%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU541^1 : 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:26:38 AM UTC 2026
% Result : Theorem 0.25s 0.28s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU541^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n016.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:54:04 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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.wylVP6Tkmr/E---3.1_384939.p
% 0.25/0.28 % Version: 3.5.1-ho
% 0.25/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.25/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.28 % Starting sh5l with 300s (1) cores
% 0.25/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.25/0.28 % new_ho_10 with pid 384952 completed with status 0
% 0.25/0.28 % Result found by new_ho_10
% 0.25/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.25/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.28 % No SInE strategy applied
% 0.25/0.28 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.25/0.28 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.28 % Starting SubtermCWHack with 151s (1) cores
% 0.25/0.28 % Starting new_ho_10 with 901s (1) cores
% 0.25/0.28 % Starting sh5l with 151s (1) cores
% 0.25/0.28 % Starting new_bool_1 with 151s (1) cores
% 0.25/0.28 % Starting new_bool_2 with 146s (1) cores
% 0.25/0.28 % new_ho_10 with pid 384957 completed with status 0
% 0.25/0.28 % Result found by new_ho_10
% 0.25/0.28 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.25/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.28 % No SInE strategy applied
% 0.25/0.28 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.25/0.28 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.28 % Starting SubtermCWHack with 151s (1) cores
% 0.25/0.28 % Starting new_ho_10 with 901s (1) cores
% 0.25/0.28 % Preprocessing time : 0.002 s
% 0.25/0.28 % Presaturation interreduction done
% 0.25/0.28
% 0.25/0.28 % Proof found!
% 0.25/0.28 % SZS status Theorem
% 0.25/0.28 % SZS output start CNFRefutation
% 0.25/0.28 thf(decl_23, type, in: $i > $i > $o).
% 0.25/0.28 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.25/0.28 thf(decl_25, type, setextAx: $o).
% 0.25/0.28 thf(decl_26, type, emptyset: $i).
% 0.25/0.28 thf(decl_27, type, emptysetAx: $o).
% 0.25/0.28 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.25/0.28 thf(decl_29, type, setadjoinAx: $o).
% 0.25/0.28 thf(decl_30, type, powerset: $i > $i).
% 0.25/0.28 thf(decl_31, type, powersetAx: $o).
% 0.25/0.28 thf(decl_32, type, setunion: $i > $i).
% 0.25/0.28 thf(decl_33, type, setunionAx: $o).
% 0.25/0.28 thf(decl_34, type, omega: $i).
% 0.25/0.28 thf(decl_35, type, omega0Ax: $o).
% 0.25/0.28 thf(decl_36, type, omegaSAx: $o).
% 0.25/0.28 thf(decl_37, type, omegaIndAx: $o).
% 0.25/0.28 thf(decl_38, type, replAx: $o).
% 0.25/0.28 thf(decl_39, type, foundationAx: $o).
% 0.25/0.28 thf(decl_40, type, wellorderingAx: $o).
% 0.25/0.28 thf(decl_41, type, descr: ($i > $o) > $i).
% 0.25/0.28 thf(decl_42, type, descrp: $o).
% 0.25/0.28 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.25/0.28 thf(decl_44, type, dsetconstrI: $o).
% 0.25/0.28 thf(decl_45, type, dsetconstrEL: $o).
% 0.25/0.28 thf(decl_46, type, dsetconstrER: $o).
% 0.25/0.28 thf(decl_47, type, exuE1: $o).
% 0.25/0.28 thf(decl_48, type, prop2set: $o > $i).
% 0.25/0.28 thf(decl_49, type, prop2setE: $o).
% 0.25/0.28 thf(decl_50, type, emptysetE: $o).
% 0.25/0.28 thf(decl_51, type, emptysetimpfalse: $o).
% 0.25/0.28 thf(decl_52, type, notinemptyset: $o).
% 0.25/0.28 thf(decl_53, type, exuE3e: $o).
% 0.25/0.28 thf(decl_54, type, setext: $o).
% 0.25/0.28 thf(decl_55, type, emptyI: $o).
