%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU541^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:26 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : CNFRefutation 0.23s
% 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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.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 13:49:49 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.26 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p
% 0.23/0.29 % Version: 3.5.1-ho
% 0.23/0.29 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.29 % Starting sh5l with 300s (1) cores
% 0.23/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.29 % new_bool_2 with pid 1081945 completed with status 0
% 0.23/0.29 % Result found by new_bool_2
% 0.23/0.29 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.29 % Starting sh5l with 300s (1) cores
% 0.23/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.29 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.29 % Search class: HGHSM-FFMM31-SHFSMSBN
% 0.23/0.29 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.23/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.29 % SubtermCWHack with pid 1081949 completed with status 0
% 0.23/0.29 % Result found by SubtermCWHack
% 0.23/0.29 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.29 % Starting sh5l with 300s (1) cores
% 0.23/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.29 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.29 % Search class: HGHSM-FFMM31-SHFSMSBN
% 0.23/0.29 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.23/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.29 % Preprocessing time : 0.002 s
% 0.23/0.29
% 0.23/0.29 % Proof found!
% 0.23/0.29 % SZS status Theorem
% 0.23/0.29 % SZS output start CNFRefutation
% 0.23/0.29 thf(decl_23, type, in: $i > $i > $o).
% 0.23/0.29 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.23/0.29 thf(decl_25, type, setextAx: $o).
% 0.23/0.29 thf(decl_26, type, emptyset: $i).
% 0.23/0.29 thf(decl_27, type, emptysetAx: $o).
% 0.23/0.29 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.23/0.29 thf(decl_29, type, setadjoinAx: $o).
% 0.23/0.29 thf(decl_30, type, powerset: $i > $i).
% 0.23/0.29 thf(decl_31, type, powersetAx: $o).
% 0.23/0.29 thf(decl_32, type, setunion: $i > $i).
% 0.23/0.29 thf(decl_33, type, setunionAx: $o).
% 0.23/0.29 thf(decl_34, type, omega: $i).
% 0.23/0.29 thf(decl_35, type, omega0Ax: $o).
% 0.23/0.29 thf(decl_36, type, omegaSAx: $o).
% 0.23/0.29 thf(decl_37, type, omegaIndAx: $o).
% 0.23/0.29 thf(decl_38, type, replAx: $o).
% 0.23/0.29 thf(decl_39, type, foundationAx: $o).
% 0.23/0.29 thf(decl_40, type, wellorderingAx: $o).
% 0.23/0.29 thf(decl_42, type, descrp: $o).
% 0.23/0.29 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_44, type, dsetconstrI: $o).
% 0.23/0.29 thf(decl_45, type, dsetconstrEL: $o).
% 0.23/0.29 thf(decl_46, type, dsetconstrER: $o).
% 0.23/0.29 thf(decl_47, type, exuE1: $o).
% 0.23/0.29 thf(decl_48, type, prop2set: $o > $i).
% 0.23/0.29 thf(decl_49, type, prop2setE: $o).
% 0.23/0.29 thf(decl_50, type, emptysetE: $o).
% 0.23/0.29 thf(decl_51, type, emptysetimpfalse: $o).
% 0.23/0.29 thf(decl_52, type, notinemptyset: $o).
% 0.23/0.29 thf(decl_53, type, exuE3e: $o).
% 0.23/0.29 thf(decl_54, type, setext: $o).
% 0.23/0.29 thf(decl_55, type, emptyI: $o).
% 0.23/0.29 thf(decl_56, type, noeltsimpempty: $o).
% 0.23/0.29 thf(decl_57, type, setbeta: $o).
% 0.23/0.29 thf(decl_58, type, nonempty: $i > $o).
% 0.23/0.29 thf(decl_59, type, nonemptyE1: $o).
% 0.23/0.29 thf(decl_60, type, nonemptyI: $o).
% 0.23/0.29 thf(decl_61, type, nonemptyI1: $o).
% 0.23/0.29 thf(decl_62, type, setadjoinIL: $o).
% 0.23/0.29 thf(decl_63, type, emptyinunitempty: $o).
% 0.23/0.29 thf(decl_64, type, setadjoinIR: $o).
% 0.23/0.29 thf(decl_65, type, setadjoinE: $o).
% 0.23/0.29 thf(decl_66, type, setadjoinOr: $o).
% 0.23/0.29 thf(decl_67, type, setoftrueEq: $o).
% 0.23/0.29 thf(decl_68, type, powersetI: $o).
% 0.23/0.29 thf(decl_69, type, emptyinPowerset: $o).
% 0.23/0.29 thf(decl_70, type, emptyInPowerset: $o).
% 0.23/0.29 thf(decl_71, type, powersetE: $o).
% 0.23/0.29 thf(decl_72, type, setunionI: $o).
% 0.23/0.29 thf(decl_73, type, setunionE: $o).
% 0.23/0.29 thf(decl_74, type, subPowSU: $o).
% 0.23/0.29 thf(decl_75, type, exuE2: $o).
% 0.23/0.29 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.23/0.29 thf(decl_77, type, uniqinunit: $o).
% 0.23/0.29 thf(decl_78, type, notinsingleton: $o).
% 0.23/0.29 thf(decl_79, type, eqinunit: $o).
% 0.23/0.29 thf(decl_80, type, singletonsswitch: $o).
% 0.23/0.29 thf(decl_81, type, upairsetE: $o).
% 0.23/0.29 thf(decl_82, type, upairsetIL: $o).
% 0.23/0.29 thf(decl_83, type, upairsetIR: $o).
% 0.23/0.29 thf(decl_84, type, emptyE1: $o).
% 0.23/0.29 thf(decl_85, type, vacuousDall: $o).
