%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU540^1 : 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 : n018.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 08:24:26 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU540^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:51:11 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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.vU7R8sN6SF/E---3.1_99646.p
% 0.22/0.30 % Version: 3.5.1-ho
% 0.22/0.30 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.30 % Starting sh5l with 300s (1) cores
% 0.22/0.30 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.30 % Starting new_bool_2 with 300s (1) cores
% 0.22/0.30 % new_ho_10 with pid 99659 completed with status 0
% 0.22/0.30 % Result found by new_ho_10
% 0.22/0.30 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.30 % No SInE strategy applied
% 0.22/0.30 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.22/0.30 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.30 % Starting SubtermCWHack with 151s (1) cores
% 0.22/0.30 % Starting new_ho_10 with 901s (1) cores
% 0.22/0.30 % Starting sh5l with 151s (1) cores
% 0.22/0.30 % Starting new_bool_1 with 151s (1) cores
% 0.22/0.30 % Starting new_bool_2 with 146s (1) cores
% 0.22/0.30 % SubtermCWHack with pid 99665 completed with status 0
% 0.22/0.30 % Result found by SubtermCWHack
% 0.22/0.30 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.30 % No SInE strategy applied
% 0.22/0.30 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.22/0.30 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.30 % Starting SubtermCWHack with 151s (1) cores
% 0.22/0.30 % Preprocessing time : 0.002 s
% 0.22/0.30
% 0.22/0.30 % Proof found!
% 0.22/0.30 % SZS status Theorem
% 0.22/0.30 % SZS output start CNFRefutation
% 0.22/0.30 thf(decl_23, type, in: $i > $i > $o).
% 0.22/0.30 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.22/0.30 thf(decl_25, type, setextAx: $o).
% 0.22/0.30 thf(decl_26, type, emptyset: $i).
% 0.22/0.30 thf(decl_27, type, emptysetAx: $o).
% 0.22/0.30 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.22/0.30 thf(decl_29, type, setadjoinAx: $o).
% 0.22/0.30 thf(decl_30, type, powerset: $i > $i).
% 0.22/0.30 thf(decl_31, type, powersetAx: $o).
% 0.22/0.30 thf(decl_32, type, setunion: $i > $i).
% 0.22/0.30 thf(decl_33, type, setunionAx: $o).
% 0.22/0.30 thf(decl_34, type, omega: $i).
% 0.22/0.30 thf(decl_35, type, omega0Ax: $o).
% 0.22/0.30 thf(decl_36, type, omegaSAx: $o).
% 0.22/0.30 thf(decl_37, type, omegaIndAx: $o).
% 0.22/0.30 thf(decl_38, type, replAx: $o).
% 0.22/0.30 thf(decl_39, type, foundationAx: $o).
% 0.22/0.30 thf(decl_40, type, wellorderingAx: $o).
% 0.22/0.30 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.22/0.30 thf(decl_42, type, descrp: $o).
% 0.22/0.30 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.22/0.30 thf(decl_44, type, dsetconstrI: $o).
% 0.22/0.30 thf(decl_45, type, dsetconstrEL: $o).
% 0.22/0.30 thf(decl_46, type, dsetconstrER: $o).
% 0.22/0.30 thf(decl_47, type, exuE1: $o).
% 0.22/0.30 thf(decl_48, type, prop2set: $o > $i).
% 0.22/0.30 thf(decl_49, type, prop2setE: $o).
% 0.22/0.30 thf(decl_50, type, emptysetE: $o).
% 0.22/0.30 thf(decl_51, type, emptysetimpfalse: $o).
% 0.22/0.30 thf(decl_52, type, notinemptyset: $o).
% 0.22/0.30 thf(decl_53, type, exuE3e: $o).
% 0.22/0.30 thf(decl_54, type, setext: $o).
% 0.22/0.30 thf(decl_55, type, emptyI: $o).
% 0.22/0.30 thf(decl_56, type, noeltsimpempty: $o).
% 0.22/0.30 thf(decl_57, type, setbeta: $o).
% 0.22/0.30 thf(decl_58, type, nonempty: $i > $o).
% 0.22/0.30 thf(decl_59, type, nonemptyE1: $o).
% 0.22/0.30 thf(decl_60, type, nonemptyI: $o).
% 0.22/0.30 thf(decl_61, type, nonemptyI1: $o).
% 0.22/0.30 thf(decl_62, type, setadjoinIL: $o).
% 0.22/0.30 thf(decl_63, type, emptyinunitempty: $o).
% 0.22/0.30 thf(decl_64, type, setadjoinIR: $o).
% 0.22/0.30 thf(decl_65, type, setadjoinE: $o).
% 0.22/0.30 thf(decl_66, type, setadjoinOr: $o).
% 0.22/0.30 thf(decl_67, type, setoftrueEq: $o).
% 0.22/0.30 thf(decl_68, type, powersetI: $o).
% 0.22/0.30 thf(decl_69, type, emptyinPowerset: $o).
% 0.22/0.30 thf(decl_70, type, emptyInPowerset: $o).
% 0.22/0.30 thf(decl_71, type, powersetE: $o).
% 0.22/0.30 thf(decl_72, type, setunionI: $o).
% 0.22/0.30 thf(decl_73, type, setunionE: $o).
% 0.22/0.30 thf(decl_74, type, subPowSU: $o).
% 0.22/0.30 thf(decl_75, type, exuE2: $o).
% 0.22/0.30 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.22/0.30 thf(decl_77, type, uniqinunit: $o).
% 0.22/0.30 thf(decl_78, type, notinsingleton: $o).
% 0.22/0.30 thf(decl_79, type, eqinunit: $o).
% 0.22/0.30 thf(decl_80, type, singletonsswitch: $o).
% 0.22/0.30 thf(decl_81, type, upairsetE: $o).
% 0.22/0.30 thf(decl_82, type, upairsetIL: $o).
% 0.22/0.30 thf(decl_83, type, upairsetIR: $o).
% 0.22/0.30 thf(decl_84, type, emptyE1: $o).