% 0.25/0.28 thf(decl_56, type, noeltsimpempty: $o).
% 0.25/0.28 thf(decl_57, type, setbeta: $o).
% 0.25/0.28 thf(decl_58, type, nonempty: $i > $o).
% 0.25/0.28 thf(decl_59, type, nonemptyE1: $o).
% 0.25/0.28 thf(decl_60, type, nonemptyI: $o).
% 0.25/0.28 thf(decl_61, type, nonemptyI1: $o).
% 0.25/0.28 thf(decl_62, type, setadjoinIL: $o).
% 0.25/0.28 thf(decl_63, type, emptyinunitempty: $o).
% 0.25/0.28 thf(decl_64, type, setadjoinIR: $o).
% 0.25/0.28 thf(decl_65, type, setadjoinE: $o).
% 0.25/0.28 thf(decl_66, type, setadjoinOr: $o).
% 0.25/0.28 thf(decl_67, type, setoftrueEq: $o).
% 0.25/0.28 thf(decl_68, type, powersetI: $o).
% 0.25/0.28 thf(decl_69, type, emptyinPowerset: $o).
% 0.25/0.28 thf(decl_70, type, emptyInPowerset: $o).
% 0.25/0.28 thf(decl_71, type, powersetE: $o).
% 0.25/0.28 thf(decl_72, type, setunionI: $o).
% 0.25/0.28 thf(decl_73, type, setunionE: $o).
% 0.25/0.28 thf(decl_74, type, subPowSU: $o).
% 0.25/0.28 thf(decl_75, type, exuE2: $o).
% 0.25/0.28 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.25/0.28 thf(decl_77, type, uniqinunit: $o).
% 0.25/0.28 thf(decl_78, type, notinsingleton: $o).
% 0.25/0.28 thf(decl_79, type, eqinunit: $o).
% 0.25/0.28 thf(decl_80, type, singletonsswitch: $o).
% 0.25/0.28 thf(decl_81, type, upairsetE: $o).
% 0.25/0.28 thf(decl_82, type, upairsetIL: $o).
% 0.25/0.28 thf(decl_83, type, upairsetIR: $o).
% 0.25/0.28 thf(decl_84, type, emptyE1: $o).
% 0.25/0.28 thf(decl_85, type, vacuousDall: $o).
% 0.25/0.28 thf(decl_86, type, quantDeMorgan1: $o).
% 0.25/0.28 thf(decl_87, type, quantDeMorgan2: $o).
% 0.25/0.28 thf(decl_88, type, quantDeMorgan3: $o).
% 0.25/0.28 thf(decl_89, type, quantDeMorgan4: $o).
% 0.25/0.28 thf(decl_90, type, prop2setI: $o).
% 0.25/0.28 thf(decl_91, type, set2prop: $i > $o).
% 0.25/0.28 thf(decl_92, type, epred1_0: $o).
% 0.25/0.28 thf(decl_93, type, esk1_2: $i > $i > $i).
% 0.25/0.28 thf(decl_94, type, esk2_2: $i > $i > $i).
% 0.25/0.28 thf(decl_95, type, esk3_2: $i > $i > $i).
% 0.25/0.28 thf(decl_96, type, esk4_1: $i > $i).
% 0.25/0.28 thf(decl_97, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.25/0.28 thf(decl_98, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.25/0.28 thf(decl_99, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.25/0.28 thf(decl_100, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.25/0.28 thf(decl_101, type, esk9_1: $i > $i).
% 0.25/0.28 thf(decl_102, type, esk10_2: ($i > $o) > $i > $i).
% 0.25/0.28 thf(decl_103, type, esk11_2: ($i > $o) > $i > $i).
% 0.25/0.28 thf(decl_104, type, esk12_1: ($i > $o) > $i).
% 0.25/0.28 thf(decl_105, type, esk13_2: ($i > $o) > $i > $i).
% 0.25/0.28 thf(decl_106, type, esk14_1: ($i > $o) > $i).
% 0.25/0.28 thf(decl_107, type, esk15_2: $i > $i > $i).
