%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU544^1 : 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 : n012.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 08:26:39 AM UTC 2026
% Result : Theorem 0.09s 0.16s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU544^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 13:48:48 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.12 Running higher-order theorem proving
% 0.09/0.13 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.sWohEi44hV/E---3.1_131901.p
% 0.09/0.16 % Version: 3.5.1-ho
% 0.09/0.16 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.09/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.16 % Starting sh5l with 300s (1) cores
% 0.09/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.16 % Starting new_bool_2 with 300s (1) cores
% 0.09/0.16 % new_bool_2 with pid 131936 completed with status 0
% 0.09/0.16 % Result found by new_bool_2
% 0.09/0.16 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.09/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.16 % Starting sh5l with 300s (1) cores
% 0.09/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.16 % Starting new_bool_2 with 300s (1) cores
% 0.09/0.16 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.16 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.16 % Search class: HGHSM-FFMM31-SHSSMSBN
% 0.09/0.16 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.16 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.16 % SubtermCWHack with pid 131939 completed with status 0
% 0.09/0.16 % Result found by SubtermCWHack
% 0.09/0.16 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.09/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.16 % Starting sh5l with 300s (1) cores
% 0.09/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.16 % Starting new_bool_2 with 300s (1) cores
% 0.09/0.16 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.16 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.16 % Search class: HGHSM-FFMM31-SHSSMSBN
% 0.09/0.16 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.16 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.16 % Preprocessing time : 0.002 s
% 0.09/0.16
% 0.09/0.16 % Proof found!
% 0.09/0.16 % SZS status Theorem
% 0.09/0.16 % SZS output start CNFRefutation
% 0.09/0.16 thf(decl_23, type, in: $i > $i > $o).
% 0.09/0.16 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.09/0.16 thf(decl_25, type, setextAx: $o).
% 0.09/0.16 thf(decl_26, type, emptyset: $i).
% 0.09/0.16 thf(decl_27, type, emptysetAx: $o).
% 0.09/0.16 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.09/0.16 thf(decl_29, type, setadjoinAx: $o).
% 0.09/0.16 thf(decl_30, type, powerset: $i > $i).
% 0.09/0.16 thf(decl_31, type, powersetAx: $o).
% 0.09/0.16 thf(decl_32, type, setunion: $i > $i).
% 0.09/0.16 thf(decl_33, type, setunionAx: $o).
% 0.09/0.16 thf(decl_34, type, omega: $i).
% 0.09/0.16 thf(decl_35, type, omega0Ax: $o).
% 0.09/0.16 thf(decl_36, type, omegaSAx: $o).
% 0.09/0.16 thf(decl_37, type, omegaIndAx: $o).
% 0.09/0.16 thf(decl_38, type, replAx: $o).
% 0.09/0.16 thf(decl_39, type, foundationAx: $o).
% 0.09/0.16 thf(decl_40, type, wellorderingAx: $o).
% 0.09/0.16 thf(decl_42, type, descrp: $o).
% 0.09/0.16 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.09/0.16 thf(decl_44, type, dsetconstrI: $o).
% 0.09/0.16 thf(decl_45, type, dsetconstrEL: $o).
% 0.09/0.16 thf(decl_46, type, dsetconstrER: $o).
% 0.09/0.16 thf(decl_47, type, exuE1: $o).
% 0.09/0.16 thf(decl_48, type, prop2set: $o > $i).
% 0.09/0.16 thf(decl_49, type, prop2setE: $o).
% 0.09/0.16 thf(decl_50, type, emptysetE: $o).
% 0.09/0.16 thf(decl_51, type, emptysetimpfalse: $o).
% 0.09/0.16 thf(decl_52, type, notinemptyset: $o).
% 0.09/0.16 thf(decl_53, type, exuE3e: $o).
% 0.09/0.16 thf(decl_54, type, setext: $o).
% 0.09/0.16 thf(decl_55, type, emptyI: $o).
% 0.09/0.16 thf(decl_56, type, noeltsimpempty: $o).
% 0.09/0.16 thf(decl_57, type, setbeta: $o).
% 0.09/0.16 thf(decl_58, type, nonempty: $i > $o).
% 0.09/0.16 thf(decl_59, type, nonemptyE1: $o).
% 0.09/0.16 thf(decl_60, type, nonemptyI: $o).
% 0.09/0.16 thf(decl_61, type, nonemptyI1: $o).
% 0.09/0.16 thf(decl_62, type, setadjoinIL: $o).
% 0.09/0.16 thf(decl_63, type, emptyinunitempty: $o).
% 0.09/0.16 thf(decl_64, type, setadjoinIR: $o).
% 0.09/0.16 thf(decl_65, type, setadjoinE: $o).
% 0.09/0.16 thf(decl_66, type, setadjoinOr: $o).
% 0.09/0.16 thf(decl_67, type, setoftrueEq: $o).
% 0.09/0.16 thf(decl_68, type, powersetI: $o).
% 0.09/0.16 thf(decl_69, type, emptyinPowerset: $o).
% 0.09/0.16 thf(decl_70, type, emptyInPowerset: $o).
% 0.09/0.16 thf(decl_71, type, powersetE: $o).
% 0.09/0.16 thf(decl_72, type, setunionI: $o).
% 0.09/0.16 thf(decl_73, type, setunionE: $o).
% 0.09/0.16 thf(decl_74, type, subPowSU: $o).
% 0.09/0.16 thf(decl_75, type, exuE2: $o).
% 0.09/0.16 thf(decl_76, type, nonemptyImpWitness: $o).
% 0.09/0.16 thf(decl_77, type, uniqinunit: $o).
% 0.09/0.16 thf(decl_78, type, notinsingleton: $o).
% 0.09/0.16 thf(decl_79, type, eqinunit: $o).
% 0.09/0.16 thf(decl_80, type, singletonsswitch: $o).
% 0.09/0.16 thf(decl_81, type, upairsetE: $o).
% 0.09/0.16 thf(decl_82, type, upairsetIL: $o).
% 0.09/0.16 thf(decl_83, type, upairsetIR: $o).