% 0.22/0.30 thf(decl_85, type, vacuousDall: $o).
% 0.22/0.30 thf(decl_86, type, quantDeMorgan1: $o).
% 0.22/0.30 thf(decl_87, type, quantDeMorgan2: $o).
% 0.22/0.30 thf(decl_88, type, quantDeMorgan3: $o).
% 0.22/0.30 thf(decl_89, type, quantDeMorgan4: $o).
% 0.22/0.30 thf(decl_90, type, epred1_0: $o).
% 0.22/0.30 thf(decl_91, type, esk1_2: $i > $i > $i).
% 0.22/0.30 thf(decl_92, type, esk2_2: $i > $i > $i).
% 0.22/0.30 thf(decl_93, type, esk3_2: $i > $i > $i).
% 0.22/0.30 thf(decl_94, type, esk4_1: $i > $i).
% 0.22/0.30 thf(decl_95, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.22/0.30 thf(decl_96, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.30 thf(decl_97, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.22/0.30 thf(decl_98, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.22/0.30 thf(decl_99, type, esk9_1: $i > $i).
% 0.22/0.30 thf(decl_100, type, esk10_2: ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_101, type, esk11_2: ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_102, type, esk12_1: ($i > $o) > $i).
% 0.22/0.30 thf(decl_103, type, esk13_2: ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_104, type, esk14_1: ($i > $o) > $i).
% 0.22/0.30 thf(decl_105, type, esk15_2: $i > $i > $i).
% 0.22/0.30 thf(decl_106, type, esk16_2: $i > $i > $i).
% 0.22/0.30 thf(decl_107, type, esk17_1: $i > $i).
% 0.22/0.30 thf(decl_108, type, esk18_1: $i > $i).
% 0.22/0.30 thf(decl_109, type, esk19_1: $i > $i).
% 0.22/0.30 thf(decl_110, type, esk20_2: $i > $i > $i).
% 0.22/0.30 thf(decl_111, type, esk21_3: $i > $i > $o > $i).
% 0.22/0.30 thf(decl_112, type, esk22_2: ($i > $o) > $i > $i).
% 0.22/0.30 thf(decl_113, type, esk23_1: ($i > $o) > $i).
% 0.22/0.30 thf(decl_114, type, esk24_1: $i > $i).
% 0.22/0.30 thf(decl_115, type, esk25_2: $i > ($i > $o) > $i).
% 0.22/0.30 thf(decl_116, type, esk26_2: $i > ($i > $o) > $i).
% 0.22/0.30 thf(decl_117, type, esk27_2: $i > ($i > $o) > $i).
% 0.22/0.30 thf(decl_118, type, esk28_2: $i > ($i > $o) > $i).
% 0.22/0.30 thf(decl_119, type, epred2_0: $o).
% 0.22/0.30 thf(decl_125, type, epred3_1: $o > $i > $o).
% 0.22/0.30 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', replAx)).
% 0.22/0.30 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', exu)).
% 0.22/0.30 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', descrp)).
% 0.22/0.30 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', exuE1)).
% 0.22/0.30 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', exuE3e)).
% 0.22/0.30 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', nonempty)).
% 0.22/0.30 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', nonemptyI)).
% 0.22/0.30 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', exuE2)).
% 0.22/0.30 thf(prop2setI, 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)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>![X16:$o]:(((X16)=>(in @ emptyset @ (prop2set @ ((X16)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', prop2setI)).
% 0.22/0.30 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', dsetconstrI)).
% 0.22/0.30 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', dsetconstrEL)).
% 0.22/0.30 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', dsetconstrER)).
% 0.22/0.30 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', setbeta)).
% 0.22/0.30 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', nonemptyE1)).
% 0.22/0.30 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', nonemptyI1)).
% 0.22/0.30 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', setoftrueEq)).
% 0.22/0.30 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', nonemptyImpWitness)).
% 0.22/0.30 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', emptyE1)).
% 0.22/0.30 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', setextAx)).
% 0.22/0.30 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', emptysetAx)).
% 0.22/0.30 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', setadjoinAx)).
% 0.22/0.30 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', powersetAx)).
% 0.22/0.30 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', setunionAx)).
% 0.22/0.30 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', omega0Ax)).
% 0.22/0.30 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', omegaSAx)).
% 0.22/0.30 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', omegaIndAx)).
% 0.22/0.30 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', foundationAx)).
% 0.22/0.30 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.vU7R8sN6SF/E---3.1_99646.p', wellorderingAx)).
% 0.22/0.30 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', prop2setE)).
% 0.22/0.30 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', emptysetE)).
% 0.22/0.30 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', emptysetimpfalse)).
% 0.22/0.30 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', notinemptyset)).
% 0.22/0.30 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', setext)).
% 0.22/0.30 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', emptyI)).
% 0.22/0.30 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', noeltsimpempty)).
% 0.22/0.30 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', setadjoinIL)).
% 0.22/0.30 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', emptyinunitempty)).
% 0.22/0.30 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', setadjoinIR)).
% 0.22/0.30 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.vU7R8sN6SF/E---3.1_99646.p', setadjoinE)).
% 0.22/0.30 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', setadjoinOr)).
% 0.22/0.30 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', powersetI)).
% 0.22/0.30 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', emptyinPowerset)).
% 0.22/0.30 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', emptyInPowerset)).
% 0.22/0.30 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', powersetE)).
% 0.22/0.30 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', setunionI)).
% 0.22/0.30 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.vU7R8sN6SF/E---3.1_99646.p', setunionE)).
% 0.22/0.30 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', subPowSU)).
% 0.22/0.30 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', uniqinunit)).
% 0.22/0.30 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', notinsingleton)).
% 0.22/0.30 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', eqinunit)).
% 0.22/0.30 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', singletonsswitch)).
% 0.22/0.30 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X15:$i]:(((in @ X15 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X15)=(X2))|((X15)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', upairsetE)).
% 0.22/0.30 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', upairsetIL)).
% 0.22/0.30 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', upairsetIR)).
