X1 @ X154)))=>(((X153)=(X154))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_54, c_0_52])).
% 0.10/0.27 thf(c_0_66, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X155:$i]:(((((X1 @ X155)))&(![X156:$i]:(((((X1 @ X156)))=>(((X155)=(X156))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_55, c_0_52])).
% 0.10/0.27 thf(c_0_67, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.10/0.27 thf(c_0_68, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_56])).
% 0.10/0.27 thf(c_0_69, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_57, c_0_56])).
% 0.10/0.27 thf(c_0_70, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_56])).
% 0.10/0.27 thf(c_0_71, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.10/0.27 thf(c_0_72, plain, ((exuE2)=(![X1:$i > $o]:((((?[X157:$i]:(((((X1 @ X157)))&(![X158:$i]:(((((X1 @ X158)))=>(((X157)=(X158))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_58, c_0_52])).
% 0.10/0.27 thf(c_0_73, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_56])).
% 0.10/0.27 thf(c_0_74, plain, ((epred1_0)<=>![X188:$i]:(?[X189:$i]:((((![X190:$i]:(((in @ X190 @ X189)=>![X191:$i]:(((in @ X191 @ X190)=>(in @ X191 @ X188)))))&![X192:$i, X193:$i]:((((in @ X192 @ X188)&(in @ X193 @ X188))=>(![X194:$i]:(((in @ X194 @ X189)=>((in @ X192 @ X194)<=>(in @ X193 @ X194))))=>((X192)=(X193))))))&![X195:$i, X196:$i]:((((in @ X195 @ X189)&(in @ X196 @ X189))=>(![X197:$i]:(((in @ X197 @ X195)=>(in @ X197 @ X196)))|![X198:$i]:(((in @ X198 @ X196)=>(in @ X198 @ X195)))))))&![X199:$i]:(((![X200:$i]:(((in @ X200 @ X199)=>(in @ X200 @ X188)))&?[X201:$i]:((in @ X201 @ X199)))=>?[X202:$i, X203:$i]:(((((in @ X202 @ X189)&(in @ X203 @ X199))&~(?[X204:$i]:(((in @ X204 @ X202)&(in @ X204 @ X199)))))&![X205:$i]:(((in @ X205 @ X189)=>(![X206:$i]:(((in @ X206 @ X205)=>(in @ X206 @ X202)))|(in @ X203 @ X205)))))))))))), introduced(definition)).
% 0.10/0.27 thf(c_0_75, negated_conjecture, ~((![X159:$i, X160:$i]:((![X161:$i]:(((in @ X161 @ X159)<=>(in @ X161 @ X160)))=>((X159)=(X160))))=>(![X162:$i]:(~(in @ X162 @ emptyset))=>(![X163:$i, X164:$i, X165:$i]:(((in @ X165 @ (setadjoin @ X163 @ X164))<=>(((X165)=(X163))|(in @ X165 @ X164))))=>(![X166:$i, X167:$i]:(((in @ X167 @ (powerset @ X166))<=>![X168:$i]:(((in @ X168 @ X167)=>(in @ X168 @ X166)))))=>(![X169:$i, X170:$i]:(((in @ X170 @ (setunion @ X169))<=>?[X171:$i]:(((in @ X170 @ X171)&(in @ X171 @ X169)))))=>((in @ emptyset @ omega)=>(![X172:$i]:(((in @ X172 @ omega)=>(in @ (setadjoin @ X172 @ X172) @ omega)))=>(![X173:$i]:((((in @ emptyset @ X173)&![X174:$i]:((((in @ X174 @ omega)&(in @ X174 @ X173))=>(in @ (setadjoin @ X174 @ X174) @ X173))))=>![X175:$i]:(((in @ X175 @ omega)=>(in @ X175 @ X173)))))=>(![X176:$i > $i > $o, X177:$i]:((![X178:$i]:(((in @ X178 @ X177)=>?