% 0.09/0.16 thf(decl_84, type, emptyE1: $o).
% 0.09/0.16 thf(decl_85, type, vacuousDall: $o).
% 0.09/0.16 thf(decl_86, type, quantDeMorgan1: $o).
% 0.09/0.16 thf(decl_87, type, quantDeMorgan2: $o).
% 0.09/0.16 thf(decl_88, type, quantDeMorgan3: $o).
% 0.09/0.16 thf(decl_89, type, quantDeMorgan4: $o).
% 0.09/0.16 thf(decl_90, type, prop2setI: $o).
% 0.09/0.16 thf(decl_92, type, prop2set2propI: $o).
% 0.09/0.16 thf(decl_93, type, notdexE: $o).
% 0.09/0.16 thf(decl_94, type, notdallE: $o).
% 0.09/0.16 thf(decl_95, type, epred1_0: $o).
% 0.09/0.16 thf(decl_96, type, esk1_2: $i > $i > $i).
% 0.09/0.16 thf(decl_97, type, esk2_2: $i > $i > $i).
% 0.09/0.16 thf(decl_98, type, esk3_2: $i > $i > $i).
% 0.09/0.16 thf(decl_99, type, esk4_1: $i > $i).
% 0.09/0.16 thf(decl_100, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.09/0.16 thf(decl_101, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.09/0.16 thf(decl_102, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.09/0.16 thf(decl_103, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.09/0.16 thf(decl_104, type, esk9_1: $i > $i).
% 0.09/0.16 thf(decl_105, type, esk10_2: ($i > $o) > $i > $i).
% 0.09/0.16 thf(decl_106, type, esk11_1: ($i > $o) > $i).
% 0.09/0.16 thf(decl_107, type, esk12_2: ($i > $o) > $i > $i).
% 0.09/0.16 thf(decl_108, type, esk13_1: ($i > $o) > $i).
% 0.09/0.16 thf(decl_109, type, esk14_2: $i > $i > $i).
% 0.09/0.16 thf(decl_110, type, esk15_2: $i > $i > $i).
% 0.09/0.16 thf(decl_111, type, esk16_1: $i > $i).
% 0.09/0.16 thf(decl_112, type, esk17_1: $i > $i).
% 0.09/0.16 thf(decl_113, type, esk18_1: $i > $i).
% 0.09/0.16 thf(decl_114, type, esk19_2: $i > $i > $i).
% 0.09/0.16 thf(decl_115, type, esk20_3: $i > $i > $o > $i).
% 0.09/0.16 thf(decl_116, type, esk21_2: ($i > $o) > $i > $i).
% 0.09/0.16 thf(decl_117, type, esk22_1: ($i > $o) > $i).
% 0.09/0.16 thf(decl_118, type, esk23_1: $i > $i).
% 0.09/0.16 thf(decl_119, type, esk24_2: $i > ($i > $o) > $i).
% 0.09/0.16 thf(decl_120, type, esk25_2: $i > ($i > $o) > $i).
% 0.09/0.16 thf(decl_121, type, esk26_2: $i > ($i > $o) > $i).
% 0.09/0.16 thf(decl_122, type, esk27_2: $i > ($i > $o) > $i).
% 0.09/0.16 thf(decl_123, type, esk28_2: $i > ($i > $o) > $i).
% 0.09/0.16 thf(decl_124, type, esk29_2: $i > ($i > $o) > $i).
% 0.09/0.16 thf(decl_125, type, epred2_0: $i > $o).
% 0.09/0.16 thf(decl_126, type, esk30_0: $i).
% 0.09/0.16 thf(decl_127, type, esk31_1: $i > $i).
% 0.09/0.16 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', exuE1)).
% 0.09/0.16 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', exu)).
% 0.09/0.16 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', replAx)).
% 0.09/0.16 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', exuE3e)).
% 0.09/0.16 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', nonempty)).
% 0.09/0.16 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', nonemptyI)).
% 0.09/0.16 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', exuE2)).
% 0.09/0.16 thf(exuI1, 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)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', exuI1)).
% 0.09/0.16 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.sWohEi44hV/E---3.1_131901.p', emptyE1)).
% 0.09/0.16 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', dsetconstrER)).
% 0.09/0.16 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', dsetconstrEL)).
% 0.09/0.16 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', dsetconstrI)).
% 0.09/0.16 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', setbeta)).
% 0.09/0.16 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', nonemptyI1)).
% 0.09/0.16 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', nonemptyE1)).
% 0.09/0.16 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', setoftrueEq)).
% 0.09/0.16 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', nonemptyImpWitness)).
% 0.09/0.16 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', singletonsswitch)).
% 0.09/0.16 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', eqinunit)).
% 0.09/0.16 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', upairsetE)).
% 0.09/0.16 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', upairsetIL)).
% 0.09/0.16 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', omegaSAx)).
% 0.09/0.16 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', upairsetIR)).
% 0.09/0.16 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', omega0Ax)).
% 0.09/0.16 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', setunionAx)).
% 0.09/0.16 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', vacuousDall)).
% 0.09/0.16 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', powersetAx)).
% 0.09/0.16 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', quantDeMorgan1)).
% 0.09/0.16 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', setadjoinAx)).
% 0.09/0.16 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', quantDeMorgan2)).
% 0.09/0.16 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', emptysetAx)).
% 0.09/0.16 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', quantDeMorgan3)).
% 0.09/0.16 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.sWohEi44hV/E---3.1_131901.p', omegaIndAx)).
% 0.09/0.16 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', quantDeMorgan4)).
% 0.09/0.16 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', prop2setI)).
% 0.09/0.16 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', notdexE)).
% 0.09/0.16 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', notdallE)).
% 0.09/0.16 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', setadjoinE)).
% 0.09/0.16 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', setadjoinIR)).
% 0.09/0.16 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', wellorderingAx)).
% 0.09/0.16 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', foundationAx)).
% 0.09/0.16 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', prop2setE)).
% 0.09/0.16 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', noeltsimpempty)).
% 0.09/0.16 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', emptyI)).
% 0.09/0.16 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', setext)).