% 0.25/0.28 thf(decl_108, type, esk16_2: $i > $i > $i).
% 0.25/0.28 thf(decl_109, type, esk17_1: $i > $i).
% 0.25/0.28 thf(decl_110, type, esk18_1: $i > $i).
% 0.25/0.28 thf(decl_111, type, esk19_1: $i > $i).
% 0.25/0.28 thf(decl_112, type, esk20_2: $i > $i > $i).
% 0.25/0.28 thf(decl_113, type, esk21_3: $i > $i > $o > $i).
% 0.25/0.28 thf(decl_114, type, esk22_2: ($i > $o) > $i > $i).
% 0.25/0.28 thf(decl_115, type, esk23_1: ($i > $o) > $i).
% 0.25/0.28 thf(decl_116, type, esk24_1: $i > $i).
% 0.25/0.28 thf(decl_117, type, esk25_2: $i > ($i > $o) > $i).
% 0.25/0.28 thf(decl_118, type, esk26_2: $i > ($i > $o) > $i).
% 0.25/0.28 thf(decl_119, type, esk27_2: $i > ($i > $o) > $i).
% 0.25/0.28 thf(decl_120, type, esk28_2: $i > ($i > $o) > $i).
% 0.25/0.28 thf(decl_121, type, epred2_0: $o).
% 0.25/0.28 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', replAx)).
% 0.25/0.28 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', exu)).
% 0.25/0.28 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', descrp)).
% 0.25/0.28 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', exuE1)).
% 0.25/0.28 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', exuE3e)).
% 0.25/0.28 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', nonempty)).
% 0.25/0.28 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', nonemptyI)).
% 0.25/0.28 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', exuE2)).
% 0.25/0.28 thf(prop2set2propI, 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)=>((prop2setI)=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', prop2set2propI)).
% 0.25/0.28 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', dsetconstrI)).
% 0.25/0.28 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', dsetconstrEL)).
% 0.25/0.28 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', dsetconstrER)).
% 0.25/0.28 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', setbeta)).
% 0.25/0.28 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', nonemptyE1)).
% 0.25/0.28 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', nonemptyI1)).
% 0.25/0.28 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', setoftrueEq)).
% 0.25/0.28 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', nonemptyImpWitness)).
% 0.25/0.28 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.wylVP6Tkmr/E---3.1_384939.p', emptyE1)).
% 0.25/0.28 thf(set2prop, axiom, ((set2prop)=(^[X4:$i]:((in @ emptyset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', set2prop)).
% 0.25/0.28 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', setextAx)).
% 0.25/0.28 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', emptysetAx)).
% 0.25/0.28 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', setadjoinAx)).
% 0.25/0.28 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', powersetAx)).
% 0.25/0.28 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', setunionAx)).
% 0.25/0.28 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', omega0Ax)).
% 0.25/0.28 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', omegaSAx)).
% 0.25/0.28 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.wylVP6Tkmr/E---3.1_384939.p', omegaIndAx)).
% 0.25/0.28 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.wylVP6Tkmr/E---3.1_384939.p', foundationAx)).
% 0.25/0.28 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', wellorderingAx)).
% 0.25/0.28 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', prop2setE)).
% 0.25/0.28 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', emptysetE)).
% 0.25/0.28 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', emptysetimpfalse)).
% 0.25/0.28 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', notinemptyset)).
% 0.25/0.28 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.wylVP6Tkmr/E---3.1_384939.p', setext)).
% 0.25/0.28 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', emptyI)).
% 0.25/0.28 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', noeltsimpempty)).
% 0.25/0.28 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', setadjoinIL)).
% 0.25/0.28 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', emptyinunitempty)).
% 0.25/0.28 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', setadjoinIR)).
% 0.25/0.28 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', setadjoinE)).
% 0.25/0.28 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', setadjoinOr)).
% 0.25/0.28 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', powersetI)).
% 0.25/0.28 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', emptyinPowerset)).
% 0.25/0.28 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', emptyInPowerset)).
% 0.25/0.28 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', powersetE)).
% 0.25/0.28 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', setunionI)).