% 0.23/0.29 thf(decl_86, type, quantDeMorgan1: $o).
% 0.23/0.29 thf(decl_87, type, quantDeMorgan2: $o).
% 0.23/0.29 thf(decl_88, type, quantDeMorgan3: $o).
% 0.23/0.29 thf(decl_89, type, quantDeMorgan4: $o).
% 0.23/0.29 thf(decl_90, type, prop2setI: $o).
% 0.23/0.29 thf(decl_91, type, set2prop: $i > $o).
% 0.23/0.29 thf(decl_92, type, epred1_0: $o).
% 0.23/0.29 thf(decl_93, type, esk1_2: $i > $i > $i).
% 0.23/0.29 thf(decl_94, type, esk2_2: $i > $i > $i).
% 0.23/0.29 thf(decl_95, type, esk3_2: $i > $i > $i).
% 0.23/0.29 thf(decl_96, type, esk4_1: $i > $i).
% 0.23/0.29 thf(decl_97, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.23/0.29 thf(decl_98, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.29 thf(decl_99, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.23/0.29 thf(decl_100, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.29 thf(decl_101, type, esk9_1: $i > $i).
% 0.23/0.29 thf(decl_102, type, esk10_2: ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_103, type, esk11_1: ($i > $o) > $i).
% 0.23/0.29 thf(decl_104, type, esk12_2: ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_105, type, esk13_1: ($i > $o) > $i).
% 0.23/0.29 thf(decl_106, type, esk14_2: $i > $i > $i).
% 0.23/0.29 thf(decl_107, type, esk15_2: $i > $i > $i).
% 0.23/0.29 thf(decl_108, type, esk16_1: $i > $i).
% 0.23/0.29 thf(decl_109, type, esk17_1: $i > $i).
% 0.23/0.29 thf(decl_110, type, esk18_1: $i > $i).
% 0.23/0.29 thf(decl_111, type, esk19_2: $i > $i > $i).
% 0.23/0.29 thf(decl_112, type, esk20_3: $i > $i > $o > $i).
% 0.23/0.29 thf(decl_113, type, esk21_2: ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_114, type, esk22_1: ($i > $o) > $i).
% 0.23/0.29 thf(decl_115, type, esk23_1: $i > $i).
% 0.23/0.29 thf(decl_116, type, esk24_2: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_117, type, esk25_2: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_118, type, esk26_2: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_119, type, esk27_2: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_120, type, epred2_0: $o).
% 0.23/0.29 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', exuE1)).
% 0.23/0.29 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', exu)).
% 0.23/0.29 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', nonempty)).
% 0.23/0.29 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', exuE3e)).
% 0.23/0.29 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', replAx)).
% 0.23/0.29 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', nonemptyI)).
% 0.23/0.29 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', exuE2)).
% 0.23/0.29 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:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', prop2set2propI)).
% 0.23/0.29 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', dsetconstrEL)).
% 0.23/0.29 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', emptyE1)).
% 0.23/0.29 thf(set2prop, axiom, ((set2prop)=(^[X4:$i]:((in @ emptyset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', set2prop)).
% 0.23/0.29 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', dsetconstrER)).
% 0.23/0.29 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', dsetconstrI)).
% 0.23/0.29 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', nonemptyE1)).
% 0.23/0.29 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', setbeta)).
% 0.23/0.29 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', setoftrueEq)).
% 0.23/0.29 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', nonemptyI1)).
% 0.23/0.29 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', nonemptyImpWitness)).
% 0.23/0.29 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', upairsetIL)).
% 0.23/0.29 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', upairsetE)).
% 0.23/0.29 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', upairsetIR)).
% 0.23/0.29 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', vacuousDall)).
% 0.23/0.29 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', quantDeMorgan1)).
% 0.23/0.29 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', quantDeMorgan2)).
% 0.23/0.29 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', quantDeMorgan3)).
% 0.23/0.29 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', quantDeMorgan4)).
% 0.23/0.29 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', prop2setI)).
% 0.23/0.29 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', prop2setE)).
% 0.23/0.29 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', omegaIndAx)).
% 0.23/0.29 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', emptysetE)).
% 0.23/0.29 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', setadjoinIR)).
% 0.23/0.29 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', emptyinunitempty)).
% 0.23/0.29 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', wellorderingAx)).
% 0.23/0.29 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', foundationAx)).
% 0.23/0.29 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', emptysetimpfalse)).
% 0.23/0.29 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', noeltsimpempty)).
% 0.23/0.29 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', emptyI)).
% 0.23/0.29 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', setext)).
% 0.23/0.29 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', notinemptyset)).
% 0.23/0.29 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', setadjoinOr)).
% 0.23/0.29 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', setadjoinE)).
% 0.23/0.29 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', setadjoinIL)).
% 0.23/0.29 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', powersetI)).
% 0.23/0.29 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', subPowSU)).
% 0.23/0.29 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/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', setunionE)).
% 0.23/0.29 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', setunionI)).
% 0.23/0.29 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', powersetE)).
% 0.23/0.29 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', emptyInPowerset)).
% 0.23/0.29 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', uniqinunit)).
% 0.23/0.29 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', notinsingleton)).
% 0.23/0.29 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', eqinunit)).
% 0.23/0.29 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', singletonsswitch)).
% 0.23/0.29 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', emptyinPowerset)).
% 0.23/0.29 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', omegaSAx)).
% 0.23/0.29 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', omega0Ax)).
% 0.23/0.29 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', setunionAx)).
% 0.23/0.29 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', powersetAx)).
% 0.23/0.29 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', setadjoinAx)).
% 0.23/0.29 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', emptysetAx)).
% 0.23/0.29 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.GHfjeRGbsC/E---3.1_1081907.p', setextAx)).