% 0.09/0.16 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', notinemptyset)).
% 0.09/0.16 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', emptysetimpfalse)).
% 0.09/0.16 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', emptysetE)).
% 0.09/0.16 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', emptyinunitempty)).
% 0.09/0.16 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', setadjoinIL)).
% 0.09/0.16 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', setadjoinOr)).
% 0.09/0.16 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', setunionE)).
% 0.09/0.16 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', setunionI)).
% 0.09/0.16 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', powersetE)).
% 0.09/0.16 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', emptyInPowerset)).
% 0.09/0.16 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', emptyinPowerset)).
% 0.09/0.16 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', powersetI)).
% 0.09/0.16 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', uniqinunit)).
% 0.09/0.16 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', notinsingleton)).
% 0.09/0.16 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', subPowSU)).
% 0.09/0.16 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.sWohEi44hV/E---3.1_131901.p', setextAx)).
% 0.09/0.16 thf(c_0_61, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.09/0.16 thf(c_0_62, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.09/0.16 thf(c_0_63, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.09/0.16 thf(c_0_64, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.09/0.16 thf(c_0_65, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.09/0.16 thf(c_0_66, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.09/0.16 thf(c_0_67, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.09/0.16 thf(c_0_68, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[exuI1])).
% 0.09/0.16 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])).
% 0.09/0.16 thf(c_0_70, plain, ((exuE1)=(![X1:$i > $o]:((((?[X186:$i]:(((((X1 @ X186)))&(![X187:$i]:(((((X1 @ X187)))=>(((X186)=(X187))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_61, c_0_62])).
% 0.09/0.16 thf(c_0_71, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.09/0.16 thf(c_0_72, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.09/0.16 thf(c_0_73, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.09/0.16 thf(c_0_74, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X184:$i]:(((((X6 @ X2 @ X184)))&(![X185:$i]:(((((X6 @ X2 @ X185)))=>(((X184)=(X185)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_63, c_0_62])).
% 0.09/0.16 thf(c_0_75, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X188:$i]:(((((X1 @ X188)))&(![X189:$i]:(((((X1 @ X189)))=>(((X188)=(X189))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_64, c_0_62])).
% 0.09/0.16 thf(c_0_76, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.09/0.16 thf(c_0_77, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_65])).
% 0.09/0.16 thf(c_0_78, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_66, c_0_65])).
% 0.09/0.16 thf(c_0_79, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_65])).
% 0.09/0.16 thf(c_0_80, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.09/0.16 thf(c_0_81, plain, ((exuE2)=(![X1:$i > $o]:((((?[X190:$i]:(((((X1 @ X190)))&(![X191:$i]:(((((X1 @ X191)))=>(((X190)=(X191))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_67, c_0_62])).
% 0.09/0.16 thf(c_0_82, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_65])).
% 0.09/0.16 thf(c_0_83, plain, ((epred1_0)<=>![X221:$i]:(?[X222:$i]:((((![X223:$i]:(((in @ X223 @ X222)=>![X224:$i]:(((in @ X224 @ X223)=>(in @ X224 @ X221)))))&![X225:$i, X226:$i]:((((in @ X225 @ X221)&(in @ X226 @ X221))=>(![X227:$i]:(((in @ X227 @ X222)=>((in @ X225 @ X227)<=>(in @ X226 @ X227))))=>((X225)=(X226))))))&![X228:$i, X229:$i]:((((in @ X228 @ X222)&(in @ X229 @ X222))=>(![X230:$i]:(((in @ X230 @ X228)=>(in @ X230 @ X229)))|![X231:$i]:(((in @ X231 @ X229)=>(in @ X231 @ X228)))))))&![X232:$i]:(((![X233:$i]:(((in @ X233 @ X232)=>(in @ X233 @ X221)))&?[X234:$i]:((in @ X234 @ X232)))=>?[X235:$i, X236:$i]:(((((in @ X235 @ X222)&(in @ X236 @ X232))&~(?[X237:$i]:(((in @ X237 @ X235)&(in @ X237 @ X232)))))&![X238:$i]:(((in @ X238 @ X222)=>(![X239:$i]:(((in @ X239 @ X238)=>(in @ X239 @ X235)))|(in @ X236 @ X238)))))))))))), introduced(definition)).