% 0.25/0.28 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', setunionE)).
% 0.25/0.28 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', subPowSU)).
% 0.25/0.28 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', uniqinunit)).
% 0.25/0.28 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', notinsingleton)).
% 0.25/0.28 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', eqinunit)).
% 0.25/0.28 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', singletonsswitch)).
% 0.25/0.28 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', upairsetE)).
% 0.25/0.28 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', upairsetIL)).
% 0.25/0.28 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', upairsetIR)).
% 0.25/0.28 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', vacuousDall)).
% 0.25/0.28 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', quantDeMorgan1)).
% 0.25/0.28 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', quantDeMorgan2)).
% 0.25/0.28 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', quantDeMorgan3)).
% 0.25/0.28 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', quantDeMorgan4)).
% 0.25/0.28 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.wylVP6Tkmr/E---3.1_384939.p', prop2setI)).
% 0.25/0.28 thf(c_0_61, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.25/0.28 thf(c_0_62, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.25/0.28 thf(c_0_63, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.25/0.28 thf(c_0_64, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.25/0.28 thf(c_0_65, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.25/0.28 thf(c_0_66, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.25/0.28 thf(c_0_67, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.25/0.28 thf(c_0_68, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.25/0.28 thf(c_0_69, 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)=>((prop2setI)=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[prop2set2propI])).
% 0.25/0.28 thf(c_0_70, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X175:$i]:(((((X6 @ X2 @ X175)))&(![X176:$i]:(((((X6 @ X2 @ X176)))=>(((X175)=(X176)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_61, c_0_62])).
% 0.25/0.28 thf(c_0_71, plain, ((descrp)=(![X1:$i > $o]:((((?[X177:$i]:(((((X1 @ X177)))&(![X178:$i]:(((((X1 @ X178)))=>(((X177)=(X178))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_63, c_0_62])).
% 0.25/0.28 thf(c_0_72, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.25/0.28 thf(c_0_73, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.25/0.28 thf(c_0_74, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.25/0.28 thf(c_0_75, plain, ((exuE1)=(![X1:$i > $o]:((((?[X179:$i]:(((((X1 @ X179)))&(![X180:$i]:(((((X1 @ X180)))=>(((X179)=(X180))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_64, c_0_62])).
% 0.25/0.28 thf(c_0_76, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X181:$i]:(((((X1 @ X181)))&(![X182:$i]:(((((X1 @ X182)))=>(((X181)=(X182))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_65, c_0_62])).
% 0.25/0.28 thf(c_0_77, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.25/0.28 thf(c_0_78, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_66])).
% 0.25/0.28 thf(c_0_79, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_67, c_0_66])).
% 0.25/0.28 thf(c_0_80, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_66])).
% 0.25/0.28 thf(c_0_81, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.25/0.28 thf(c_0_82, plain, ((exuE2)=(![X1:$i > $o]:((((?[X183:$i]:(((((X1 @ X183)))&(![X184:$i]:(((((X1 @ X184)))=>(((X183)=(X184))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_68, c_0_62])).
% 0.25/0.28 thf(c_0_83, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_66])).
% 0.25/0.28 thf(c_0_84, 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])).
% 0.25/0.28 thf(c_0_85, plain, ((set2prop)=(^[Z0:$i]:((in @ emptyset @ Z0)))), inference(fof_simplification,[status(thm)],[set2prop])).