% 0.22/0.30 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', vacuousDall)).
% 0.22/0.30 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', quantDeMorgan1)).
% 0.22/0.30 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', quantDeMorgan2)).
% 0.22/0.30 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', quantDeMorgan3)).
% 0.22/0.30 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', quantDeMorgan4)).
% 0.22/0.30 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox2/tmp/tmp.vU7R8sN6SF/E---3.1_99646.p', prop2set)).
% 0.22/0.30 thf(c_0_60, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.22/0.30 thf(c_0_61, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.22/0.30 thf(c_0_62, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.22/0.30 thf(c_0_63, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.22/0.30 thf(c_0_64, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.22/0.30 thf(c_0_65, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.22/0.30 thf(c_0_66, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.22/0.30 thf(c_0_67, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.22/0.30 thf(c_0_68, 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)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>![X16:$o]:(((X16)=>(in @ emptyset @ (prop2set @ ((X16))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[prop2setI])).
% 0.22/0.30 thf(c_0_69, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X174:$i]:(((((X6 @ X2 @ X174)))&(![X175:$i]:(((((X6 @ X2 @ X175)))=>(((X174)=(X175)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_60, c_0_61])).
% 0.22/0.30 thf(c_0_70, plain, ((descrp)=(![X1:$i > $o]:((((?[X176:$i]:(((((X1 @ X176)))&(![X177:$i]:(((((X1 @ X177)))=>(((X176)=(X177))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_62, c_0_61])).
% 0.22/0.30 thf(c_0_71, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.22/0.30 thf(c_0_72, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.22/0.30 thf(c_0_73, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.22/0.30 thf(c_0_74, plain, ((exuE1)=(![X1:$i > $o]:((((?[X178:$i]:(((((X1 @ X178)))&(![X179:$i]:(((((X1 @ X179)))=>(((X178)=(X179))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_63, c_0_61])).
% 0.22/0.30 thf(c_0_75, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X180:$i]:(((((X1 @ X180)))&(![X181:$i]:(((((X1 @ X181)))=>(((X180)=(X181))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_64, c_0_61])).
% 0.22/0.30 thf(c_0_76, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.22/0.30 thf(c_0_77, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_65])).
% 0.22/0.30 thf(c_0_78, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_66, c_0_65])).
% 0.22/0.30 thf(c_0_79, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_65])).
% 0.22/0.30 thf(c_0_80, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.22/0.30 thf(c_0_81, plain, ((exuE2)=(![X1:$i > $o]:((((?[X182:$i]:(((((X1 @ X182)))&(![X183:$i]:(((((X1 @ X183)))=>(((X182)=(X183))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_67, c_0_61])).
% 0.22/0.30 thf(c_0_82, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_65])).
% 0.22/0.30 thf(c_0_83, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 0.22/0.30 thf(c_0_84, plain, ((epred1_0)<=>![X213:$i]:(?[X214:$i]:((((![X215:$i]:(((in @ X215 @ X214)=>![X216:$i]:(((in @ X216 @ X215)=>(in @ X216 @ X213)))))&![X217:$i, X218:$i]:((((in @ X217 @ X213)&(in @ X218 @ X213))=>(![X219:$i]:(((in @ X219 @ X214)=>((in @ X217 @ X219)<=>(in @ X218 @ X219))))=>((X217)=(X218))))))&![X220:$i, X221:$i]:((((in @ X220 @ X214)&(in @ X221 @ X214))=>(![X222:$i]:(((in @ X222 @ X220)=>(in @ X222 @ X221)))|![X223:$i]:(((in @ X223 @ X221)=>(in @ X223 @ X220)))))))&![X224:$i]:(((![X225:$i]:(((in @ X225 @ X224)=>(in @ X225 @ X213)))&?[X226:$i]:((in @ X226 @ X224)))=>?[X227:$i, X228:$i]:(((((in @ X227 @ X214)&(in @ X228 @ X224))&~(?[X229:$i]:(((in @ X229 @ X227)&(in @ X229 @ X224)))))&![X230:$i]:(((in @ X230 @ X214)=>(![X231:$i]:(((in @ X231 @ X230)=>(in @ X231 @ X227)))|(in @ X228 @ X230)))))))))))), introduced(definition)).