% 0.09/0.16 thf(c_0_84, negated_conjecture, ~((![X192:$i, X193:$i]:((![X194:$i]:(((in @ X194 @ X192)<=>(in @ X194 @ X193)))=>((X192)=(X193))))=>(![X195:$i]:(~(in @ X195 @ emptyset))=>(![X196:$i, X197:$i, X198:$i]:(((in @ X198 @ (setadjoin @ X196 @ X197))<=>(((X198)=(X196))|(in @ X198 @ X197))))=>(![X199:$i, X200:$i]:(((in @ X200 @ (powerset @ X199))<=>![X201:$i]:(((in @ X201 @ X200)=>(in @ X201 @ X199)))))=>(![X202:$i, X203:$i]:(((in @ X203 @ (setunion @ X202))<=>?[X204:$i]:(((in @ X203 @ X204)&(in @ X204 @ X202)))))=>((in @ emptyset @ omega)=>(![X205:$i]:(((in @ X205 @ omega)=>(in @ (setadjoin @ X205 @ X205) @ omega)))=>(![X206:$i]:((((in @ emptyset @ X206)&![X207:$i]:((((in @ X207 @ omega)&(in @ X207 @ X206))=>(in @ (setadjoin @ X207 @ X207) @ X206))))=>![X208:$i]:(((in @ X208 @ omega)=>(in @ X208 @ X206)))))=>(![X209:$i > $i > $o, X210:$i]:((![X211:$i]:(((in @ X211 @ X210)=>?[X212:$i]:(((X209 @ X211 @ X212)&![X213:$i]:(((X209 @ X211 @ X213)=>((X212)=(X213))))))))=>?[X214:$i]:(![X215:$i]:(((in @ X215 @ X214)<=>?[X216:$i]:(((in @ X216 @ X210)&(X209 @ X216 @ X215))))))))=>(![X217:$i]:((?[X218:$i]:((in @ X218 @ X217))=>?[X219:$i]:(((in @ X219 @ X217)&~(?[X220:$i]:(((in @ X220 @ X219)&(in @ X220 @ X217))))))))=>((epred1_0)=>((descrp)=>(![X240:$i, X241:$i > $o, X242:$i]:(((in @ X242 @ X240)=>((X241 @ X242)=>(in @ X242 @ (dsetconstr @ X240 @ (^[Z0:$i]:((X241 @ Z0))))))))=>(![X243:$i, X244:$i > $o, X245:$i]:(((in @ X245 @ (dsetconstr @ X243 @ (^[Z0:$i]:((X244 @ Z0)))))=>(in @ X245 @ X243)))=>(![X246:$i, X247:$i > $o, X248:$i]:(((in @ X248 @ (dsetconstr @ X246 @ (^[Z0:$i]:((X247 @ Z0)))))=>(X247 @ X248)))=>(![X249:$i > $o]:((?[X250:$i]:(((X249 @ X250)&![X251:$i]:(((X249 @ X251)=>((X250)=(X251))))))=>?[X252:$i]:(((X249 @ X252)&![X253:$i]:(((X249 @ X253)=>((X252)=(X253))))))))=>(![X254:$o, X255:$i]:(((in @ X255 @ (prop2set @ ((X254))))=>(X254)))=>(![X256:$i]:(((in @ X256 @ emptyset)=>![X257:$o]:((X257))))=>(![X258:$i]:(~(in @ X258 @ emptyset))=>(![X259:$i]:(~(in @ X259 @ emptyset))=>(![X260:$i > $o]:((?[X261:$i]:(((X260 @ X261)&![X262:$i]:(((X260 @ X262)=>((X261)=(X262))))))=>?[X263:$i]:((X260 @ X263))))=>(![X264:$i, X265:$i]:((![X266:$i]:(((in @ X266 @ X264)=>(in @ X266 @ X265)))=>(![X267:$i]:(((in @ X267 @ X265)=>(in @ X267 @ X264)))=>((X264)=(X265)))))=>(![X268:$i]:((![X269:$i]:(~(in @ X269 @ X268))=>((X268)=(emptyset))))=>(![X270:$i]:((![X271:$i]:(~(in @ X271 @ X270))=>((X270)=(emptyset))))=>(![X272:$i, X273:$i > $o, X274:$i]:(((in @ X274 @ X272)=>((in @ X274 @ (dsetconstr @ X272 @ (^[Z0:$i]:((X273 @ Z0)))))<=>(X273 @ X274))))=>(![X275:$i]:((((X275)!=(emptyset))=>?[X276:$i]:((in @ X276 @ X275))))=>(![X277:$i, X278:$i > $o, X279:$i]:(((in @ X279 @ X277)=>((X278 @ X279)=>((dsetconstr @ X277 @ (^[Z0:$i]:((X278 @ Z0))))!=(emptyset)))))=>(![X280:$i]:((?[X281:$i]:((in @ X281 @ X280))=>((X280)!=(emptyset))))=>(![X282:$i, X283:$i]:((in @ X282 @ (setadjoin @ X282 @ X283)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X284:$i, X285:$i, X286:$i]:(((in @ X286 @ X285)=>(in @ X286 @ (setadjoin @ X284 @ X285))))=>(![X287:$i, X288:$i, X289:$i]:(((in @ X289 @ (setadjoin @ X287 @ X288))=>![X290:$o]:(((((X289)=(X287))=>(X290))=>(((in @ X289 @ X288)=>(X290))=>(X290))))))=>(![X291:$i, X292:$i, X293:$i]:(((in @ X293 @ (setadjoin @ X291 @ X292))=>(((X293)=(X291))|(in @ X293 @ X292))))=>(![X294:$i]:(((dsetconstr @ X294 @ (^[Z0:$i]:(($true))))=(X294)))=>(![X295:$i, X296:$i]:((![X297:$i]:(((in @ X297 @ X296)=>(in @ X297 @ X295)))=>(in @ X296 @ (powerset @ X295))))=>(![X298:$i]:((in @ emptyset @ (powerset @ X298)))=>(![X299:$i]:((in @ emptyset @ (powerset @ X299)))=>(![X300:$i, X301:$i, X302:$i]:(((in @ X301 @ (powerset @ X300))=>((in @ X302 @ X301)=>(in @ X302 @ X300))))=>(![X303:$i, X304:$i, X305:$i]:(((in @ X304 @ X305)=>((in @ X305 @ X303)=>(in @ X304 @ (setunion @ X303)))))=>(![X306:$i, X307:$i]:(((in @ X307 @ (setunion @ X306))=>![X308:$o]:((![X309:$i]:(((in @ X307 @ X309)=>((in @ X309 @ X306)=>(X308))))=>(X308)))))=>(![X310:$i, X311:$i]:(((in @ X311 @ X310)=>(in @ X311 @ (powerset @ (setunion @ X310)))))=>(![X312:$i > $o]:((?