[X179:$i]:(((X176 @ X178 @ X179)&![X180:$i]:(((X176 @ X178 @ X180)=>((X179)=(X180))))))))=>?[X181:$i]:(![X182:$i]:(((in @ X182 @ X181)<=>?[X183:$i]:(((in @ X183 @ X177)&(X176 @ X183 @ X182))))))))=>(![X184:$i]:((?[X185:$i]:((in @ X185 @ X184))=>?[X186:$i]:(((in @ X186 @ X184)&~(?[X187:$i]:(((in @ X187 @ X186)&(in @ X187 @ X184))))))))=>((epred1_0)=>(![X207:$i > $o]:((?[X208:$i]:(((X207 @ X208)&![X209:$i]:(((X207 @ X209)=>((X208)=(X209))))))=>(X207 @ (descr @ (^[Z0:$i]:(X207 @ Z0))))))=>(![X210:$i, X211:$i > $o, X212:$i]:(((in @ X212 @ X210)=>((X211 @ X212)=>(in @ X212 @ (dsetconstr @ X210 @ X211)))))=>(![X213:$i, X214:$i > $o, X215:$i]:(((in @ X215 @ (dsetconstr @ X213 @ X214))=>(in @ X215 @ X213)))=>(![X216:$i, X217:$i > $o, X218:$i]:(((in @ X218 @ (dsetconstr @ X216 @ X217))=>(X217 @ X218)))=>(![X219:$i > $o]:((?[X220:$i]:(((X219 @ X220)&![X221:$i]:(((X219 @ X221)=>((X220)=(X221))))))=>?[X222:$i]:(((X219 @ X222)&![X223:$i]:(((X219 @ X223)=>((X222)=(X223))))))))=>(![X224:$o, X225:$i]:(((in @ X225 @ (prop2set @ ((X224))))=>(X224)))=>(![X226:$i]:(((in @ X226 @ emptyset)=>![X227:$o]:((X227))))=>(![X228:$i]:(((in @ X228 @ emptyset)=>~($true)))=>(![X229:$i]:(~(in @ X229 @ emptyset))=>(![X230:$i > $o]:((?[X231:$i]:(((X230 @ X231)&![X232:$i]:(((X230 @ X232)=>((X231)=(X232))))))=>?[X233:$i]:((X230 @ X233))))=>(![X234:$i, X235:$i]:((![X236:$i]:(((in @ X236 @ X234)=>(in @ X236 @ X235)))=>(![X237:$i]:(((in @ X237 @ X235)=>(in @ X237 @ X234)))=>((X234)=(X235)))))=>(![X238:$i]:((![X239:$i]:(~(in @ X239 @ X238))=>((X238)=(emptyset))))=>(![X240:$i]:((![X241:$i]:(~(in @ X241 @ X240))=>((X240)=(emptyset))))=>(![X242:$i, X243:$i > $o, X244:$i]:(((in @ X244 @ X242)=>((in @ X244 @ (dsetconstr @ X242 @ X243))<=>(X243 @ X244))))=>(![X245:$i]:((((X245)!=(emptyset))=>?[X246:$i]:((in @ X246 @ X245))))=>(![X247:$i, X248:$i > $o, X249:$i]:(((in @ X249 @ X247)=>((X248 @ X249)=>((dsetconstr @ X247 @ X248)!=(emptyset)))))=>(![X250:$i]:((?[X251:$i]:((in @ X251 @ X250))=>((X250)!=(emptyset))))=>(![X252:$i, X253:$i]:((in @ X252 @ (setadjoin @ X252 @ X253)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X254:$i, X255:$i, X256:$i]:(((in @ X256 @ X255)=>(in @ X256 @ (setadjoin @ X254 @ X255))))=>(![X257:$i, X258:$i, X259:$i]:(((in @ X259 @ (setadjoin @ X257 @ X258))=>![X260:$o]:(((((X259)=(X257))=>(X260))=>(((in @ X259 @ X258)=>(X260))=>(X260))))))=>(![X261:$i, X262:$i, X263:$i]:(((in @ X263 @ (setadjoin @ X261 @ X262))=>(((X263)=(X261))|(in @ X263 @ X262))))=>(![X264:$i]:(((dsetconstr @ X264 @ (^[Z0:$i]:($true)))=(X264)))=>(![X265:$i, X266:$i]:((![X267:$i]:(((in @ X267 @ X266)=>(in @ X267 @ X265)))=>(in @ X266 @ (powerset @ X265))))=>(![X268:$i]:((in @ emptyset @ (powerset @ X268)))=>(![X269:$i]:((in @ emptyset @ (powerset @ X269)))=>(![X270:$i, X271:$i, X272:$i]:(((in @ X271 @ (powerset @ X270))=>((in @ X272 @ X271)=>(in @ X272 @ X270))))=>(![X273:$i, X274:$i, X275:$i]:(((in @ X274 @ X275)=>((in @ X275 @ X273)=>(in @ X274 @ (setunion @ X273)))))=>(![X276:$i, X277:$i]:(((in @ X277 @ (setunion @ X276))=>![X278:$o]:((![X279:$i]:(((in @ X277 @ X279)=>((in @ X279 @ X276)=>(X278))))=>(X278)))))=>(![X280:$i, X281:$i]:(((in @ X281 @ X280)=>(in @ X281 @ (powerset @ (setunion @ X280)))))=>(![X282:$i > $o]:((?[X283:$i]:(((X282 @ X283)&![X284:$i]:(((X282 @ X284)=>((X283)=(X284))))))=>?[X285:$i]:(![X286:$i]:(((X282 @ X286)<=>((X286)=(X285)))))))=>(![X287:$i]:((((X287)!=(emptyset))=>?[X288:$i]:(((in @ X288 @ X287)&$true))))=>(![X289:$i, X290:$i]:(((in @ X289 @ (setadjoin @ X290 @ emptyset))=>((X289)=(X290))))=>(![X291:$i, X292:$i]:((((X291)!=(X292))=>~(in @ X292 @ (setadjoin @ X291 @ emptyset))))=>(![X293:$i, X294:$i]:((((X293)=(X294))=>(in @ X293 @ (setadjoin @ X294 @ emptyset))))=>(![X295:$i, X296:$i]:(((in @ X295 @ (setadjoin @ X296 @ emptyset))=>(in @ X296 @ (setadjoin @ X295 @ emptyset))))=>(![X297:$i, X298:$i, X299:$i]:(((in @ X299 @ (setadjoin @ X297 @ (setadjoin @ X298 @ emptyset)))=>(((X299)=(X297))|((X299)=(X298)))))=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[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_59, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_60]), foundationAx]), wellorderingAx]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_66]), setext]), emptyI]), noeltsimpempty]), c_0_67]), c_0_68]), c_0_69]), c_0_70]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_71]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_72]), c_0_73]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE])])]), c_0_74])).
% 0.10/0.27 thf(c_0_76, negated_conjecture, ![X302:$i, X303:$i, X305:$i, X306:$i, X307:$i, X308:$i, X309:$i, X310:$i, X311:$i, X312:$i, X313:$i, X315:$i, X316:$i, X318:$i, X319:$i, X320:$i, X321:$i, X322:$i, X324:$i, X325:$i > $i > $o, X326:$i, X328:$i, X331:$i, X333:$i, X334:$i, X335:$i, X336:$i, X338:$i, X339:$i > $o, X340:$i, X342:$i, X343:$i > $o, X344:$i, X345:$i, X346:$i > $o, X347:$i, X348:$i, X349:$i > $o, X350:$i, X351:$i > $o, X352:$i, X355:$i, X356:$o, X357:$i, X358:$i, X359:$o, X360:$i, X361:$i, X362:$i > $o, X363:$i, X366:$i, X367:$i, X370:$i, X372:$i, X374:$i, X375:$i > $o, X376:$i, X377:$i, X379:$i, X380:$i > $o, X381:$i, X382:$i, X383:$i, X384:$i, X385:$i, X386:$i, X387:$i, X388:$i, X389:$i, X390:$i, X391:$i, X392:$o, X393:$i, X394:$i, X395:$i, X396:$i, X397:$i, X398:$i, X400:$i, X401:$i, X402:$i, X403:$i, X404:$i, X405:$i, X406:$i, X407:$i, X408:$i, X409:$i, X410:$o, X412:$i, X413:$i, X414:$i > $o, X415:$i, X418:$i, X419:$i, X420:$i, X422:$i, X423:$i, X424:$i, X425:$i, X426:$i, X427:$i, X428:$i, X429:$i, X430:$i, X431:$i, X432:$i]:((((~(in @ (esk1_2 @ X302 @ X303) @ X302)|~(in @ (esk1_2 @ X302 @ X303) @ X303)|((X302)=(X303)))&((in @ (esk1_2 @ X302 @ X303) @ X302)|(in @ (esk1_2 @ X302 @ X303) @ X303)|((X302)=(X303))))&(~(in @ X305 @ emptyset)&(((~(in @ X308 @ (setadjoin @ X306 @ X307))|(((X308)=(X306))|(in @ X308 @ X307)))&((((X308)!=(X306))|(in @ X308 @ (setadjoin @ X306 @ X307)))&(~(in @ X308 @ X307)|(in @ X308 @ (setadjoin @ X306 @ X307)))))&(((~(in @ X310 @ (powerset @ X309))|(~(in @ X311 @ X310)|(in @ X311 @ X309)))&(((in @ (esk2_2 @ X312 @ X313) @ X313)|(in @ X313 @ (powerset @ X312)))&(~(in @ (esk2_2 @ X312 @ X313) @ X312)|(in @ X313 @ (powerset @ X312)))))&(((((in @ X316 @ (esk3_2 @ X315 @ X316))|~(in @ X316 @ (setunion @ X315)))&((in @ (esk3_2 @ X315 @ X316) @ X315)|~(in @ X316 @ (setunion @ X315))))&(~(in @ X319 @ X320)|~(in @ X320 @ X318)|(in @ X319 @ (setunion @ X318))))&((in @ emptyset @ omega)&((~(in @ X321 @ omega)|(in @ (setadjoin @ X321 @ X321) @ omega))&(((((in @ (esk4_1 @ X322) @ omega)|~(in @ emptyset @ X322)|(~(in @ X324 @ omega)|(in @ X324 @ X322)))&((in @ (esk4_1 @ X322) @ X322)|~(in @ emptyset @ X322)|(~(in @ X324 @ omega)|(in @ X324 @ X322))))&(~(in @ (setadjoin @ (esk4_1 @ X322) @ (esk4_1 @ X322)) @ X322)|~(in @ emptyset @ X322)|(~(in @ X324 @ omega)|(in @ X324 @ X322))))&((((((in @ (esk8_3 @ X325 @ X326 @ X331) @ X326)|~(in @ X331 @ (esk7_2 @ X325 @ X326))|(in @ (esk5_2 @ X325 @ X326) @ X326))&((X325 @ (esk8_3 @ X325 @ X326 @ X331) @ X331)|~(in @ X331 @ (esk7_2 @ X325 @ X326))|(in @ (esk5_2 @ X325 @ X326) @ X326)))&(~(in @ X334 @ X326)|~(X325 @ X334 @ X333)|(in @ X333 @ (esk7_2 @ X325 @ X326))|(in @ (esk5_2 @ X325 @ X326) @ X326)))&(((((in @ (esk8_3 @ X325 @ X326 @ X331) @ X326)|~(in @ X331 @ (esk7_2 @ X325 @ X326))|((X325 @ (esk5_2 @ X325 @ X326) @ (esk6_3 @ X325 @ X326 @ X328))|~(X325 @ (esk5_2 @ X325 @ X326) @ X328)))&((X325 @ (esk8_3 @ X325 @ X326 @ X331) @ X331)|~(in @ X331 @ (esk7_2 @ X325 @ X326))|((X325 @ (esk5_2 @ X325 @ X326) @ (esk6_3 @ X325 @ X326 @ X328))|~(X325 @ (esk5_2 @ X325 @ X326) @ X328))))&(~(in @ X334 @ X326)|~(X325 @ X334 @ X333)|(in @ X333 @ (esk7_2 @ X325 @ X326))|((X325 @ (esk5_2 @ X325 @ X326) @ (esk6_3 @ X325 @ X326 @ X328))|~(X325 @ (esk5_2 @ X325 @ X326) @ X328))))&((((in @ (esk8_3 @ X325 @ X326 @ X331) @ X326)|~(in @ X331 @ (esk7_2 @ X325 @ X326))|(((X328)!