% 0.22/0.30 thf(c_0_85, negated_conjecture, ~((![X184:$i, X185:$i]:((![X186:$i]:(((in @ X186 @ X184)<=>(in @ X186 @ X185)))=>((X184)=(X185))))=>(![X187:$i]:(~(in @ X187 @ emptyset))=>(![X188:$i, X189:$i, X190:$i]:(((in @ X190 @ (setadjoin @ X188 @ X189))<=>(((X190)=(X188))|(in @ X190 @ X189))))=>(![X191:$i, X192:$i]:(((in @ X192 @ (powerset @ X191))<=>![X193:$i]:(((in @ X193 @ X192)=>(in @ X193 @ X191)))))=>(![X194:$i, X195:$i]:(((in @ X195 @ (setunion @ X194))<=>?[X196:$i]:(((in @ X195 @ X196)&(in @ X196 @ X194)))))=>((in @ emptyset @ omega)=>(![X197:$i]:(((in @ X197 @ omega)=>(in @ (setadjoin @ X197 @ X197) @ omega)))=>(![X198:$i]:((((in @ emptyset @ X198)&![X199:$i]:((((in @ X199 @ omega)&(in @ X199 @ X198))=>(in @ (setadjoin @ X199 @ X199) @ X198))))=>![X200:$i]:(((in @ X200 @ omega)=>(in @ X200 @ X198)))))=>(![X201:$i > $i > $o, X202:$i]:((![X203:$i]:(((in @ X203 @ X202)=>?[X204:$i]:(((X201 @ X203 @ X204)&![X205:$i]:(((X201 @ X203 @ X205)=>((X204)=(X205))))))))=>?[X206:$i]:(![X207:$i]:(((in @ X207 @ X206)<=>?[X208:$i]:(((in @ X208 @ X202)&(X201 @ X208 @ X207))))))))=>(![X209:$i]:((?[X210:$i]:((in @ X210 @ X209))=>?[X211:$i]:(((in @ X211 @ X209)&~(?[X212:$i]:(((in @ X212 @ X211)&(in @ X212 @ X209))))))))=>((epred1_0)=>(![X232:$i > $o]:((?[X233:$i]:(((X232 @ X233)&![X234:$i]:(((X232 @ X234)=>((X233)=(X234))))))=>(X232 @ (descr @ (^[Z0:$i]:(X232 @ Z0))))))=>(![X235:$i, X236:$i > $o, X237:$i]:(((in @ X237 @ X235)=>((X236 @ X237)=>(in @ X237 @ (dsetconstr @ X235 @ X236)))))=>(![X238:$i, X239:$i > $o, X240:$i]:(((in @ X240 @ (dsetconstr @ X238 @ X239))=>(in @ X240 @ X238)))=>(![X241:$i, X242:$i > $o, X243:$i]:(((in @ X243 @ (dsetconstr @ X241 @ X242))=>(X242 @ X243)))=>(![X244:$i > $o]:((?[X245:$i]:(((X244 @ X245)&![X246:$i]:(((X244 @ X246)=>((X245)=(X246))))))=>?[X247:$i]:(((X244 @ X247)&![X248:$i]:(((X244 @ X248)=>((X247)=(X248))))))))=>(![X249:$o, X250:$i]:(((in @ X250 @ (prop2set @ ((X249))))=>(X249)))=>(![X251:$i]:(((in @ X251 @ emptyset)=>![X252:$o]:((X252))))=>(![X253:$i]:(((in @ X253 @ emptyset)=>~($true)))=>(![X254:$i]:(~(in @ X254 @ emptyset))=>(![X255:$i > $o]:((?[X256:$i]:(((X255 @ X256)&![X257:$i]:(((X255 @ X257)=>((X256)=(X257))))))=>?[X258:$i]:((X255 @ X258))))=>(![X259:$i, X260:$i]:((![X261:$i]:(((in @ X261 @ X259)=>(in @ X261 @ X260)))=>(![X262:$i]:(((in @ X262 @ X260)=>(in @ X262 @ X259)))=>((X259)=(X260)))))=>(![X263:$i]:((![X264:$i]:(~(in @ X264 @ X263))=>((X263)=(emptyset))))=>(![X265:$i]:((![X266:$i]:(~(in @ X266 @ X265))=>((X265)=(emptyset))))=>(![X267:$i, X268:$i > $o, X269:$i]:(((in @ X269 @ X267)=>((in @ X269 @ (dsetconstr @ X267 @ X268))<=>(X268 @ X269))))=>(![X270:$i]:((((X270)!=(emptyset))=>?[X271:$i]:((in @ X271 @ X270))))=>(![X272:$i, X273:$i > $o, X274:$i]:(((in @ X274 @ X272)=>((X273 @ X274)=>((dsetconstr @ X272 @ X273)!=(emptyset)))))=>(![X275:$i]:((?[X276:$i]:((in @ X276 @ X275))=>((X275)!=(emptyset))))=>(![X277:$i, X278:$i]:((in @ X277 @ (setadjoin @ X277 @ X278)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X279:$i, X280:$i, X281:$i]:(((in @ X281 @ X280)=>(in @ X281 @ (setadjoin @ X279 @ X280))))=>(![X282:$i, X283:$i, X284:$i]:(((in @ X284 @ (setadjoin @ X282 @ X283))=>![X285:$o]:(((((X284)=(X282))=>(X285))=>(((in @ X284 @ X283)=>(X285))=>(X285))))))=>(![X286:$i, X287:$i, X288:$i]:(((in @ X288 @ (setadjoin @ X286 @ X287))=>(((X288)=(X286))|(in @ X288 @ X287))))=>(![X289:$i]:(((dsetconstr @ X289 @ (^[Z0:$i]:($true)))=(X289)))=>(![X290:$i, X291:$i]:((![X292:$i]:(((in @ X292 @ X291)=>(in @ X292 @ X290)))=>(in @ X291 @ (powerset @ X290))))=>(![X293:$i]:((in @ emptyset @ (powerset @ X293)))=>(![X294:$i]:((in @ emptyset @ (powerset @ X294)))=>(![X295:$i, X296:$i, X297:$i]:(((in @ X296 @ (powerset @ X295))=>((in @ X297 @ X296)=>(in @ X297 @ X295))))=>(![X298:$i, X299:$i, X300:$i]:(((in @ X299 @ X300)=>((in @ X300 @ X298)=>(in @ X299 @ (setunion @ X298)))))=>(![X301:$i, X302:$i]:(((in @ X302 @ (setunion @ X301))=>![X303:$o]:((![X304:$i]:(((in @ X302 @ X304)=>((in @ X304 @ X301)=>(X303))))=>(X303)))))=>(![X305:$i, X306:$i]:(((in @ X306 @ X305)=>(in @ X306 @ (powerset @ (setunion @ X305)))))=>(![X307:$i > $o]:((?