[X313:$i]:(((X312 @ X313)&![X314:$i]:(((X312 @ X314)=>((X313)=(X314))))))=>?[X315:$i]:(![X316:$i]:(((X312 @ X316)<=>((X316)=(X315)))))))=>(![X317:$i]:((((X317)!=(emptyset))=>?[X318:$i]:((in @ X318 @ X317))))=>(![X319:$i, X320:$i]:(((in @ X319 @ (setadjoin @ X320 @ emptyset))=>((X319)=(X320))))=>(![X321:$i, X322:$i]:((((X321)!=(X322))=>~(in @ X322 @ (setadjoin @ X321 @ emptyset))))=>(![X323:$i, X324:$i]:((((X323)=(X324))=>(in @ X323 @ (setadjoin @ X324 @ emptyset))))=>(![X325:$i, X326:$i]:(((in @ X325 @ (setadjoin @ X326 @ emptyset))=>(in @ X326 @ (setadjoin @ X325 @ emptyset))))=>(![X327:$i, X328:$i, X329:$i]:(((in @ X329 @ (setadjoin @ X327 @ (setadjoin @ X328 @ emptyset)))=>(((X329)=(X327))|((X329)=(X328)))))=>(![X330:$i, X331:$i]:((in @ X330 @ (setadjoin @ X330 @ (setadjoin @ X331 @ emptyset))))=>(![X332:$i, X333:$i]:((in @ X333 @ (setadjoin @ X332 @ (setadjoin @ X333 @ emptyset))))=>(![X334:$i, X335:$i > $o]:((?[X336:$i]:(((in @ X336 @ X334)&(X335 @ X336)))=>((dsetconstr @ X334 @ (^[Z0:$i]:((X335 @ Z0))))!=(emptyset))))=>(![X337:$i > $o, X338:$i]:(((in @ X338 @ emptyset)=>(X337 @ 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:$i]:(((in @ X350 @ X347)=>~(X348 @ X350)))))=>(![X351:$i, X352:$i > $o]:((?[X353:$i]:(((in @ X353 @ X351)&~(X352 @ X353)))=>~(![X354:$i]:(((in @ X354 @ X351)=>(X352 @ X354))))))=>(![X355:$o]:(((X355)=>(in @ emptyset @ (prop2set @ ((X355))))))=>((prop2set2propI)=>(![X356:$i, X357:$i > $o]:((~(?[X358:$i]:(((in @ X358 @ X356)&(X357 @ X358))))=>![X359:$i]:(((in @ X359 @ X356)=>~(X357 @ X359)))))=>(![X360:$i, X361:$i > $o]:((~(![X362:$i]:(((in @ X362 @ X360)=>(X361 @ X362))))=>?[X363:$i]:(((in @ X363 @ X360)&~(X361 @ X363)))))=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>?[X364:$i]:(((X1 @ X364)&![X365:$i]:(((X1 @ X365)=>((X364)=(X365))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_68]), singletonsswitch]), eqinunit]), upairsetE]), upairsetIL]), omegaSAx]), upairsetIR]), omega0Ax]), c_0_69]), setunionAx]), vacuousDall]), powersetAx]), quantDeMorgan1]), setadjoinAx]), quantDeMorgan2]), emptysetAx]), quantDeMorgan3]), omegaIndAx]), quantDeMorgan4]), prop2setI]), notdexE]), notdallE]), c_0_62]), setadjoinE]), setadjoinIR]), c_0_70]), c_0_71]), c_0_72]), c_0_73]), wellorderingAx]), foundationAx]), c_0_74]), prop2setE]), noeltsimpempty]), emptyI]), setext]), c_0_75]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_76]), emptyinunitempty]), setadjoinIL]), c_0_77]), c_0_78]), c_0_79]), setadjoinOr]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), powersetI]), c_0_80]), c_0_81]), c_0_82]), uniqinunit]), notinsingleton]), subPowSU]), setextAx])]), c_0_83])).
% 0.09/0.16 thf(c_0_85, negated_conjecture, ![X366:$i, X367:$i, X369:$i, X370:$i, X371:$i, X372:$i, X373:$i, X374:$i, X375:$i, X376:$i, X377:$i, X379:$i, X380:$i, X382:$i, X383:$i, X384:$i, X385:$i, X386:$i, X388:$i, X389:$i > $i > $o, X390:$i, X392:$i, X395:$i, X397:$i, X398:$i, X399:$i, X400:$i, X402:$i, X403:$i, X404:$i > $o, X405:$i, X406:$i, X407:$i > $o, X408:$i, X409:$i, X410:$i > $o, X411:$i, X412:$i > $o, X413:$i, X416:$i, X417:$o, X418:$i, X419:$i, X420:$o, X421:$i, X422:$i, X423:$i > $o, X424:$i, X427:$i, X428:$i, X431:$i, X433:$i, X435:$i, X436:$i > $o, X437:$i, X438:$i, X440:$i, X441:$i > $o, X442:$i, X443:$i, X444:$i, X445:$i, X446:$i, X447:$i, X448:$i, X449:$i, X450:$i, X451:$i, X452:$i, X453:$o, X454:$i, X455:$i, X456:$i, X457:$i, X458:$i, X459:$i, X461:$i, X462:$i, X463:$i, X464:$i, X465:$i, X466:$i, X467:$i, X468:$i, X469:$i, X470:$i, X471:$o, X473:$i, X474:$i, X475:$i > $o, X476:$i, X479:$i, X480:$i, X481:$i, X483:$i, X484:$i, X485:$i, X486:$i, X487:$i, X488:$i, X489:$i, X490:$i, X491:$i, X492:$i, X493:$i, X494:$i, X495:$i, X496:$i, X497:$i, X498:$i, X499:$i > $o, X500:$i, X501:$i > $o, X502:$i, X503:$i, X504:$i > $o, X505:$i, X507:$i, X508:$i > $o, X510:$i, X511:$i, X512:$i > $o, X514:$i, X515:$i, X516:$i > $o, X517:$i, X519:$o, X520:$i, X521:$i > $o, X523:$i, X524:$i, X525:$i > $o, X526:$i, X530:$i, X531:$i]:((((~(in @ (esk1_2 @ X366 @ X367) @ X366)|~(in @ (esk1_2 @ X366 @ X367) @ X367)|((X366)=(X367)))&((in @ (esk1_2 @ X366 @ X367) @ X366)|(in @ (esk1_2 @ X366 @ X367) @ X367)|((X366)=(X367))))&(~(in @ X369 @ emptyset)&(((~(in @ X372 @ (setadjoin @ X370 @ X371))|(((X372)=(X370))|(in @ X372 @ X371)))&((((X372)!