=(esk6_3 @ X325 @ X326 @ X328))|~(X325 @ (esk5_2 @ X325 @ X326) @ X328)))&((X325 @ (esk8_3 @ X325 @ X326 @ X331) @ X331)|~(in @ X331 @ (esk7_2 @ X325 @ X326))|(((X328)!=(esk6_3 @ X325 @ X326 @ X328))|~(X325 @ (esk5_2 @ X325 @ X326) @ X328))))&(~(in @ X334 @ X326)|~(X325 @ X334 @ X333)|(in @ X333 @ (esk7_2 @ X325 @ X326))|(((X328)!=(esk6_3 @ X325 @ X326 @ X328))|~(X325 @ (esk5_2 @ X325 @ X326) @ X328))))))&((((in @ (esk9_1 @ X335) @ X335)|~(in @ X336 @ X335))&(~(in @ X338 @ (esk9_1 @ X335))|~(in @ X338 @ X335)|~(in @ X336 @ X335)))&((epred1_0)&((((X339 @ (esk10_2 @ X339 @ X340))|~(X339 @ X340)|(X339 @ (descr @ X339)))&(((X340)!=(esk10_2 @ X339 @ X340))|~(X339 @ X340)|(X339 @ (descr @ X339))))&((~(in @ X344 @ X342)|(~(X343 @ X344)|(in @ X344 @ (dsetconstr @ X342 @ X343))))&((~(in @ X347 @ (dsetconstr @ X345 @ X346))|(in @ X347 @ X345))&((~(in @ X350 @ (dsetconstr @ X348 @ X349))|(X349 @ X350))&(((((X351 @ (esk12_1 @ X351))|((X351 @ (esk11_2 @ X351 @ X352))|~(X351 @ X352)))&(~(X351 @ X355)|((esk12_1 @ X351)=(X355))|((X351 @ (esk11_2 @ X351 @ X352))|~(X351 @ X352))))&(((X351 @ (esk12_1 @ X351))|(((X352)!=(esk11_2 @ X351 @ X352))|~(X351 @ X352)))&(~(X351 @ X355)|((esk12_1 @ X351)=(X355))|(((X352)!=(esk11_2 @ X351 @ X352))|~(X351 @ X352)))))&((~(in @ X357 @ (prop2set @ ((X356))))|(X356))&((~(in @ X358 @ emptyset)|(X359))&((~(in @ X360 @ emptyset)|~($true))&(~(in @ X361 @ emptyset)&((((X362 @ (esk13_2 @ X362 @ X363))|~(X362 @ X363)|(X362 @ (esk14_1 @ X362)))&(((X363)!=(esk13_2 @ X362 @ X363))|~(X362 @ X363)|(X362 @ (esk14_1 @ X362))))&(((((in @ (esk16_2 @ X366 @ X367) @ X367)|((X366)=(X367))|(in @ (esk15_2 @ X366 @ X367) @ X366))&(~(in @ (esk16_2 @ X366 @ X367) @ X366)|((X366)=(X367))|(in @ (esk15_2 @ X366 @ X367) @ X366)))&(((in @ (esk16_2 @ X366 @ X367) @ X367)|((X366)=(X367))|~(in @ (esk15_2 @ X366 @ X367) @ X367))&(~(in @ (esk16_2 @ X366 @ X367) @ X366)|((X366)=(X367))|~(in @ (esk15_2 @ X366 @ X367) @ X367))))&(((in @ (esk17_1 @ X370) @ X370)|((X370)=(emptyset)))&(((in @ (esk18_1 @ X372) @ X372)|((X372)=(emptyset)))&(((~(in @ X376 @ (dsetconstr @ X374 @ X375))|(X375 @ X376)|~(in @ X376 @ X374))&(~(X375 @ X376)|(in @ X376 @ (dsetconstr @ X374 @ X375))|~(in @ X376 @ X374)))&((((X377)=(emptyset))|(in @ (esk19_1 @ X377) @ X377))&((~(in @ X381 @ X379)|(~(X380 @ X381)|((dsetconstr @ X379 @ X380)!=(emptyset))))&((~(in @ X383 @ X382)|((X382)!