[X308:$i]:(((X307 @ X308)&![X309:$i]:(((X307 @ X309)=>((X308)=(X309))))))=>?[X310:$i]:(![X311:$i]:(((X307 @ X311)<=>((X311)=(X310)))))))=>(![X312:$i]:((((X312)!=(emptyset))=>?[X313:$i]:(((in @ X313 @ X312)&$true))))=>(![X314:$i, X315:$i]:(((in @ X314 @ (setadjoin @ X315 @ emptyset))=>((X314)=(X315))))=>(![X316:$i, X317:$i]:((((X316)!=(X317))=>~(in @ X317 @ (setadjoin @ X316 @ emptyset))))=>(![X318:$i, X319:$i]:((((X318)=(X319))=>(in @ X318 @ (setadjoin @ X319 @ emptyset))))=>(![X320:$i, X321:$i]:(((in @ X320 @ (setadjoin @ X321 @ emptyset))=>(in @ X321 @ (setadjoin @ X320 @ emptyset))))=>(![X322:$i, X323:$i, X324:$i]:(((in @ X324 @ (setadjoin @ X322 @ (setadjoin @ X323 @ emptyset)))=>(((X324)=(X322))|((X324)=(X323)))))=>(![X325:$i, X326:$i]:((in @ X325 @ (setadjoin @ X325 @ (setadjoin @ X326 @ emptyset))))=>(![X327:$i, X328:$i]:((in @ X328 @ (setadjoin @ X327 @ (setadjoin @ X328 @ emptyset))))=>(![X329:$i, X330:$i > $o]:((?[X331:$i]:(((in @ X331 @ X329)&(X330 @ X331)))=>(((dsetconstr @ X329 @ X330)=(emptyset))=>~($true))))=>(![X332:$i > $o, X333:$i]:(((in @ X333 @ emptyset)=>(X332 @ X333)))=>(![X334:$i, X335:$i > $o]:((~(![X336:$i]:(((in @ X336 @ X334)=>(X335 @ X336))))=>?[X337:$i]:(((in @ X337 @ X334)&~((X335 @ X337))))))=>(![X338:$i, X339:$i > $o]:((![X340:$i]:(((in @ X340 @ X338)=>~((X339 @ X340))))=>~(?[X341:$i]:(((in @ X341 @ X338)&(X339 @ X341))))))=>(![X342:$i, X343:$i > $o]:((~(?[X344:$i]:(((in @ X344 @ X342)&(X343 @ X344))))=>![X345:$i]:(((in @ X345 @ X342)=>~((X343 @ X345))))))=>(![X346:$i, X347:$i > $o]:((?[X348:$i]:(((in @ X348 @ X346)&~((X347 @ X348))))=>~(![X349:$i]:(((in @ X349 @ X346)=>(X347 @ X349))))))=>![X16:$o]:(((X16)=>(in @ emptyset @ (prop2set @ ((X16))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[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_68, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_69]), foundationAx]), wellorderingAx]), c_0_70]), c_0_71]), c_0_72]), c_0_73]), c_0_74]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_75]), setext]), emptyI]), noeltsimpempty]), c_0_76]), c_0_77]), c_0_78]), c_0_79]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_80]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_81]), c_0_82]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_83]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4])])]), c_0_84])).
% 0.22/0.30 thf(c_0_86, plain, ![X350:$o]:(((prop2set @ ((X350)))=(dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X350)))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[prop2set])])).
% 0.22/0.30 thf(c_0_87, negated_conjecture, ![X352:$i, X353:$i, X355:$i, X356:$i, X357:$i, X358:$i, X359:$i, X360:$i, X361:$i, X362:$i, X363:$i, X365:$i, X366:$i, X368:$i, X369:$i, X370:$i, X371:$i, X372:$i, X374:$i, X375:$i > $i > $o, X376:$i, X378:$i, X381:$i, X383:$i, X384:$i, X385:$i, X386:$i, X388:$i, X389:$i > $o, X390:$i, X392:$i, X393:$i > $o, X394:$i, X395:$i, X396:$i > $o, X397:$i, X398:$i, X399:$i > $o, X400:$i, X401:$i > $o, X402:$i, X405:$i, X406:$o, X407:$i, X408:$i, X409:$o, X410:$i, X411:$i, X412:$i > $o, X413:$i, X416:$i, X417:$i, X420:$i, X422:$i, X424:$i, X425:$i > $o, X426:$i, X427:$i, X429:$i, X430:$i > $o, X431:$i, X432:$i, X433:$i, X434:$i, X435:$i, X436:$i, X437:$i, X438:$i, X439:$i, X440:$i, X441:$i, X442:$o, X443:$i, X444:$i, X445:$i, X446:$i, X447:$i, X448:$i, X450:$i, X451:$i, X452:$i, X453:$i, X454:$i, X455:$i, X456:$i, X457:$i, X458:$i, X459:$i, X460:$o, X462:$i, X463:$i, X464:$i > $o, X465:$i, X468:$i, X469:$i, X470:$i, X472:$i, X473:$i, X474:$i, X475:$i, X476:$i, X477:$i, X478:$i, X479:$i, X480:$i, X481:$i, X482:$i, X483:$i, X484:$i, X485:$i, X486:$i, X487:$i, X488:$i > $o, X489:$i, X490:$i > $o, X491:$i, X492:$i, X493:$i > $o, X494:$i, X496:$i, X497:$i > $o, X499:$i, X500:$i, X501:$i > $o, X503:$i, X504:$i, X505:$i > $o, X506:$i]:((((~(in @ (esk1_2 @ X352 @ X353) @ X352)|~(in @ (esk1_2 @ X352 @ X353) @ X353)|((X352)=(X353)))&((in @ (esk1_2 @ X352 @ X353) @ X352)|(in @ (esk1_2 @ X352 @ X353) @ X353)|((X352)=(X353))))&(~(in @ X355 @ emptyset)&(((~(in @ X358 @ (setadjoin @ X356 @ X357))|(((X358)=(X356))|(in @ X358 @ X357)))&((((X358)!