=(X370))|(in @ X372 @ (setadjoin @ X370 @ X371)))&(~(in @ X372 @ X371)|(in @ X372 @ (setadjoin @ X370 @ X371)))))&(((~(in @ X374 @ (powerset @ X373))|(~(in @ X375 @ X374)|(in @ X375 @ X373)))&(((in @ (esk2_2 @ X376 @ X377) @ X377)|(in @ X377 @ (powerset @ X376)))&(~(in @ (esk2_2 @ X376 @ X377) @ X376)|(in @ X377 @ (powerset @ X376)))))&(((((in @ X380 @ (esk3_2 @ X379 @ X380))|~(in @ X380 @ (setunion @ X379)))&((in @ (esk3_2 @ X379 @ X380) @ X379)|~(in @ X380 @ (setunion @ X379))))&(~(in @ X383 @ X384)|~(in @ X384 @ X382)|(in @ X383 @ (setunion @ X382))))&((in @ emptyset @ omega)&((~(in @ X385 @ omega)|(in @ (setadjoin @ X385 @ X385) @ omega))&(((((in @ (esk4_1 @ X386) @ omega)|~(in @ emptyset @ X386)|(~(in @ X388 @ omega)|(in @ X388 @ X386)))&((in @ (esk4_1 @ X386) @ X386)|~(in @ emptyset @ X386)|(~(in @ X388 @ omega)|(in @ X388 @ X386))))&(~(in @ (setadjoin @ (esk4_1 @ X386) @ (esk4_1 @ X386)) @ X386)|~(in @ emptyset @ X386)|(~(in @ X388 @ omega)|(in @ X388 @ X386))))&((((((in @ (esk8_3 @ X389 @ X390 @ X395) @ X390)|~(in @ X395 @ (esk7_2 @ X389 @ X390))|(in @ (esk5_2 @ X389 @ X390) @ X390))&((X389 @ (esk8_3 @ X389 @ X390 @ X395) @ X395)|~(in @ X395 @ (esk7_2 @ X389 @ X390))|(in @ (esk5_2 @ X389 @ X390) @ X390)))&(~(in @ X398 @ X390)|~(X389 @ X398 @ X397)|(in @ X397 @ (esk7_2 @ X389 @ X390))|(in @ (esk5_2 @ X389 @ X390) @ X390)))&(((((in @ (esk8_3 @ X389 @ X390 @ X395) @ X390)|~(in @ X395 @ (esk7_2 @ X389 @ X390))|((X389 @ (esk5_2 @ X389 @ X390) @ (esk6_3 @ X389 @ X390 @ X392))|~(X389 @ (esk5_2 @ X389 @ X390) @ X392)))&((X389 @ (esk8_3 @ X389 @ X390 @ X395) @ X395)|~(in @ X395 @ (esk7_2 @ X389 @ X390))|((X389 @ (esk5_2 @ X389 @ X390) @ (esk6_3 @ X389 @ X390 @ X392))|~(X389 @ (esk5_2 @ X389 @ X390) @ X392))))&(~(in @ X398 @ X390)|~(X389 @ X398 @ X397)|(in @ X397 @ (esk7_2 @ X389 @ X390))|((X389 @ (esk5_2 @ X389 @ X390) @ (esk6_3 @ X389 @ X390 @ X392))|~(X389 @ (esk5_2 @ X389 @ X390) @ X392))))&((((in @ (esk8_3 @ X389 @ X390 @ X395) @ X390)|~(in @ X395 @ (esk7_2 @ X389 @ X390))|(((X392)!=(esk6_3 @ X389 @ X390 @ X392))|~(X389 @ (esk5_2 @ X389 @ X390) @ X392)))&((X389 @ (esk8_3 @ X389 @ X390 @ X395) @ X395)|~(in @ X395 @ (esk7_2 @ X389 @ X390))|(((X392)!=(esk6_3 @ X389 @ X390 @ X392))|~(X389 @ (esk5_2 @ X389 @ X390) @ X392))))&(~(in @ X398 @ X390)|~(X389 @ X398 @ X397)|(in @ X397 @ (esk7_2 @ X389 @ X390))|(((X392)!=(esk6_3 @ X389 @ X390 @ X392))|~(X389 @ (esk5_2 @ X389 @ X390) @ X392))))))&((((in @ (esk9_1 @ X399) @ X399)|~(in @ X400 @ X399))&(~(in @ X402 @ (esk9_1 @ X399))|~(in @ X402 @ X399)|~(in @ X400 @ X399)))&((epred1_0)&((descrp)&((~(in @ X405 @ X403)|(~(X404 @ X405)|(in @ X405 @ (dsetconstr @ X403 @ (^[Z0:$i]:((X404 @ Z0)))))))&((~(in @ X408 @ (dsetconstr @ X406 @ (^[Z0:$i]:((X407 @ Z0)))))|(in @ X408 @ X406))&((~(in @ X411 @ (dsetconstr @ X409 @ (^[Z0:$i]:((X410 @ Z0)))))|(X410 @ X411))&(((((X412 @ (esk11_1 @ X412))|((X412 @ (esk10_2 @ X412 @ X413))|~(X412 @ X413)))&(~(X412 @ X416)|((esk11_1 @ X412)=(X416))|((X412 @ (esk10_2 @ X412 @ X413))|~(X412 @ X413))))&(((X412 @ (esk11_1 @ X412))|(((X413)!=(esk10_2 @ X412 @ X413))|~(X412 @ X413)))&(~(X412 @ X416)|((esk11_1 @ X412)=(X416))|(((X413)!=(esk10_2 @ X412 @ X413))|~(X412 @ X413)))))&((~(in @ X418 @ (prop2set @ ((X417))))|(X417))&((~(in @ X419 @ emptyset)|(X420))&(~(in @ X421 @ emptyset)&(~(in @ X422 @ emptyset)&((((X423 @ (esk12_2 @ X423 @ X424))|~(X423 @ X424)|(X423 @ (esk13_1 @ X423)))&(((X424)!