% 0.25/0.28 thf(c_0_86, plain, ((epred1_0)<=>![X214:$i]:(?[X215:$i]:((((![X216:$i]:(((in @ X216 @ X215)=>![X217:$i]:(((in @ X217 @ X216)=>(in @ X217 @ X214)))))&![X218:$i, X219:$i]:((((in @ X218 @ X214)&(in @ X219 @ X214))=>(![X220:$i]:(((in @ X220 @ X215)=>((in @ X218 @ X220)<=>(in @ X219 @ X220))))=>((X218)=(X219))))))&![X221:$i, X222:$i]:((((in @ X221 @ X215)&(in @ X222 @ X215))=>(![X223:$i]:(((in @ X223 @ X221)=>(in @ X223 @ X222)))|![X224:$i]:(((in @ X224 @ X222)=>(in @ X224 @ X221)))))))&![X225:$i]:(((![X226:$i]:(((in @ X226 @ X225)=>(in @ X226 @ X214)))&?[X227:$i]:((in @ X227 @ X225)))=>?[X228:$i, X229:$i]:(((((in @ X228 @ X215)&(in @ X229 @ X225))&~(?[X230:$i]:(((in @ X230 @ X228)&(in @ X230 @ X225)))))&![X231:$i]:(((in @ X231 @ X215)=>(![X232:$i]:(((in @ X232 @ X231)=>(in @ X232 @ X228)))|(in @ X229 @ X231)))))))))))), introduced(definition)).
% 0.25/0.28 thf(c_0_87, negated_conjecture, ~((![X185:$i, X186:$i]:((![X187:$i]:(((in @ X187 @ X185)<=>(in @ X187 @ X186)))=>((X185)=(X186))))=>(![X188:$i]:(~(in @ X188 @ emptyset))=>(![X189:$i, X190:$i, X191:$i]:(((in @ X191 @ (setadjoin @ X189 @ X190))<=>(((X191)=(X189))|(in @ X191 @ X190))))=>(![X192:$i, X193:$i]:(((in @ X193 @ (powerset @ X192))<=>![X194:$i]:(((in @ X194 @ X193)=>(in @ X194 @ X192)))))=>(![X195:$i, X196:$i]:(((in @ X196 @ (setunion @ X195))<=>?[X197:$i]:(((in @ X196 @ X197)&(in @ X197 @ X195)))))=>((in @ emptyset @ omega)=>(![X198:$i]:(((in @ X198 @ omega)=>(in @ (setadjoin @ X198 @ X198) @ omega)))=>(![X199:$i]:((((in @ emptyset @ X199)&![X200:$i]:((((in @ X200 @ omega)&(in @ X200 @ X199))=>(in @ (setadjoin @ X200 @ X200) @ X199))))=>![X201:$i]:(((in @ X201 @ omega)=>(in @ X201 @ X199)))))=>(![X202:$i > $i > $o, X203:$i]:((![X204:$i]:(((in @ X204 @ X203)=>?[X205:$i]:(((X202 @ X204 @ X205)&![X206:$i]:(((X202 @ X204 @ X206)=>((X205)=(X206))))))))=>?[X207:$i]:(![X208:$i]:(((in @ X208 @ X207)<=>?[X209:$i]:(((in @ X209 @ X203)&(X202 @ X209 @ X208))))))))=>(![X210:$i]:((?[X211:$i]:((in @ X211 @ X210))=>?[X212:$i]:(((in @ X212 @ X210)&~(?[X213:$i]:(((in @ X213 @ X212)&(in @ X213 @ X210))))))))=>((epred1_0)=>(![X233:$i > $o]:((?[X234:$i]:(((X233 @ X234)&![X235:$i]:(((X233 @ X235)=>((X234)=(X235))))))=>(X233 @ (descr @ (^[Z0:$i]:(X233 @ Z0))))))=>(![X236:$i, X237:$i > $o, X238:$i]:(((in @ X238 @ X236)=>((X237 @ X238)=>(in @ X238 @ (dsetconstr @ X236 @ X237)))))=>(![X239:$i, X240:$i > $o, X241:$i]:(((in @ X241 @ (dsetconstr @ X239 @ X240))=>(in @ X241 @ X239)))=>(![X242:$i, X243:$i > $o, X244:$i]:(((in @ X244 @ (dsetconstr @ X242 @ X243))=>(X243 @ X244)))=>(![X245:$i > $o]:((?[X246:$i]:(((X245 @ X246)&![X247:$i]:(((X245 @ X247)=>((X246)=(X247))))))=>?