=(X356))|(in @ X358 @ (setadjoin @ X356 @ X357)))&(~(in @ X358 @ X357)|(in @ X358 @ (setadjoin @ X356 @ X357)))))&(((~(in @ X360 @ (powerset @ X359))|(~(in @ X361 @ X360)|(in @ X361 @ X359)))&(((in @ (esk2_2 @ X362 @ X363) @ X363)|(in @ X363 @ (powerset @ X362)))&(~(in @ (esk2_2 @ X362 @ X363) @ X362)|(in @ X363 @ (powerset @ X362)))))&(((((in @ X366 @ (esk3_2 @ X365 @ X366))|~(in @ X366 @ (setunion @ X365)))&((in @ (esk3_2 @ X365 @ X366) @ X365)|~(in @ X366 @ (setunion @ X365))))&(~(in @ X369 @ X370)|~(in @ X370 @ X368)|(in @ X369 @ (setunion @ X368))))&((in @ emptyset @ omega)&((~(in @ X371 @ omega)|(in @ (setadjoin @ X371 @ X371) @ omega))&(((((in @ (esk4_1 @ X372) @ omega)|~(in @ emptyset @ X372)|(~(in @ X374 @ omega)|(in @ X374 @ X372)))&((in @ (esk4_1 @ X372) @ X372)|~(in @ emptyset @ X372)|(~(in @ X374 @ omega)|(in @ X374 @ X372))))&(~(in @ (setadjoin @ (esk4_1 @ X372) @ (esk4_1 @ X372)) @ X372)|~(in @ emptyset @ X372)|(~(in @ X374 @ omega)|(in @ X374 @ X372))))&((((((in @ (esk8_3 @ X375 @ X376 @ X381) @ X376)|~(in @ X381 @ (esk7_2 @ X375 @ X376))|(in @ (esk5_2 @ X375 @ X376) @ X376))&((X375 @ (esk8_3 @ X375 @ X376 @ X381) @ X381)|~(in @ X381 @ (esk7_2 @ X375 @ X376))|(in @ (esk5_2 @ X375 @ X376) @ X376)))&(~(in @ X384 @ X376)|~(X375 @ X384 @ X383)|(in @ X383 @ (esk7_2 @ X375 @ X376))|(in @ (esk5_2 @ X375 @ X376) @ X376)))&(((((in @ (esk8_3 @ X375 @ X376 @ X381) @ X376)|~(in @ X381 @ (esk7_2 @ X375 @ X376))|((X375 @ (esk5_2 @ X375 @ X376) @ (esk6_3 @ X375 @ X376 @ X378))|~(X375 @ (esk5_2 @ X375 @ X376) @ X378)))&((X375 @ (esk8_3 @ X375 @ X376 @ X381) @ X381)|~(in @ X381 @ (esk7_2 @ X375 @ X376))|((X375 @ (esk5_2 @ X375 @ X376) @ (esk6_3 @ X375 @ X376 @ X378))|~(X375 @ (esk5_2 @ X375 @ X376) @ X378))))&(~(in @ X384 @ X376)|~(X375 @ X384 @ X383)|(in @ X383 @ (esk7_2 @ X375 @ X376))|((X375 @ (esk5_2 @ X375 @ X376) @ (esk6_3 @ X375 @ X376 @ X378))|~(X375 @ (esk5_2 @ X375 @ X376) @ X378))))&((((in @ (esk8_3 @ X375 @ X376 @ X381) @ X376)|~(in @ X381 @ (esk7_2 @ X375 @ X376))|(((X378)!=(esk6_3 @ X375 @ X376 @ X378))|~(X375 @ (esk5_2 @ X375 @ X376) @ X378)))&((X375 @ (esk8_3 @ X375 @ X376 @ X381) @ X381)|~(in @ X381 @ (esk7_2 @ X375 @ X376))|(((X378)!=(esk6_3 @ X375 @ X376 @ X378))|~(X375 @ (esk5_2 @ X375 @ X376) @ X378))))&(~(in @ X384 @ X376)|~(X375 @ X384 @ X383)|(in @ X383 @ (esk7_2 @ X375 @ X376))|(((X378)!=(esk6_3 @ X375 @ X376 @ X378))|~(X375 @ (esk5_2 @ X375 @ X376) @ X378))))))&((((in @ (esk9_1 @ X385) @ X385)|~(in @ X386 @ X385))&(~(in @ X388 @ (esk9_1 @ X385))|~(in @ X388 @ X385)|~(in @ X386 @ X385)))&((epred1_0)&((((X389 @ (esk10_2 @ X389 @ X390))|~(X389 @ X390)|(X389 @ (descr @ X389)))&(((X390)!=(esk10_2 @ X389 @ X390))|~(X389 @ X390)|(X389 @ (descr @ X389))))&((~(in @ X394 @ X392)|(~(X393 @ X394)|(in @ X394 @ (dsetconstr @ X392 @ X393))))&((~(in @ X397 @ (dsetconstr @ X395 @ X396))|(in @ X397 @ X395))&((~(in @ X400 @ (dsetconstr @ X398 @ X399))|(X399 @ X400))&(((((X401 @ (esk12_1 @ X401))|((X401 @ (esk11_2 @ X401 @ X402))|~(X401 @ X402)))&(~(X401 @ X405)|((esk12_1 @ X401)=(X405))|((X401 @ (esk11_2 @ X401 @ X402))|~(X401 @ X402))))&(((X401 @ (esk12_1 @ X401))|(((X402)!=(esk11_2 @ X401 @ X402))|~(X401 @ X402)))&(~(X401 @ X405)|((esk12_1 @ X401)=(X405))|(((X402)!=(esk11_2 @ X401 @ X402))|~(X401 @ X402)))))&((~(in @ X407 @ (prop2set @ ((X406))))|(X406))&((~(in @ X408 @ emptyset)|(X409))&((~(in @ X410 @ emptyset)|~($true))&(~(in @ X411 @ emptyset)&((((X412 @ (esk13_2 @ X412 @ X413))|~(X412 @ X413)|(X412 @ (esk14_1 @ X412)))&(((X413)!