% 0.23/0.29 thf(c_0_60, 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])).
% 0.23/0.29 thf(c_0_61, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.23/0.29 thf(c_0_62, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.23/0.29 thf(c_0_63, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.23/0.29 thf(c_0_64, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.23/0.29 thf(c_0_65, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.23/0.29 thf(c_0_66, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.23/0.29 thf(c_0_67, 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:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[prop2set2propI])).
% 0.23/0.29 thf(c_0_68, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.23/0.29 thf(c_0_69, plain, ((emptyE1)<=>![X4:$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])).
% 0.23/0.29 thf(c_0_70, plain, ((set2prop)=(^[Z0:$i]:((in @ emptyset @ Z0)))), inference(fof_simplification,[status(thm)],[set2prop])).
% 0.23/0.29 thf(c_0_71, plain, ((exuE1)=(![X1:$i > $o]:((((?[X176:$i]:(((((X1 @ X176)))&(![X177:$i]:(((((X1 @ X177)))=>(((X176)=(X177))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_60, c_0_61])).
% 0.23/0.29 thf(c_0_72, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.23/0.29 thf(c_0_73, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.23/0.29 thf(c_0_74, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_62])).
% 0.23/0.29 thf(c_0_75, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.23/0.29 thf(c_0_76, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X178:$i]:(((((X1 @ X178)))&(![X179:$i]:(((((X1 @ X179)))=>(((X178)=(X179))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_63, c_0_61])).
% 0.23/0.29 thf(c_0_77, 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_64, c_0_61])).
% 0.23/0.29 thf(c_0_78, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_65, c_0_62])).
% 0.23/0.29 thf(c_0_79, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.23/0.29 thf(c_0_80, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_62])).
% 0.23/0.29 thf(c_0_81, plain, ((exuE2)=(![X1:$i > $o]:((((?[X180:$i]:(((((X1 @ X180)))&(![X181:$i]:(((((X1 @ X181)))=>(((X180)=(X181))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_66, c_0_61])).
% 0.23/0.29 thf(c_0_82, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_62])).
% 0.23/0.29 thf(c_0_83, plain, ((epred1_0)<=>![X211:$i]:(?[X212:$i]:((((![X213:$i]:(((in @ X213 @ X212)=>![X214:$i]:(((in @ X214 @ X213)=>(in @ X214 @ X211)))))&![X215:$i, X216:$i]:((((in @ X215 @ X211)&(in @ X216 @ X211))=>(![X217:$i]:(((in @ X217 @ X212)=>((in @ X215 @ X217)<=>(in @ X216 @ X217))))=>((X215)=(X216))))))&![X218:$i, X219:$i]:((((in @ X218 @ X212)&(in @ X219 @ X212))=>(![X220:$i]:(((in @ X220 @ X218)=>(in @ X220 @ X219)))|![X221:$i]:(((in @ X221 @ X219)=>(in @ X221 @ X218)))))))&![X222:$i]:(((![X223:$i]:(((in @ X223 @ X222)=>(in @ X223 @ X211)))&?[X224:$i]:((in @ X224 @ X222)))=>?[X225:$i, X226:$i]:(((((in @ X225 @ X212)&(in @ X226 @ X222))&~(?[X227:$i]:(((in @ X227 @ X225)&(in @ X227 @ X222)))))&![X228:$i]:(((in @ X228 @ X212)=>(![X229:$i]:(((in @ X229 @ X228)=>(in @ X229 @ X225)))|(in @ X226 @ X228)))))))))))), introduced(definition)).