[X248:$i]:(((X245 @ X248)&![X249:$i]:(((X245 @ X249)=>((X248)=(X249))))))))=>(![X250:$o, X251:$i]:(((in @ X251 @ (prop2set @ ((X250))))=>(X250)))=>(![X252:$i]:(((in @ X252 @ emptyset)=>![X253:$o]:((X253))))=>(![X254:$i]:(((in @ X254 @ emptyset)=>~($true)))=>(![X255:$i]:(~(in @ X255 @ emptyset))=>(![X256:$i > $o]:((?[X257:$i]:(((X256 @ X257)&![X258:$i]:(((X256 @ X258)=>((X257)=(X258))))))=>?[X259:$i]:((X256 @ X259))))=>(![X260:$i, X261:$i]:((![X262:$i]:(((in @ X262 @ X260)=>(in @ X262 @ X261)))=>(![X263:$i]:(((in @ X263 @ X261)=>(in @ X263 @ X260)))=>((X260)=(X261)))))=>(![X264:$i]:((![X265:$i]:(~(in @ X265 @ X264))=>((X264)=(emptyset))))=>(![X266:$i]:((![X267:$i]:(~(in @ X267 @ X266))=>((X266)=(emptyset))))=>(![X268:$i, X269:$i > $o, X270:$i]:(((in @ X270 @ X268)=>((in @ X270 @ (dsetconstr @ X268 @ X269))<=>(X269 @ X270))))=>(![X271:$i]:((((X271)!=(emptyset))=>?[X272:$i]:((in @ X272 @ X271))))=>(![X273:$i, X274:$i > $o, X275:$i]:(((in @ X275 @ X273)=>((X274 @ X275)=>((dsetconstr @ X273 @ X274)!=(emptyset)))))=>(![X276:$i]:((?[X277:$i]:((in @ X277 @ X276))=>((X276)!=(emptyset))))=>(![X278:$i, X279:$i]:((in @ X278 @ (setadjoin @ X278 @ X279)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X280:$i, X281:$i, X282:$i]:(((in @ X282 @ X281)=>(in @ X282 @ (setadjoin @ X280 @ X281))))=>(![X283:$i, X284:$i, X285:$i]:(((in @ X285 @ (setadjoin @ X283 @ X284))=>![X286:$o]:(((((X285)=(X283))=>(X286))=>(((in @ X285 @ X284)=>(X286))=>(X286))))))=>(![X287:$i, X288:$i, X289:$i]:(((in @ X289 @ (setadjoin @ X287 @ X288))=>(((X289)=(X287))|(in @ X289 @ X288))))=>(![X290:$i]:(((dsetconstr @ X290 @ (^[Z0:$i]:($true)))=(X290)))=>(![X291:$i, X292:$i]:((![X293:$i]:(((in @ X293 @ X292)=>(in @ X293 @ X291)))=>(in @ X292 @ (powerset @ X291))))=>(![X294:$i]:((in @ emptyset @ (powerset @ X294)))=>(![X295:$i]:((in @ emptyset @ (powerset @ X295)))=>(![X296:$i, X297:$i, X298:$i]:(((in @ X297 @ (powerset @ X296))=>((in @ X298 @ X297)=>(in @ X298 @ X296))))=>(![X299:$i, X300:$i, X301:$i]:(((in @ X300 @ X301)=>((in @ X301 @ X299)=>(in @ X300 @ (setunion @ X299)))))=>(![X302:$i, X303:$i]:(((in @ X303 @ (setunion @ X302))=>![X304:$o]:((![X305:$i]:(((in @ X303 @ X305)=>((in @ X305 @ X302)=>(X304))))=>(X304)))))=>(![X306:$i, X307:$i]:(((in @ X307 @ X306)=>(in @ X307 @ (powerset @ (setunion @ X306)))))=>(![X308:$i > $o]:((?[X309:$i]:(((X308 @ X309)&![X310:$i]:(((X308 @ X310)=>((X309)=(X310))))))=>?[X311:$i]:(![X312:$i]:(((X308 @ X312)<=>((X312)=(X311)))))))=>(![X313:$i]:((((X313)!=(emptyset))=>?[X314:$i]:(((in @ X314 @ X313)&$true))))=>(![X315:$i, X316:$i]:(((in @ X315 @ (setadjoin @ X316 @ emptyset))=>((X315)=(X316))))=>(![X317:$i, X318:$i]:((((X317)!