=(esk13_2 @ X412 @ X413))|~(X412 @ X413)|(X412 @ (esk14_1 @ X412))))&(((((in @ (esk16_2 @ X416 @ X417) @ X417)|((X416)=(X417))|(in @ (esk15_2 @ X416 @ X417) @ X416))&(~(in @ (esk16_2 @ X416 @ X417) @ X416)|((X416)=(X417))|(in @ (esk15_2 @ X416 @ X417) @ X416)))&(((in @ (esk16_2 @ X416 @ X417) @ X417)|((X416)=(X417))|~(in @ (esk15_2 @ X416 @ X417) @ X417))&(~(in @ (esk16_2 @ X416 @ X417) @ X416)|((X416)=(X417))|~(in @ (esk15_2 @ X416 @ X417) @ X417))))&(((in @ (esk17_1 @ X420) @ X420)|((X420)=(emptyset)))&(((in @ (esk18_1 @ X422) @ X422)|((X422)=(emptyset)))&(((~(in @ X426 @ (dsetconstr @ X424 @ X425))|(X425 @ X426)|~(in @ X426 @ X424))&(~(X425 @ X426)|(in @ X426 @ (dsetconstr @ X424 @ X425))|~(in @ X426 @ X424)))&((((X427)=(emptyset))|(in @ (esk19_1 @ X427) @ X427))&((~(in @ X431 @ X429)|(~(X430 @ X431)|((dsetconstr @ X429 @ X430)!=(emptyset))))&((~(in @ X433 @ X432)|((X432)!=(emptyset)))&((in @ X434 @ (setadjoin @ X434 @ X435))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X438 @ X437)|(in @ X438 @ (setadjoin @ X436 @ X437)))&(((((in @ X441 @ X440)|(X442)|((X441)=(X439))|~(in @ X441 @ (setadjoin @ X439 @ X440)))&(~(X442)|(X442)|((X441)=(X439))|~(in @ X441 @ (setadjoin @ X439 @ X440))))&(((in @ X441 @ X440)|(X442)|~(X442)|~(in @ X441 @ (setadjoin @ X439 @ X440)))&(~(X442)|(X442)|~(X442)|~(in @ X441 @ (setadjoin @ X439 @ X440)))))&((~(in @ X445 @ (setadjoin @ X443 @ X444))|(((X445)=(X443))|(in @ X445 @ X444)))&(((dsetconstr @ X446 @ (^[Z0:$i]:($true)))=(X446))&((((in @ (esk20_2 @ X447 @ X448) @ X448)|(in @ X448 @ (powerset @ X447)))&(~(in @ (esk20_2 @ X447 @ X448) @ X447)|(in @ X448 @ (powerset @ X447))))&((in @ emptyset @ (powerset @ X450))&((in @ emptyset @ (powerset @ X451))&((~(in @ X453 @ (powerset @ X452))|(~(in @ X454 @ X453)|(in @ X454 @ X452)))&((~(in @ X456 @ X457)|(~(in @ X457 @ X455)|(in @ X456 @ (setunion @ X455))))&((((in @ X459 @ (esk21_3 @ X458 @ X459 @ X460))|(X460)|~(in @ X459 @ (setunion @ X458)))&(((in @ (esk21_3 @ X458 @ X459 @ X460) @ X458)|(X460)|~(in @ X459 @ (setunion @ X458)))&(~(X460)|(X460)|~(in @ X459 @ (setunion @ X458)))))&((~(in @ X463 @ X462)|(in @ X463 @ (powerset @ (setunion @ X462))))&((((~(X464 @ X468)|((X468)=(esk23_1 @ X464))|((X464 @ (esk22_2 @ X464 @ X465))|~(X464 @ X465)))&(((X469)!=(esk23_1 @ X464))|(X464 @ X469)|((X464 @ (esk22_2 @ X464 @ X465))|~(X464 @ X465))))&((~(X464 @ X468)|((X468)=(esk23_1 @ X464))|(((X465)!=(esk22_2 @ X464 @ X465))|~(X464 @ X465)))&(((X469)!=(esk23_1 @ X464))|(X464 @ X469)|(((X465)!=(esk22_2 @ X464 @ X465))|~(X464 @ X465)))))&((((in @ (esk24_1 @ X470) @ X470)|((X470)=(emptyset)))&(($true)|((X470)=(emptyset))))&((~(in @ X472 @ (setadjoin @ X473 @ emptyset))|((X472)=(X473)))&((((X474)=(X475))|~(in @ X475 @ (setadjoin @ X474 @ emptyset)))&((((X476)!=(X477))|(in @ X476 @ (setadjoin @ X477 @ emptyset)))&((~(in @ X478 @ (setadjoin @ X479 @ emptyset))|(in @ X479 @ (setadjoin @ X478 @ emptyset)))&((~(in @ X482 @ (setadjoin @ X480 @ (setadjoin @ X481 @ emptyset)))|(((X482)=(X480))|((X482)=(X481))))&((in @ X483 @ (setadjoin @ X483 @ (setadjoin @ X484 @ emptyset)))&((in @ X486 @ (setadjoin @ X485 @ (setadjoin @ X486 @ emptyset)))&((~(in @ X489 @ X487)|~(X488 @ X489)|(((dsetconstr @ X487 @ X488)!=(emptyset))|~($true)))&((~(in @ X491 @ emptyset)|(X490 @ X491))&((((in @ (esk25_2 @ X492 @ X493) @ X492)|(~(in @ X494 @ X492)|(X493 @ X494)))&(~(X493 @ (esk25_2 @ X492 @ X493))|(~(in @ X494 @ X492)|(X493 @ X494))))&((((in @ (esk26_2 @ X496 @ X497) @ X496)|(~(in @ X499 @ X496)|~(X497 @ X499)))&((X497 @ (esk26_2 @ X496 @ X497))|(~(in @ X499 @ X496)|~(X497 @ X499))))&((((in @ (esk27_2 @ X500 @ X501) @ X500)|(~(in @ X503 @ X500)|~(X501 @ X503)))&((X501 @ (esk27_2 @ X500 @ X501))|(~(in @ X503 @ X500)|~(X501 @ X503))))&((((in @ (esk28_2 @ X504 @ X505) @ X504)|(~(in @ X506 @ X504)|(X505 @ X506)))&(~(X505 @ (esk28_2 @ X504 @ X505))|(~(in @ X506 @ X504)|(X505 @ X506))))&((epred2_0)&(((~(epred2_0)|(epred2_0))&(~(in @ emptyset @ (prop2set @ $false))|(epred2_0)))&((~(epred2_0)|~(in @ emptyset @ (prop2set @ $true)))&(~(in @ emptyset @ (prop2set @ $false))|~(in @ emptyset @ (prop2set @ $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_85])])])])])])])])).