% 0.23/0.29 thf(c_0_84, negated_conjecture, ~((![X182:$i, X183:$i]:((![X184:$i]:(((in @ X184 @ X182)<=>(in @ X184 @ X183)))=>((X182)=(X183))))=>(![X185:$i]:(~(in @ X185 @ emptyset))=>(![X186:$i, X187:$i, X188:$i]:(((in @ X188 @ (setadjoin @ X186 @ X187))<=>(((X188)=(X186))|(in @ X188 @ X187))))=>(![X189:$i, X190:$i]:(((in @ X190 @ (powerset @ X189))<=>![X191:$i]:(((in @ X191 @ X190)=>(in @ X191 @ X189)))))=>(![X192:$i, X193:$i]:(((in @ X193 @ (setunion @ X192))<=>?[X194:$i]:(((in @ X193 @ X194)&(in @ X194 @ X192)))))=>((in @ emptyset @ omega)=>(![X195:$i]:(((in @ X195 @ omega)=>(in @ (setadjoin @ X195 @ X195) @ omega)))=>(![X196:$i]:((((in @ emptyset @ X196)&![X197:$i]:((((in @ X197 @ omega)&(in @ X197 @ X196))=>(in @ (setadjoin @ X197 @ X197) @ X196))))=>![X198:$i]:(((in @ X198 @ omega)=>(in @ X198 @ X196)))))=>(![X199:$i > $i > $o, X200:$i]:((![X201:$i]:(((in @ X201 @ X200)=>?[X202:$i]:(((X199 @ X201 @ X202)&![X203:$i]:(((X199 @ X201 @ X203)=>((X202)=(X203))))))))=>?[X204:$i]:(![X205:$i]:(((in @ X205 @ X204)<=>?[X206:$i]:(((in @ X206 @ X200)&(X199 @ X206 @ X205))))))))=>(![X207:$i]:((?[X208:$i]:((in @ X208 @ X207))=>?[X209:$i]:(((in @ X209 @ X207)&~(?[X210:$i]:(((in @ X210 @ X209)&(in @ X210 @ X207))))))))=>((epred1_0)=>((descrp)=>(![X230:$i, X231:$i > $o, X232:$i]:(((in @ X232 @ X230)=>((X231 @ X232)=>(in @ X232 @ (dsetconstr @ X230 @ (^[Z0:$i]:((X231 @ Z0))))))))=>(![X233:$i, X234:$i > $o, X235:$i]:(((in @ X235 @ (dsetconstr @ X233 @ (^[Z0:$i]:((X234 @ Z0)))))=>(in @ X235 @ X233)))=>(![X236:$i, X237:$i > $o, X238:$i]:(((in @ X238 @ (dsetconstr @ X236 @ (^[Z0:$i]:((X237 @ Z0)))))=>(X237 @ X238)))=>(![X239:$i > $o]:((?[X240:$i]:(((X239 @ X240)&![X241:$i]:(((X239 @ X241)=>((X240)=(X241))))))=>?[X242:$i]:(((X239 @ X242)&![X243:$i]:(((X239 @ X243)=>((X242)=(X243))))))))=>(![X244:$o, X245:$i]:(((in @ X245 @ (prop2set @ ((X244))))=>(X244)))=>(![X246:$i]:(((in @ X246 @ emptyset)=>![X247:$o]:((X247))))=>(![X248:$i]:(~(in @ X248 @ emptyset))=>(![X249:$i]:(~(in @ X249 @ emptyset))=>(![X250:$i > $o]:((?[X251:$i]:(((X250 @ X251)&![X252:$i]:(((X250 @ X252)=>((X251)=(X252))))))=>?[X253:$i]:((X250 @ X253))))=>(![X254:$i, X255:$i]:((![X256:$i]:(((in @ X256 @ X254)=>(in @ X256 @ X255)))=>(![X257:$i]:(((in @ X257 @ X255)=>(in @ X257 @ X254)))=>((X254)=(X255)))))=>(![X258:$i]:((![X259:$i]:(~(in @ X259 @ X258))=>((X258)=(emptyset))))=>(![X260:$i]:((![X261:$i]:(~(in @ X261 @ X260))=>((X260)=(emptyset))))=>(![X262:$i, X263:$i > $o, X264:$i]:(((in @ X264 @ X262)=>((in @ X264 @ (dsetconstr @ X262 @ (^[Z0:$i]:((X263 @ Z0)))))<=>(X263 @ X264))))=>(![X265:$i]:((((X265)!=(emptyset))=>?[X266:$i]:((in @ X266 @ X265))))=>(![X267:$i, X268:$i > $o, X269:$i]:(((in @ X269 @ X267)=>((X268 @ X269)=>((dsetconstr @ X267 @ (^[Z0:$i]:((X268 @ Z0))))!=(emptyset)))))=>(![X270:$i]:((?[X271:$i]:((in @ X271 @ X270))=>((X270)!=(emptyset))))=>(![X272:$i, X273:$i]:((in @ X272 @ (setadjoin @ X272 @ X273)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X274:$i, X275:$i, X276:$i]:(((in @ X276 @ X275)=>(in @ X276 @ (setadjoin @ X274 @ X275))))=>(![X277:$i, X278:$i, X279:$i]:(((in @ X279 @ (setadjoin @ X277 @ X278))=>![X280:$o]:(((((X279)=(X277))=>(X280))=>(((in @ X279 @ X278)=>(X280))=>(X280))))))=>(![X281:$i, X282:$i, X283:$i]:(((in @ X283 @ (setadjoin @ X281 @ X282))=>(((X283)=(X281))|(in @ X283 @ X282))))=>(![X284:$i]:(((dsetconstr @ X284 @ (^[Z0:$i]:(($true))))=(X284)))=>(![X285:$i, X286:$i]:((![X287:$i]:(((in @ X287 @ X286)=>(in @ X287 @ X285)))=>(in @ X286 @ (powerset @ X285))))=>(![X288:$i]:((in @ emptyset @ (powerset @ X288)))=>(![X289:$i]:((in @ emptyset @ (powerset @ X289)))=>(![X290:$i, X291:$i, X292:$i]:(((in @ X291 @ (powerset @ X290))=>((in @ X292 @ X291)=>(in @ X292 @ X290))))=>(![X293:$i, X294:$i, X295:$i]:(((in @ X294 @ X295)=>((in @ X295 @ X293)=>(in @ X294 @ (setunion @ X293)))))=>(![X296:$i, X297:$i]:(((in @ X297 @ (setunion @ X296))=>![X298:$o]:((![X299:$i]:(((in @ X297 @ X299)=>((in @ X299 @ X296)=>(X298))))=>(X298)))))=>(![X300:$i, X301:$i]:(((in @ X301 @ X300)=>(in @ X301 @ (powerset @ (setunion @ X300)))))=>(![X302:$i > $o]:((?[X303:$i]:(((X302 @ X303)&![X304:$i]:(((X302 @ X304)=>((X303)=(X304))))))=>?[X305:$i]:(![X306:$i]:(((X302 @ X306)<=>((X306)=(X305)))))))=>(![X307:$i]:((((X307)!=(emptyset))=>?[X308:$i]:((in @ X308 @ X307))))=>(![X309:$i, X310:$i]:(((in @ X309 @ (setadjoin @ X310 @ emptyset))=>((X309)=(X310))))=>(![X311:$i, X312:$i]:((((X311)!