=(X318))=>~(in @ X318 @ (setadjoin @ X317 @ emptyset))))=>(![X319:$i, X320:$i]:((((X319)=(X320))=>(in @ X319 @ (setadjoin @ X320 @ emptyset))))=>(![X321:$i, X322:$i]:(((in @ X321 @ (setadjoin @ X322 @ emptyset))=>(in @ X322 @ (setadjoin @ X321 @ emptyset))))=>(![X323:$i, X324:$i, X325:$i]:(((in @ X325 @ (setadjoin @ X323 @ (setadjoin @ X324 @ emptyset)))=>(((X325)=(X323))|((X325)=(X324)))))=>(![X326:$i, X327:$i]:((in @ X326 @ (setadjoin @ X326 @ (setadjoin @ X327 @ emptyset))))=>(![X328:$i, X329:$i]:((in @ X329 @ (setadjoin @ X328 @ (setadjoin @ X329 @ emptyset))))=>(![X330:$i, X331:$i > $o]:((?[X332:$i]:(((in @ X332 @ X330)&(X331 @ X332)))=>(((dsetconstr @ X330 @ X331)=(emptyset))=>~($true))))=>(![X333:$i > $o, X334:$i]:(((in @ X334 @ emptyset)=>(X333 @ X334)))=>(![X335:$i, X336:$i > $o]:((~(![X337:$i]:(((in @ X337 @ X335)=>(X336 @ X337))))=>?[X338:$i]:(((in @ X338 @ X335)&~((X336 @ X338))))))=>(![X339:$i, X340:$i > $o]:((![X341:$i]:(((in @ X341 @ X339)=>~((X340 @ X341))))=>~(?[X342:$i]:(((in @ X342 @ X339)&(X340 @ X342))))))=>(![X343:$i, X344:$i > $o]:((~(?[X345:$i]:(((in @ X345 @ X343)&(X344 @ X345))))=>![X346:$i]:(((in @ X346 @ X343)=>~((X344 @ X346))))))=>(![X347:$i, X348:$i > $o]:((?[X349:$i]:(((in @ X349 @ X347)&~((X348 @ X349))))=>~(![X350:$i]:(((in @ X350 @ X347)=>(X348 @ X350))))))=>(![X351:$o]:(((X351)=>(in @ emptyset @ (prop2set @ ((X351))))))=>![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)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_69, setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_70]), foundationAx]), wellorderingAx]), c_0_71]), c_0_72]), c_0_73]), c_0_74]), c_0_75]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_76]), setext]), emptyI]), noeltsimpempty]), c_0_77]), c_0_78]), c_0_79]), c_0_80]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_81]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_82]), c_0_83]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_84]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), c_0_85])])]), c_0_86])).
% 0.25/0.28 thf(c_0_88, 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, X508:$o]:((((~(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))))&((~(X508)|(in @ emptyset @ (prop2set @ ((X508)))))&((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 @ $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_87])])])])])])])])).
% 0.25/0.28 thf(c_0_89, negated_conjecture, (~((epred2_0))|~((in @ emptyset @ (prop2set @ (($true)))))), inference(split_conjunct,[status(thm)],[c_0_88])).
% 0.25/0.28 thf(c_0_90, negated_conjecture, (epred2_0), inference(split_conjunct,[status(thm)],[c_0_88])).
% 0.25/0.28 thf(c_0_91, negated_conjecture, (in @ emptyset @ (prop2set @ (($true)))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_88])])])).
% 0.25/0.28 thf(c_0_92, negated_conjecture, ~((in @ emptyset @ (prop2set @ (($true))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89, c_0_90])])).
% 0.25/0.28 thf(c_0_93, negated_conjecture, ($false), inference(sr,[status(thm)],[c_0_91, c_0_92]), ['proof']).