% 0.22/0.30 thf(c_0_88, plain, ![X528:$i, X10:$o]:(((epred3_1 @ X10 @ X528)<=>(X10))), introduced(definition)).
% 0.22/0.30 thf(c_0_89, plain, ![X351:$o]:(((prop2set @ ((X351)))=(dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X351)))))), inference(variable_rename,[status(thm)],[c_0_86])).
% 0.22/0.30 thf(c_0_90, negated_conjecture, (~((epred2_0))|~((in @ emptyset @ (prop2set @ (($true)))))), inference(split_conjunct,[status(thm)],[c_0_87])).
% 0.22/0.30 thf(c_0_91, negated_conjecture, (epred2_0), inference(split_conjunct,[status(thm)],[c_0_87])).
% 0.22/0.30 thf(c_0_92, negated_conjecture, ![X2:$i]:(((dsetconstr @ X2 @ (epred3_1 @ (($true))))=(X2))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_87]), c_0_88])).
% 0.22/0.30 thf(c_0_93, plain, ![X10:$o]:(((prop2set @ ((X10)))=(dsetconstr @ (powerset @ emptyset) @ (epred3_1 @ ((X10)))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_89]), c_0_88])).
% 0.22/0.30 thf(c_0_94, negated_conjecture, ~((in @ emptyset @ (prop2set @ (($true))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90, c_0_91])])).
% 0.22/0.30 thf(c_0_95, negated_conjecture, ((prop2set @ (($true)))=(powerset @ emptyset)), inference(spm,[status(thm)],[c_0_92, c_0_93])).
% 0.22/0.30 thf(c_0_96, negated_conjecture, ![X2:$i]:((in @ emptyset @ (powerset @ X2))), inference(split_conjunct,[status(thm)],[c_0_87])).
% 0.22/0.30 thf(c_0_97, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94, c_0_95]), c_0_96])]), ['proof']).
% 0.22/0.30 % SZS output end CNFRefutation
% 0.22/0.30 % Parsed axioms : 127
% 0.22/0.30 % Removed by relevancy pruning/SinE : 0
% 0.22/0.30 % Initial clauses : 185
% 0.22/0.30 % Removed in clause preprocessing : 73
% 0.22/0.30 % Initial clauses in saturation : 112
% 0.22/0.30 % Processed clauses : 34
% 0.22/0.30 % ...of these trivial : 3
% 0.22/0.30 % ...subsumed : 6
% 0.22/0.30 % ...remaining for further processing : 25
% 0.22/0.30 % Other redundant clauses eliminated : 1
% 0.22/0.30 % Clauses deleted for lack of memory : 0
% 0.22/0.30 % Backward-subsumed : 0
% 0.22/0.30 % Backward-rewritten : 3
% 0.22/0.30 % Generated clauses : 20
% 0.22/0.30 % ...of the previous two non-redundant : 18
% 0.22/0.30 % ...aggressively subsumed : 0
% 0.22/0.30 % Contextual simplify-reflections : 0
% 0.22/0.30 % Paramodulations : 19
% 0.22/0.30 % Factorizations : 0
% 0.22/0.30 % NegExts : 0
% 0.22/0.30 % Equation resolutions : 1
% 0.22/0.30 % Disequality decompositions : 0
% 0.22/0.30 % Total rewrite steps : 11
% 0.22/0.30 % ...of those cached : 1
% 0.22/0.30 % Propositional unsat checks : 0
% 0.22/0.30 % Propositional check models : 0
% 0.22/0.30 % Propositional check unsatisfiable : 0
% 0.22/0.30 % Propositional clauses : 0
% 0.22/0.30 % Propositional clauses after purity: 0
% 0.22/0.30 % Propositional unsat core size : 0
% 0.22/0.30 % Propositional preprocessing time : 0.000
% 0.22/0.30 % Propositional encoding time : 0.000
% 0.22/0.30 % Propositional solver time : 0.000
% 0.22/0.30 % Success case prop preproc time : 0.000
% 0.22/0.30 % Success case prop encoding time : 0.000
% 0.22/0.30 % Success case prop solver time : 0.000
% 0.22/0.30 % Current number of processed clauses : 21
% 0.22/0.30 % Positive orientable unit clauses : 13
% 0.22/0.30 % Positive unorientable unit clauses: 0
% 0.22/0.30 % Negative unit clauses : 2
% 0.22/0.30 % Non-unit-clauses : 6
% 0.22/0.30 % Current number of unprocessed clauses: 95
% 0.22/0.30 % ...number of literals in the above : 300
% 0.22/0.30 % Current number of archived formulas : 0
% 0.22/0.30 % Current number of archived clauses : 3
% 0.22/0.30 % Clause-clause subsumption calls (NU) : 12
% 0.22/0.30 % Rec. Clause-clause subsumption calls : 12
% 0.22/0.30 % Non-unit clause-clause subsumptions : 0
% 0.22/0.30 % Unit Clause-clause subsumption calls : 0
% 0.22/0.30 % Rewrite failures with RHS unbound : 0
% 0.22/0.30 % BW rewrite match attempts : 3
% 0.22/0.30 % BW rewrite match successes : 3
% 0.22/0.30 % Condensation attempts : 0
% 0.22/0.30 % Condensation successes : 0
% 0.22/0.30 % Termbank termtop insertions : 15861
% 0.22/0.30 % Search garbage collected termcells : 6286
% 0.22/0.30
% 0.22/0.30 % -------------------------------------------------
% 0.22/0.30 % User time : 0.017 s
% 0.22/0.30 % System time : 0.007 s
% 0.22/0.30 % Total time : 0.024 s
% 0.22/0.30 % Maximum resident set size: 5044 pages
% 0.22/0.30
% 0.22/0.30 % -------------------------------------------------
% 0.22/0.30 % User time : 0.035 s
% 0.22/0.30 % System time : 0.020 s
% 0.22/0.30 % Total time : 0.055 s
% 0.22/0.30 % Maximum resident set size: 4864 pages
% 0.22/0.30 % E exiting
%------------------------------------------------------------------------------