=(X312))=>~(in @ X312 @ (setadjoin @ X311 @ emptyset))))=>(![X313:$i, X314:$i]:((((X313)=(X314))=>(in @ X313 @ (setadjoin @ X314 @ emptyset))))=>(![X315:$i, X316:$i]:(((in @ X315 @ (setadjoin @ X316 @ emptyset))=>(in @ X316 @ (setadjoin @ X315 @ emptyset))))=>(![X317:$i, X318:$i, X319:$i]:(((in @ X319 @ (setadjoin @ X317 @ (setadjoin @ X318 @ emptyset)))=>(((X319)=(X317))|((X319)=(X318)))))=>(![X320:$i, X321:$i]:((in @ X320 @ (setadjoin @ X320 @ (setadjoin @ X321 @ emptyset))))=>(![X322:$i, X323:$i]:((in @ X323 @ (setadjoin @ X322 @ (setadjoin @ X323 @ emptyset))))=>(![X324:$i, X325:$i > $o]:((?[X326:$i]:(((in @ X326 @ X324)&(X325 @ X326)))=>((dsetconstr @ X324 @ (^[Z0:$i]:((X325 @ Z0))))!=(emptyset))))=>(![X327:$i > $o, X328:$i]:(((in @ X328 @ emptyset)=>(X327 @ X328)))=>(![X329:$i, X330:$i > $o]:((~(![X331:$i]:(((in @ X331 @ X329)=>(X330 @ X331))))=>?[X332:$i]:(((in @ X332 @ X329)&~(X330 @ X332)))))=>(![X333:$i, X334:$i > $o]:((![X335:$i]:(((in @ X335 @ X333)=>~(X334 @ X335)))=>~(?[X336:$i]:(((in @ X336 @ X333)&(X334 @ X336))))))=>(![X337:$i, X338:$i > $o]:((~(?[X339:$i]:(((in @ X339 @ X337)&(X338 @ X339))))=>![X340:$i]:(((in @ X340 @ X337)=>~(X338 @ X340)))))=>(![X341:$i, X342:$i > $o]:((?[X343:$i]:(((in @ X343 @ X341)&~(X342 @ X343)))=>~(![X344:$i]:(((in @ X344 @ X341)=>(X342 @ X344))))))=>(![X345:$o]:(((X345)=>(in @ emptyset @ (prop2set @ ((X345))))))=>![X16:$o]:(((X16)=>(in @ emptyset @ (prop2set @ ((X16)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[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_67, c_0_68]), upairsetIL]), upairsetE]), upairsetIR]), c_0_69]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2setE]), c_0_70]), omegaIndAx]), emptysetE]), c_0_71]), c_0_72]), setadjoinIR]), emptyinunitempty]), c_0_73]), wellorderingAx]), foundationAx]), emptysetimpfalse]), c_0_74]), c_0_75]), noeltsimpempty]), emptyI]), setext]), c_0_76]), notinemptyset]), c_0_77]), c_0_78]), c_0_79]), setadjoinOr]), setadjoinE]), setadjoinIL]), c_0_80]), powersetI]), c_0_81]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), emptyinPowerset]), c_0_82]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])]), c_0_83])).
% 0.23/0.29 thf(c_0_85, negated_conjecture, ![X346:$i, X347:$i, X349:$i, X350:$i, X351:$i, X352:$i, X353:$i, X354:$i, X355:$i, X356:$i, X357:$i, X359:$i, X360:$i, X362:$i, X363:$i, X364:$i, X365:$i, X366:$i, X368:$i, X369:$i > $i > $o, X370:$i, X372:$i, X375:$i, X377:$i, X378:$i, X379:$i, X380:$i, X382:$i, X383:$i, X384:$i > $o, X385:$i, X386:$i, X387:$i > $o, X388:$i, X389:$i, X390:$i > $o, X391:$i, X392:$i > $o, X393:$i, X396:$i, X397:$o, X398:$i, X399:$i, X400:$o, X401:$i, X402:$i, X403:$i > $o, X404:$i, X407:$i, X408:$i, X411:$i, X413:$i, X415:$i, X416:$i > $o, X417:$i, X418:$i, X420:$i, X421:$i > $o, X422:$i, X423:$i, X424:$i, X425:$i, X426:$i, X427:$i, X428:$i, X429:$i, X430:$i, X431:$i, X432:$i, X433:$o, X434:$i, X435:$i, X436:$i, X437:$i, X438:$i, X439:$i, X441:$i, X442:$i, X443:$i, X444:$i, X445:$i, X446:$i, X447:$i, X448:$i, X449:$i, X450:$i, X451:$o, X453:$i, X454:$i, X455:$i > $o, X456:$i, X459:$i, X460:$i, X461:$i, X463:$i, X464:$i, X465:$i, X466:$i, X467:$i, X468:$i, X469:$i, X470:$i, X471:$i, X472:$i, X473:$i, X474:$i, X475:$i, X476:$i, X477:$i, X478:$i, X479:$i > $o, X480:$i, X481:$i > $o, X482:$i, X483:$i, X484:$i > $o, X485:$i, X487:$i, X488:$i > $o, X490:$i, X491:$i, X492:$i > $o, X494:$i, X495:$i, X496:$i > $o, X497:$i, X499:$o]:((((~(in @ (esk1_2 @ X346 @ X347) @ X346)|~(in @ (esk1_2 @ X346 @ X347) @ X347)|((X346)=(X347)))&((in @ (esk1_2 @ X346 @ X347) @ X346)|(in @ (esk1_2 @ X346 @ X347) @ X347)|((X346)=(X347))))&(~(in @ X349 @ emptyset)&(((~(in @ X352 @ (setadjoin @ X350 @ X351))|(((X352)=(X350))|(in @ X352 @ X351)))&((((X352)!