=(emptyset)))&((in @ X384 @ (setadjoin @ X384 @ X385))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X388 @ X387)|(in @ X388 @ (setadjoin @ X386 @ X387)))&(((((in @ X391 @ X390)|(X392)|((X391)=(X389))|~(in @ X391 @ (setadjoin @ X389 @ X390)))&(~(X392)|(X392)|((X391)=(X389))|~(in @ X391 @ (setadjoin @ X389 @ X390))))&(((in @ X391 @ X390)|(X392)|~(X392)|~(in @ X391 @ (setadjoin @ X389 @ X390)))&(~(X392)|(X392)|~(X392)|~(in @ X391 @ (setadjoin @ X389 @ X390)))))&((~(in @ X395 @ (setadjoin @ X393 @ X394))|(((X395)=(X393))|(in @ X395 @ X394)))&(((dsetconstr @ X396 @ (^[Z0:$i]:($true)))=(X396))&((((in @ (esk20_2 @ X397 @ X398) @ X398)|(in @ X398 @ (powerset @ X397)))&(~(in @ (esk20_2 @ X397 @ X398) @ X397)|(in @ X398 @ (powerset @ X397))))&((in @ emptyset @ (powerset @ X400))&((in @ emptyset @ (powerset @ X401))&((~(in @ X403 @ (powerset @ X402))|(~(in @ X404 @ X403)|(in @ X404 @ X402)))&((~(in @ X406 @ X407)|(~(in @ X407 @ X405)|(in @ X406 @ (setunion @ X405))))&((((in @ X409 @ (esk21_3 @ X408 @ X409 @ X410))|(X410)|~(in @ X409 @ (setunion @ X408)))&(((in @ (esk21_3 @ X408 @ X409 @ X410) @ X408)|(X410)|~(in @ X409 @ (setunion @ X408)))&(~(X410)|(X410)|~(in @ X409 @ (setunion @ X408)))))&((~(in @ X413 @ X412)|(in @ X413 @ (powerset @ (setunion @ X412))))&((((~(X414 @ X418)|((X418)=(esk23_1 @ X414))|((X414 @ (esk22_2 @ X414 @ X415))|~(X414 @ X415)))&(((X419)!=(esk23_1 @ X414))|(X414 @ X419)|((X414 @ (esk22_2 @ X414 @ X415))|~(X414 @ X415))))&((~(X414 @ X418)|((X418)=(esk23_1 @ X414))|(((X415)!=(esk22_2 @ X414 @ X415))|~(X414 @ X415)))&(((X419)!=(esk23_1 @ X414))|(X414 @ X419)|(((X415)!=(esk22_2 @ X414 @ X415))|~(X414 @ X415)))))&((((in @ (esk24_1 @ X420) @ X420)|((X420)=(emptyset)))&(($true)|((X420)=(emptyset))))&((~(in @ X422 @ (setadjoin @ X423 @ emptyset))|((X422)=(X423)))&((((X424)=(X425))|~(in @ X425 @ (setadjoin @ X424 @ emptyset)))&((((X426)!=(X427))|(in @ X426 @ (setadjoin @ X427 @ emptyset)))&((~(in @ X428 @ (setadjoin @ X429 @ emptyset))|(in @ X429 @ (setadjoin @ X428 @ emptyset)))&((~(in @ X432 @ (setadjoin @ X430 @ (setadjoin @ X431 @ emptyset)))|(((X432)=(X430))|((X432)=(X431))))&~(in @ esk25_0 @ (setadjoin @ esk25_0 @ (setadjoin @ esk26_0 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))), 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_75])])])])])])])).
% 0.10/0.27 thf(c_0_77, negated_conjecture, ~((in @ esk25_0 @ (setadjoin @ esk25_0 @ (setadjoin @ esk26_0 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 0.10/0.27 thf(c_0_78, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_76])).
% 0.10/0.27 thf(c_0_79, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77, c_0_78])]), ['proof']).