=(esk12_2 @ X423 @ X424))|~(X423 @ X424)|(X423 @ (esk13_1 @ X423))))&(((((in @ (esk15_2 @ X427 @ X428) @ X428)|((X427)=(X428))|(in @ (esk14_2 @ X427 @ X428) @ X427))&(~(in @ (esk15_2 @ X427 @ X428) @ X427)|((X427)=(X428))|(in @ (esk14_2 @ X427 @ X428) @ X427)))&(((in @ (esk15_2 @ X427 @ X428) @ X428)|((X427)=(X428))|~(in @ (esk14_2 @ X427 @ X428) @ X428))&(~(in @ (esk15_2 @ X427 @ X428) @ X427)|((X427)=(X428))|~(in @ (esk14_2 @ X427 @ X428) @ X428))))&(((in @ (esk16_1 @ X431) @ X431)|((X431)=(emptyset)))&(((in @ (esk17_1 @ X433) @ X433)|((X433)=(emptyset)))&(((~(in @ X437 @ (dsetconstr @ X435 @ (^[Z0:$i]:((X436 @ Z0)))))|(X436 @ X437)|~(in @ X437 @ X435))&(~(X436 @ X437)|(in @ X437 @ (dsetconstr @ X435 @ (^[Z0:$i]:((X436 @ Z0)))))|~(in @ X437 @ X435)))&((((X438)=(emptyset))|(in @ (esk18_1 @ X438) @ X438))&((~(in @ X442 @ X440)|(~(X441 @ X442)|((dsetconstr @ X440 @ (^[Z0:$i]:((X441 @ Z0))))!=(emptyset))))&((~(in @ X444 @ X443)|((X443)!=(emptyset)))&((in @ X445 @ (setadjoin @ X445 @ X446))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X449 @ X448)|(in @ X449 @ (setadjoin @ X447 @ X448)))&(((((in @ X452 @ X451)|(X453)|((X452)=(X450))|~(in @ X452 @ (setadjoin @ X450 @ X451)))&(~(X453)|(X453)|((X452)=(X450))|~(in @ X452 @ (setadjoin @ X450 @ X451))))&(((in @ X452 @ X451)|(X453)|~(X453)|~(in @ X452 @ (setadjoin @ X450 @ X451)))&(~(X453)|(X453)|~(X453)|~(in @ X452 @ (setadjoin @ X450 @ X451)))))&((~(in @ X456 @ (setadjoin @ X454 @ X455))|(((X456)=(X454))|(in @ X456 @ X455)))&(((dsetconstr @ X457 @ (^[Z0:$i]:(($true))))=(X457))&((((in @ (esk19_2 @ X458 @ X459) @ X459)|(in @ X459 @ (powerset @ X458)))&(~(in @ (esk19_2 @ X458 @ X459) @ X458)|(in @ X459 @ (powerset @ X458))))&((in @ emptyset @ (powerset @ X461))&((in @ emptyset @ (powerset @ X462))&((~(in @ X464 @ (powerset @ X463))|(~(in @ X465 @ X464)|(in @ X465 @ X463)))&((~(in @ X467 @ X468)|(~(in @ X468 @ X466)|(in @ X467 @ (setunion @ X466))))&((((in @ X470 @ (esk20_3 @ X469 @ X470 @ X471))|(X471)|~(in @ X470 @ (setunion @ X469)))&(((in @ (esk20_3 @ X469 @ X470 @ X471) @ X469)|(X471)|~(in @ X470 @ (setunion @ X469)))&(~(X471)|(X471)|~(in @ X470 @ (setunion @ X469)))))&((~(in @ X474 @ X473)|(in @ X474 @ (powerset @ (setunion @ X473))))&((((~(X475 @ X479)|((X479)=(esk22_1 @ X475))|((X475 @ (esk21_2 @ X475 @ X476))|~(X475 @ X476)))&(((X480)!=(esk22_1 @ X475))|(X475 @ X480)|((X475 @ (esk21_2 @ X475 @ X476))|~(X475 @ X476))))&((~(X475 @ X479)|((X479)=(esk22_1 @ X475))|(((X476)!=(esk21_2 @ X475 @ X476))|~(X475 @ X476)))&(((X480)!=(esk22_1 @ X475))|(X475 @ X480)|(((X476)!=(esk21_2 @ X475 @ X476))|~(X475 @ X476)))))&((((X481)=(emptyset))|(in @ (esk23_1 @ X481) @ X481))&((~(in @ X483 @ (setadjoin @ X484 @ emptyset))|((X483)=(X484)))&((((X485)=(X486))|~(in @ X486 @ (setadjoin @ X485 @ emptyset)))&((((X487)!=(X488))|(in @ X487 @ (setadjoin @ X488 @ emptyset)))&((~(in @ X489 @ (setadjoin @ X490 @ emptyset))|(in @ X490 @ (setadjoin @ X489 @ emptyset)))&((~(in @ X493 @ (setadjoin @ X491 @ (setadjoin @ X492 @ emptyset)))|(((X493)=(X491))|((X493)=(X492))))&((in @ X494 @ (setadjoin @ X494 @ (setadjoin @ X495 @ emptyset)))&((in @ X497 @ (setadjoin @ X496 @ (setadjoin @ X497 @ emptyset)))&((~(in @ X500 @ X498)|~(X499 @ X500)|((dsetconstr @ X498 @ (^[Z0:$i]:((X499 @ Z0))))!=(emptyset)))&((~(in @ X502 @ emptyset)|(X501 @ X502))&((((in @ (esk24_2 @ X503 @ X504) @ X503)|(~(in @ X505 @ X503)|(X504 @ X505)))&(~(X504 @ (esk24_2 @ X503 @ X504))|(~(in @ X505 @ X503)|(X504 @ X505))))&((((in @ (esk25_2 @ X507 @ X508) @ X507)|(~(in @ X510 @ X507)|~(X508 @ X510)))&((X508 @ (esk25_2 @ X507 @ X508))|(~(in @ X510 @ X507)|~(X508 @ X510))))&((((in @ (esk26_2 @ X511 @ X512) @ X511)|(~(in @ X514 @ X511)|~(X512 @ X514)))&((X512 @ (esk26_2 @ X511 @ X512))|(~(in @ X514 @ X511)|~(X512 @ X514))))&((((in @ (esk27_2 @ X515 @ X516) @ X515)|(~(in @ X517 @ X515)|(X516 @ X517)))&(~(X516 @ (esk27_2 @ X515 @ X516))|(~(in @ X517 @ X515)|(X516 @ X517))))&((~(X519)|(in @ emptyset @ (prop2set @ ((X519)))))&((prop2set2propI)&((((in @ (esk28_2 @ X520 @ X521) @ X520)|(~(in @ X523 @ X520)|~(X521 @ X523)))&((X521 @ (esk28_2 @ X520 @ X521))|(~(in @ X523 @ X520)|~(X521 @ X523))))&((((in @ (esk29_2 @ X524 @ X525) @ X524)|(~(in @ X526 @ X524)|(X525 @ X526)))&(~(X525 @ (esk29_2 @ X524 @ X525))|(~(in @ X526 @ X524)|(X525 @ X526))))&(((epred2_0 @ esk30_0)&(~(epred2_0 @ X530)|((esk30_0)=(X530))))&(((epred2_0 @ (esk31_1 @ X531))|~(epred2_0 @ X531))&(((X531)!=(esk31_1 @ X531))|~(epred2_0 @ X531))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_84])])])])])])).