=(X350))|(in @ X352 @ (setadjoin @ X350 @ X351)))&(~(in @ X352 @ X351)|(in @ X352 @ (setadjoin @ X350 @ X351)))))&(((~(in @ X354 @ (powerset @ X353))|(~(in @ X355 @ X354)|(in @ X355 @ X353)))&(((in @ (esk2_2 @ X356 @ X357) @ X357)|(in @ X357 @ (powerset @ X356)))&(~(in @ (esk2_2 @ X356 @ X357) @ X356)|(in @ X357 @ (powerset @ X356)))))&(((((in @ X360 @ (esk3_2 @ X359 @ X360))|~(in @ X360 @ (setunion @ X359)))&((in @ (esk3_2 @ X359 @ X360) @ X359)|~(in @ X360 @ (setunion @ X359))))&(~(in @ X363 @ X364)|~(in @ X364 @ X362)|(in @ X363 @ (setunion @ X362))))&((in @ emptyset @ omega)&((~(in @ X365 @ omega)|(in @ (setadjoin @ X365 @ X365) @ omega))&(((((in @ (esk4_1 @ X366) @ omega)|~(in @ emptyset @ X366)|(~(in @ X368 @ omega)|(in @ X368 @ X366)))&((in @ (esk4_1 @ X366) @ X366)|~(in @ emptyset @ X366)|(~(in @ X368 @ omega)|(in @ X368 @ X366))))&(~(in @ (setadjoin @ (esk4_1 @ X366) @ (esk4_1 @ X366)) @ X366)|~(in @ emptyset @ X366)|(~(in @ X368 @ omega)|(in @ X368 @ X366))))&((((((in @ (esk8_3 @ X369 @ X370 @ X375) @ X370)|~(in @ X375 @ (esk7_2 @ X369 @ X370))|(in @ (esk5_2 @ X369 @ X370) @ X370))&((X369 @ (esk8_3 @ X369 @ X370 @ X375) @ X375)|~(in @ X375 @ (esk7_2 @ X369 @ X370))|(in @ (esk5_2 @ X369 @ X370) @ X370)))&(~(in @ X378 @ X370)|~(X369 @ X378 @ X377)|(in @ X377 @ (esk7_2 @ X369 @ X370))|(in @ (esk5_2 @ X369 @ X370) @ X370)))&(((((in @ (esk8_3 @ X369 @ X370 @ X375) @ X370)|~(in @ X375 @ (esk7_2 @ X369 @ X370))|((X369 @ (esk5_2 @ X369 @ X370) @ (esk6_3 @ X369 @ X370 @ X372))|~(X369 @ (esk5_2 @ X369 @ X370) @ X372)))&((X369 @ (esk8_3 @ X369 @ X370 @ X375) @ X375)|~(in @ X375 @ (esk7_2 @ X369 @ X370))|((X369 @ (esk5_2 @ X369 @ X370) @ (esk6_3 @ X369 @ X370 @ X372))|~(X369 @ (esk5_2 @ X369 @ X370) @ X372))))&(~(in @ X378 @ X370)|~(X369 @ X378 @ X377)|(in @ X377 @ (esk7_2 @ X369 @ X370))|((X369 @ (esk5_2 @ X369 @ X370) @ (esk6_3 @ X369 @ X370 @ X372))|~(X369 @ (esk5_2 @ X369 @ X370) @ X372))))&((((in @ (esk8_3 @ X369 @ X370 @ X375) @ X370)|~(in @ X375 @ (esk7_2 @ X369 @ X370))|(((X372)!=(esk6_3 @ X369 @ X370 @ X372))|~(X369 @ (esk5_2 @ X369 @ X370) @ X372)))&((X369 @ (esk8_3 @ X369 @ X370 @ X375) @ X375)|~(in @ X375 @ (esk7_2 @ X369 @ X370))|(((X372)!=(esk6_3 @ X369 @ X370 @ X372))|~(X369 @ (esk5_2 @ X369 @ X370) @ X372))))&(~(in @ X378 @ X370)|~(X369 @ X378 @ X377)|(in @ X377 @ (esk7_2 @ X369 @ X370))|(((X372)!=(esk6_3 @ X369 @ X370 @ X372))|~(X369 @ (esk5_2 @ X369 @ X370) @ X372))))))&((((in @ (esk9_1 @ X379) @ X379)|~(in @ X380 @ X379))&(~(in @ X382 @ (esk9_1 @ X379))|~(in @ X382 @ X379)|~(in @ X380 @ X379)))&((epred1_0)&((descrp)&((~(in @ X385 @ X383)|(~(X384 @ X385)|(in @ X385 @ (dsetconstr @ X383 @ (^[Z0:$i]:((X384 @ Z0)))))))&((~(in @ X388 @ (dsetconstr @ X386 @ (^[Z0:$i]:((X387 @ Z0)))))|(in @ X388 @ X386))&((~(in @ X391 @ (dsetconstr @ X389 @ (^[Z0:$i]:((X390 @ Z0)))))|(X390 @ X391))&(((((X392 @ (esk11_1 @ X392))|((X392 @ (esk10_2 @ X392 @ X393))|~(X392 @ X393)))&(~(X392 @ X396)|((esk11_1 @ X392)=(X396))|((X392 @ (esk10_2 @ X392 @ X393))|~(X392 @ X393))))&(((X392 @ (esk11_1 @ X392))|(((X393)!=(esk10_2 @ X392 @ X393))|~(X392 @ X393)))&(~(X392 @ X396)|((esk11_1 @ X392)=(X396))|(((X393)!=(esk10_2 @ X392 @ X393))|~(X392 @ X393)))))&((~(in @ X398 @ (prop2set @ ((X397))))|(X397))&((~(in @ X399 @ emptyset)|(X400))&(~(in @ X401 @ emptyset)&(~(in @ X402 @ emptyset)&((((X403 @ (esk12_2 @ X403 @ X404))|~(X403 @ X404)|(X403 @ (esk13_1 @ X403)))&(((X404)!