% 0.10/0.27 % SZS output end CNFRefutation
% 0.10/0.27 % Parsed axioms : 111
% 0.10/0.27 % Removed by relevancy pruning/SinE : 0
% 0.10/0.27 % Initial clauses : 161
% 0.10/0.27 % Removed in clause preprocessing : 64
% 0.10/0.27 % Initial clauses in saturation : 97
% 0.10/0.27 % Processed clauses : 27
% 0.10/0.27 % ...of these trivial : 1
% 0.10/0.27 % ...subsumed : 5
% 0.10/0.27 % ...remaining for further processing : 20
% 0.10/0.27 % Other redundant clauses eliminated : 1
% 0.10/0.27 % Clauses deleted for lack of memory : 0
% 0.10/0.27 % Backward-subsumed : 0
% 0.10/0.27 % Backward-rewritten : 2
% 0.10/0.27 % Generated clauses : 16
% 0.10/0.27 % ...of the previous two non-redundant : 14
% 0.10/0.27 % ...aggressively subsumed : 0
% 0.10/0.27 % Contextual simplify-reflections : 0
% 0.10/0.27 % Paramodulations : 15
% 0.10/0.27 % Factorizations : 0
% 0.10/0.27 % NegExts : 0
% 0.10/0.27 % Equation resolutions : 1
% 0.10/0.27 % Disequality decompositions : 0
% 0.10/0.27 % Total rewrite steps : 7
% 0.10/0.27 % ...of those cached : 0
% 0.10/0.27 % Propositional unsat checks : 0
% 0.10/0.27 % Propositional check models : 0
% 0.10/0.27 % Propositional check unsatisfiable : 0
% 0.10/0.27 % Propositional clauses : 0
% 0.10/0.27 % Propositional clauses after purity: 0
% 0.10/0.27 % Propositional unsat core size : 0
% 0.10/0.27 % Propositional preprocessing time : 0.000
% 0.10/0.27 % Propositional encoding time : 0.000
% 0.10/0.27 % Propositional solver time : 0.000
% 0.10/0.27 % Success case prop preproc time : 0.000
% 0.10/0.27 % Success case prop encoding time : 0.000
% 0.10/0.27 % Success case prop solver time : 0.000
% 0.10/0.27 % Current number of processed clauses : 17
% 0.10/0.27 % Positive orientable unit clauses : 9
% 0.10/0.27 % Positive unorientable unit clauses: 0
% 0.10/0.27 % Negative unit clauses : 2
% 0.10/0.27 % Non-unit-clauses : 6
% 0.10/0.27 % Current number of unprocessed clauses: 84
% 0.10/0.27 % ...number of literals in the above : 269
% 0.10/0.27 % Current number of archived formulas : 0
% 0.10/0.27 % Current number of archived clauses : 2
% 0.10/0.27 % Clause-clause subsumption calls (NU) : 12
% 0.10/0.27 % Rec. Clause-clause subsumption calls : 12
% 0.10/0.27 % Non-unit clause-clause subsumptions : 0
% 0.10/0.27 % Unit Clause-clause subsumption calls : 5
% 0.10/0.27 % Rewrite failures with RHS unbound : 0
% 0.10/0.27 % BW rewrite match attempts : 2
% 0.10/0.27 % BW rewrite match successes : 2
% 0.10/0.27 % Condensation attempts : 0
% 0.10/0.27 % Condensation successes : 0
% 0.10/0.27 % Termbank termtop insertions : 13485
% 0.10/0.27 % Search garbage collected termcells : 5049
% 0.10/0.27
% 0.10/0.27 % -------------------------------------------------
% 0.10/0.27 % User time : 0.010 s
% 0.10/0.27 % System time : 0.007 s
% 0.10/0.27 % Total time : 0.017 s
% 0.10/0.27 % Maximum resident set size: 5028 pages
% 0.10/0.27
% 0.10/0.27 % -------------------------------------------------
% 0.10/0.27 % User time : 0.033 s
% 0.10/0.27 % System time : 0.020 s
% 0.10/0.27 % Total time : 0.053 s
% 0.10/0.27 % Maximum resident set size: 4608 pages
% 0.10/0.27 % E exiting
%------------------------------------------------------------------------------