% 0.25/0.28 % SZS output end CNFRefutation
% 0.25/0.28 % Parsed axioms : 130
% 0.25/0.28 % Removed by relevancy pruning/SinE : 0
% 0.25/0.28 % Initial clauses : 187
% 0.25/0.28 % Removed in clause preprocessing : 76
% 0.25/0.28 % Initial clauses in saturation : 111
% 0.25/0.28 % Processed clauses : 6
% 0.25/0.28 % ...of these trivial : 1
% 0.25/0.28 % ...subsumed : 0
% 0.25/0.28 % ...remaining for further processing : 4
% 0.25/0.28 % Other redundant clauses eliminated : 0
% 0.25/0.28 % Clauses deleted for lack of memory : 0
% 0.25/0.28 % Backward-subsumed : 0
% 0.25/0.28 % Backward-rewritten : 0
% 0.25/0.28 % Generated clauses : 0
% 0.25/0.28 % ...of the previous two non-redundant : 0
% 0.25/0.28 % ...aggressively subsumed : 0
% 0.25/0.28 % Contextual simplify-reflections : 0
% 0.25/0.28 % Paramodulations : 0
% 0.25/0.28 % Factorizations : 0
% 0.25/0.28 % NegExts : 0
% 0.25/0.28 % Equation resolutions : 0
% 0.25/0.28 % Disequality decompositions : 0
% 0.25/0.28 % Total rewrite steps : 2
% 0.25/0.28 % ...of those cached : 1
% 0.25/0.28 % Propositional unsat checks : 0
% 0.25/0.28 % Propositional check models : 0
% 0.25/0.28 % Propositional check unsatisfiable : 0
% 0.25/0.28 % Propositional clauses : 0
% 0.25/0.28 % Propositional clauses after purity: 0
% 0.25/0.28 % Propositional unsat core size : 0
% 0.25/0.28 % Propositional preprocessing time : 0.000
% 0.25/0.28 % Propositional encoding time : 0.000
% 0.25/0.28 % Propositional solver time : 0.000
% 0.25/0.28 % Success case prop preproc time : 0.000
% 0.25/0.28 % Success case prop encoding time : 0.000
% 0.25/0.28 % Success case prop solver time : 0.000
% 0.25/0.28 % Current number of processed clauses : 4
% 0.25/0.28 % Positive orientable unit clauses : 3
% 0.25/0.28 % Positive unorientable unit clauses: 0
% 0.25/0.28 % Negative unit clauses : 1
% 0.25/0.28 % Non-unit-clauses : 0
% 0.25/0.28 % Current number of unprocessed clauses: 105
% 0.25/0.28 % ...number of literals in the above : 309
% 0.25/0.28 % Current number of archived formulas : 0
% 0.25/0.28 % Current number of archived clauses : 0
% 0.25/0.28 % Clause-clause subsumption calls (NU) : 0
% 0.25/0.28 % Rec. Clause-clause subsumption calls : 0
% 0.25/0.28 % Non-unit clause-clause subsumptions : 0
% 0.25/0.28 % Unit Clause-clause subsumption calls : 0
% 0.25/0.28 % Rewrite failures with RHS unbound : 0
% 0.25/0.28 % BW rewrite match attempts : 0
% 0.25/0.28 % BW rewrite match successes : 0
% 0.25/0.28 % Condensation attempts : 6
% 0.25/0.28 % Condensation successes : 0
% 0.25/0.28 % Termbank termtop insertions : 15708
% 0.25/0.28 % Search garbage collected termcells : 6320
% 0.25/0.28
% 0.25/0.28 % -------------------------------------------------
% 0.25/0.28 % User time : 0.009 s
% 0.25/0.28 % System time : 0.006 s
% 0.25/0.28 % Total time : 0.015 s
% 0.25/0.28 % Maximum resident set size: 5048 pages
% 0.25/0.28
% 0.25/0.28 % -------------------------------------------------
% 0.25/0.28 % User time : 0.021 s
% 0.25/0.28 % System time : 0.021 s
% 0.25/0.28 % Total time : 0.042 s
% 0.25/0.28 % Maximum resident set size: 4864 pages
% 0.25/0.28 % E exiting
%------------------------------------------------------------------------------