=(esk12_2 @ X403 @ X404))|~(X403 @ X404)|(X403 @ (esk13_1 @ X403))))&(((((in @ (esk15_2 @ X407 @ X408) @ X408)|((X407)=(X408))|(in @ (esk14_2 @ X407 @ X408) @ X407))&(~(in @ (esk15_2 @ X407 @ X408) @ X407)|((X407)=(X408))|(in @ (esk14_2 @ X407 @ X408) @ X407)))&(((in @ (esk15_2 @ X407 @ X408) @ X408)|((X407)=(X408))|~(in @ (esk14_2 @ X407 @ X408) @ X408))&(~(in @ (esk15_2 @ X407 @ X408) @ X407)|((X407)=(X408))|~(in @ (esk14_2 @ X407 @ X408) @ X408))))&(((in @ (esk16_1 @ X411) @ X411)|((X411)=(emptyset)))&(((in @ (esk17_1 @ X413) @ X413)|((X413)=(emptyset)))&(((~(in @ X417 @ (dsetconstr @ X415 @ (^[Z0:$i]:((X416 @ Z0)))))|(X416 @ X417)|~(in @ X417 @ X415))&(~(X416 @ X417)|(in @ X417 @ (dsetconstr @ X415 @ (^[Z0:$i]:((X416 @ Z0)))))|~(in @ X417 @ X415)))&((((X418)=(emptyset))|(in @ (esk18_1 @ X418) @ X418))&((~(in @ X422 @ X420)|(~(X421 @ X422)|((dsetconstr @ X420 @ (^[Z0:$i]:((X421 @ Z0))))!=(emptyset))))&((~(in @ X424 @ X423)|((X423)!=(emptyset)))&((in @ X425 @ (setadjoin @ X425 @ X426))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X429 @ X428)|(in @ X429 @ (setadjoin @ X427 @ X428)))&(((((in @ X432 @ X431)|(X433)|((X432)=(X430))|~(in @ X432 @ (setadjoin @ X430 @ X431)))&(~(X433)|(X433)|((X432)=(X430))|~(in @ X432 @ (setadjoin @ X430 @ X431))))&(((in @ X432 @ X431)|(X433)|~(X433)|~(in @ X432 @ (setadjoin @ X430 @ X431)))&(~(X433)|(X433)|~(X433)|~(in @ X432 @ (setadjoin @ X430 @ X431)))))&((~(in @ X436 @ (setadjoin @ X434 @ X435))|(((X436)=(X434))|(in @ X436 @ X435)))&(((dsetconstr @ X437 @ (^[Z0:$i]:(($true))))=(X437))&((((in @ (esk19_2 @ X438 @ X439) @ X439)|(in @ X439 @ (powerset @ X438)))&(~(in @ (esk19_2 @ X438 @ X439) @ X438)|(in @ X439 @ (powerset @ X438))))&((in @ emptyset @ (powerset @ X441))&((in @ emptyset @ (powerset @ X442))&((~(in @ X444 @ (powerset @ X443))|(~(in @ X445 @ X444)|(in @ X445 @ X443)))&((~(in @ X447 @ X448)|(~(in @ X448 @ X446)|(in @ X447 @ (setunion @ X446))))&((((in @ X450 @ (esk20_3 @ X449 @ X450 @ X451))|(X451)|~(in @ X450 @ (setunion @ X449)))&(((in @ (esk20_3 @ X449 @ X450 @ X451) @ X449)|(X451)|~(in @ X450 @ (setunion @ X449)))&(~(X451)|(X451)|~(in @ X450 @ (setunion @ X449)))))&((~(in @ X454 @ X453)|(in @ X454 @ (powerset @ (setunion @ X453))))&((((~(X455 @ X459)|((X459)=(esk22_1 @ X455))|((X455 @ (esk21_2 @ X455 @ X456))|~(X455 @ X456)))&(((X460)!=(esk22_1 @ X455))|(X455 @ X460)|((X455 @ (esk21_2 @ X455 @ X456))|~(X455 @ X456))))&((~(X455 @ X459)|((X459)=(esk22_1 @ X455))|(((X456)!=(esk21_2 @ X455 @ X456))|~(X455 @ X456)))&(((X460)!=(esk22_1 @ X455))|(X455 @ X460)|(((X456)!=(esk21_2 @ X455 @ X456))|~(X455 @ X456)))))&((((X461)=(emptyset))|(in @ (esk23_1 @ X461) @ X461))&((~(in @ X463 @ (setadjoin @ X464 @ emptyset))|((X463)=(X464)))&((((X465)=(X466))|~(in @ X466 @ (setadjoin @ X465 @ emptyset)))&((((X467)!=(X468))|(in @ X467 @ (setadjoin @ X468 @ emptyset)))&((~(in @ X469 @ (setadjoin @ X470 @ emptyset))|(in @ X470 @ (setadjoin @ X469 @ emptyset)))&((~(in @ X473 @ (setadjoin @ X471 @ (setadjoin @ X472 @ emptyset)))|(((X473)=(X471))|((X473)=(X472))))&((in @ X474 @ (setadjoin @ X474 @ (setadjoin @ X475 @ emptyset)))&((in @ X477 @ (setadjoin @ X476 @ (setadjoin @ X477 @ emptyset)))&((~(in @ X480 @ X478)|~(X479 @ X480)|((dsetconstr @ X478 @ (^[Z0:$i]:((X479 @ Z0))))!=(emptyset)))&((~(in @ X482 @ emptyset)|(X481 @ X482))&((((in @ (esk24_2 @ X483 @ X484) @ X483)|(~(in @ X485 @ X483)|(X484 @ X485)))&(~(X484 @ (esk24_2 @ X483 @ X484))|(~(in @ X485 @ X483)|(X484 @ X485))))&((((in @ (esk25_2 @ X487 @ X488) @ X487)|(~(in @ X490 @ X487)|~(X488 @ X490)))&((X488 @ (esk25_2 @ X487 @ X488))|(~(in @ X490 @ X487)|~(X488 @ X490))))&((((in @ (esk26_2 @ X491 @ X492) @ X491)|(~(in @ X494 @ X491)|~(X492 @ X494)))&((X492 @ (esk26_2 @ X491 @ X492))|(~(in @ X494 @ X491)|~(X492 @ X494))))&((((in @ (esk27_2 @ X495 @ X496) @ X495)|(~(in @ X497 @ X495)|(X496 @ X497)))&(~(X496 @ (esk27_2 @ X495 @ X496))|(~(in @ X497 @ X495)|(X496 @ X497))))&((~(X499)|(in @ emptyset @ (prop2set @ ((X499)))))&((epred2_0)&~(in @ emptyset @ (prop2set @ ((epred2_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_84])])])])])])).