% 0.09/0.16 thf(c_0_86, negated_conjecture, ![X2:$i]:((((esk30_0)=(X2))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_85])).
% 0.09/0.16 thf(c_0_87, negated_conjecture, ![X2:$i]:(((epred2_0 @ (esk31_1 @ X2))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_85])).
% 0.09/0.16 thf(c_0_88, negated_conjecture, ![X2:$i]:((((X2)!=(esk31_1 @ X2))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_85])).
% 0.09/0.16 thf(c_0_89, negated_conjecture, ![X2:$i]:((((esk31_1 @ X2)=(esk30_0))|~((epred2_0 @ X2)))), inference(spm,[status(thm)],[c_0_86, c_0_87])).
% 0.09/0.16 thf(c_0_90, negated_conjecture, (epred2_0 @ esk30_0), inference(split_conjunct,[status(thm)],[c_0_85])).
% 0.09/0.16 thf(c_0_91, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89])]), c_0_90])]), ['proof']).
% 0.09/0.16 % SZS output end CNFRefutation
% 0.09/0.16 % Parsed axioms : 135
% 0.09/0.16 % Removed by relevancy pruning/SinE : 74
% 0.09/0.16 % Initial clauses : 118
% 0.09/0.16 % Removed in clause preprocessing : 4
% 0.09/0.16 % Initial clauses in saturation : 114
% 0.09/0.16 % Processed clauses : 26
% 0.09/0.16 % ...of these trivial : 1
% 0.09/0.16 % ...subsumed : 6
% 0.09/0.16 % ...remaining for further processing : 19
% 0.09/0.16 % Other redundant clauses eliminated : 2
% 0.09/0.16 % Clauses deleted for lack of memory : 0
% 0.09/0.16 % Backward-subsumed : 0
% 0.09/0.16 % Backward-rewritten : 2
% 0.09/0.16 % Generated clauses : 6
% 0.09/0.16 % ...of the previous two non-redundant : 4
% 0.09/0.16 % ...aggressively subsumed : 0
% 0.09/0.16 % Contextual simplify-reflections : 0
% 0.09/0.16 % Paramodulations : 4
% 0.09/0.16 % Factorizations : 0
% 0.09/0.16 % NegExts : 0
% 0.09/0.16 % Equation resolutions : 2
% 0.09/0.16 % Disequality decompositions : 0
% 0.09/0.16 % Total rewrite steps : 5
% 0.09/0.16 % ...of those cached : 1
% 0.09/0.16 % Propositional unsat checks : 0
% 0.09/0.16 % Propositional check models : 0
% 0.09/0.16 % Propositional check unsatisfiable : 0
% 0.09/0.16 % Propositional clauses : 0
% 0.09/0.16 % Propositional clauses after purity: 0
% 0.09/0.16 % Propositional unsat core size : 0
% 0.09/0.16 % Propositional preprocessing time : 0.000
% 0.09/0.16 % Propositional encoding time : 0.000
% 0.09/0.16 % Propositional solver time : 0.000
% 0.09/0.16 % Success case prop preproc time : 0.000
% 0.09/0.16 % Success case prop encoding time : 0.000
% 0.09/0.16 % Success case prop solver time : 0.000
% 0.09/0.16 % Current number of processed clauses : 16
% 0.09/0.16 % Positive orientable unit clauses : 10
% 0.09/0.16 % Positive unorientable unit clauses: 0
% 0.09/0.16 % Negative unit clauses : 1
% 0.09/0.16 % Non-unit-clauses : 5
% 0.09/0.16 % Current number of unprocessed clauses: 92
% 0.09/0.16 % ...number of literals in the above : 296
% 0.09/0.16 % Current number of archived formulas : 0
% 0.09/0.16 % Current number of archived clauses : 2
% 0.09/0.16 % Clause-clause subsumption calls (NU) : 9
% 0.09/0.16 % Rec. Clause-clause subsumption calls : 8
% 0.09/0.16 % Non-unit clause-clause subsumptions : 0
% 0.09/0.16 % Unit Clause-clause subsumption calls : 1
% 0.09/0.16 % Rewrite failures with RHS unbound : 0
% 0.09/0.16 % BW rewrite match attempts : 2
% 0.09/0.16 % BW rewrite match successes : 2
% 0.09/0.16 % Condensation attempts : 0
% 0.09/0.16 % Condensation successes : 0
% 0.09/0.16 % Termbank termtop insertions : 13241
% 0.09/0.16 % Search garbage collected termcells : 5225
% 0.09/0.16
% 0.09/0.16 % -------------------------------------------------
% 0.09/0.16 % User time : 0.005 s
% 0.09/0.16 % System time : 0.007 s
% 0.09/0.16 % Total time : 0.012 s
% 0.09/0.16 % Maximum resident set size: 5052 pages
% 0.09/0.16
% 0.09/0.16 % -------------------------------------------------
% 0.09/0.16 % User time : 0.007 s
% 0.09/0.16 % System time : 0.010 s
% 0.09/0.16 % Total time : 0.016 s
% 0.09/0.16 % Maximum resident set size: 4864 pages
% 0.09/0.16 % E exiting
%------------------------------------------------------------------------------