% 0.23/0.29 thf(c_0_86, negated_conjecture, ~((in @ emptyset @ (prop2set @ ((epred2_0))))), inference(split_conjunct,[status(thm)],[c_0_85])).
% 0.23/0.29 thf(c_0_87, negated_conjecture, (epred2_0), inference(split_conjunct,[status(thm)],[c_0_85])).
% 0.23/0.29 thf(c_0_88, negated_conjecture, (in @ emptyset @ (prop2set @ (($true)))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_85])])])).
% 0.23/0.29 thf(c_0_89, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86, c_0_87]), c_0_88])]), ['proof']).
% 0.23/0.29 % SZS output end CNFRefutation
% 0.23/0.29 % Parsed axioms : 130
% 0.23/0.29 % Removed by relevancy pruning/SinE : 70
% 0.23/0.29 % Initial clauses : 111
% 0.23/0.29 % Removed in clause preprocessing : 4
% 0.23/0.29 % Initial clauses in saturation : 107
% 0.23/0.29 % Processed clauses : 12
% 0.23/0.29 % ...of these trivial : 1
% 0.23/0.29 % ...subsumed : 3
% 0.23/0.29 % ...remaining for further processing : 7
% 0.23/0.29 % Other redundant clauses eliminated : 0
% 0.23/0.29 % Clauses deleted for lack of memory : 0
% 0.23/0.29 % Backward-subsumed : 0
% 0.23/0.29 % Backward-rewritten : 0
% 0.23/0.29 % Generated clauses : 0
% 0.23/0.29 % ...of the previous two non-redundant : 0
% 0.23/0.29 % ...aggressively subsumed : 0
% 0.23/0.29 % Contextual simplify-reflections : 0
% 0.23/0.29 % Paramodulations : 0
% 0.23/0.29 % Factorizations : 0
% 0.23/0.29 % NegExts : 0
% 0.23/0.29 % Equation resolutions : 0
% 0.23/0.29 % Disequality decompositions : 0
% 0.23/0.29 % Total rewrite steps : 3
% 0.23/0.29 % ...of those cached : 0
% 0.23/0.29 % Propositional unsat checks : 0
% 0.23/0.29 % Propositional check models : 0
% 0.23/0.29 % Propositional check unsatisfiable : 0
% 0.23/0.29 % Propositional clauses : 0
% 0.23/0.29 % Propositional clauses after purity: 0
% 0.23/0.29 % Propositional unsat core size : 0
% 0.23/0.29 % Propositional preprocessing time : 0.000
% 0.23/0.29 % Propositional encoding time : 0.000
% 0.23/0.29 % Propositional solver time : 0.000
% 0.23/0.29 % Success case prop preproc time : 0.000
% 0.23/0.29 % Success case prop encoding time : 0.000
% 0.23/0.29 % Success case prop solver time : 0.000
% 0.23/0.29 % Current number of processed clauses : 7
% 0.23/0.29 % Positive orientable unit clauses : 6
% 0.23/0.29 % Positive unorientable unit clauses: 0
% 0.23/0.29 % Negative unit clauses : 1
% 0.23/0.29 % Non-unit-clauses : 0
% 0.23/0.29 % Current number of unprocessed clauses: 95
% 0.23/0.29 % ...number of literals in the above : 294
% 0.23/0.29 % Current number of archived formulas : 0
% 0.23/0.29 % Current number of archived clauses : 0
% 0.23/0.29 % Clause-clause subsumption calls (NU) : 0
% 0.23/0.29 % Rec. Clause-clause subsumption calls : 0
% 0.23/0.29 % Non-unit clause-clause subsumptions : 0
% 0.23/0.29 % Unit Clause-clause subsumption calls : 0
% 0.23/0.29 % Rewrite failures with RHS unbound : 0
% 0.23/0.29 % BW rewrite match attempts : 0
% 0.23/0.29 % BW rewrite match successes : 0
% 0.23/0.29 % Condensation attempts : 0
% 0.23/0.29 % Condensation successes : 0
% 0.23/0.29 % Termbank termtop insertions : 12386
% 0.23/0.29 % Search garbage collected termcells : 4800
% 0.23/0.29
% 0.23/0.29 % -------------------------------------------------
% 0.23/0.29 % User time : 0.013 s
% 0.23/0.29 % System time : 0.004 s
% 0.23/0.29 % Total time : 0.016 s
% 0.23/0.29 % Maximum resident set size: 4996 pages
% 0.23/0.29
% 0.23/0.29 % -------------------------------------------------
% 0.23/0.29 % User time : 0.015 s
% 0.23/0.29 % System time : 0.007 s
% 0.23/0.29 % Total time : 0.022 s
% 0.23/0.29 % Maximum resident set size: 5120 pages
% 0.23/0.29 % E exiting
%------------------------------------------------------------------------------