%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU539^1 : 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 : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:26:38 AM UTC 2026
% Result : Theorem 0.23s 0.28s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU539^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:48:45 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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.NPJUoKqEn0/E---3.1_2689923.p
% 0.23/0.28 % Version: 3.5.1-ho
% 0.23/0.28 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.28 % Starting sh5l with 300s (1) cores
% 0.23/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.28 % sh5l with pid 2689937 completed with status 0
% 0.23/0.28 % Result found by sh5l
% 0.23/0.28 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.28 % Starting sh5l with 300s (1) cores
% 0.23/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.28 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.28 % Search class: HGHSM-FFMS31-SHSSMSBN
% 0.23/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.28 % SubtermCWHack with pid 2689940 completed with status 0
% 0.23/0.28 % Result found by SubtermCWHack
% 0.23/0.28 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.28 % Starting sh5l with 300s (1) cores
% 0.23/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.28 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.28 % Search class: HGHSM-FFMS31-SHSSMSBN
% 0.23/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.28 % Preprocessing time : 0.003 s
% 0.23/0.28
% 0.23/0.28 % Proof found!
% 0.23/0.28 % SZS status Theorem
% 0.23/0.28 % SZS output start CNFRefutation
% 0.23/0.28 thf(decl_23, type, in: $i > $i > $o).
% 0.23/0.28 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.23/0.28 thf(decl_25, type, setextAx: $o).
% 0.23/0.28 thf(decl_26, type, emptyset: $i).
% 0.23/0.28 thf(decl_27, type, emptysetAx: $o).
% 0.23/0.28 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.23/0.28 thf(decl_29, type, setadjoinAx: $o).
% 0.23/0.28 thf(decl_30, type, powerset: $i > $i).
% 0.23/0.28 thf(decl_31, type, powersetAx: $o).
% 0.23/0.28 thf(decl_32, type, setunion: $i > $i).
% 0.23/0.28 thf(decl_33, type, setunionAx: $o).
% 0.23/0.28 thf(decl_34, type, omega: $i).
% 0.23/0.28 thf(decl_35, type, omega0Ax: $o).
% 0.23/0.28 thf(decl_36, type, omegaSAx: $o).
% 0.23/0.28 thf(decl_37, type, omegaIndAx: $o).
% 0.23/0.28 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: $o).
% 0.23/0.29 thf(decl_41, type, descr: ($i > $o) > $i).
% 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, epred1_0: $o).
% 0.23/0.29 thf(decl_90, type, esk1_2: $i > $i > $i).
% 0.23/0.29 thf(decl_91, type, esk2_2: $i > $i > $i).
% 0.23/0.29 thf(decl_92, type, esk3_2: $i > $i > $i).
% 0.23/0.29 thf(decl_93, type, esk4_1: $i > $i).
% 0.23/0.29 thf(decl_94, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.23/0.29 thf(decl_95, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.29 thf(decl_96, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.23/0.29 thf(decl_97, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.23/0.29 thf(decl_98, type, esk9_1: $i > $i).
% 0.23/0.29 thf(decl_99, type, esk10_2: ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_100, type, esk11_2: ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_101, type, esk12_1: ($i > $o) > $i).
% 0.23/0.29 thf(decl_102, type, esk13_2: ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_103, type, esk14_1: ($i > $o) > $i).
% 0.23/0.29 thf(decl_104, type, esk15_2: $i > $i > $i).
% 0.23/0.29 thf(decl_105, type, esk16_2: $i > $i > $i).
% 0.23/0.29 thf(decl_106, type, esk17_1: $i > $i).
% 0.23/0.29 thf(decl_107, type, esk18_1: $i > $i).
% 0.23/0.29 thf(decl_108, type, esk19_1: $i > $i).
% 0.23/0.29 thf(decl_109, type, esk20_2: $i > $i > $i).
% 0.23/0.29 thf(decl_110, type, esk21_3: $i > $i > $o > $i).
% 0.23/0.29 thf(decl_111, type, esk22_2: ($i > $o) > $i > $i).
% 0.23/0.29 thf(decl_112, type, esk23_1: ($i > $o) > $i).
% 0.23/0.29 thf(decl_113, type, esk24_1: $i > $i).
% 0.23/0.29 thf(decl_114, type, esk25_2: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_115, type, esk26_2: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_116, type, esk27_2: $i > ($i > $o) > $i).
% 0.23/0.29 thf(decl_117, type, esk28_0: $i).
% 0.23/0.29 thf(decl_118, type, epred2_0: $i > $o).
% 0.23/0.29 thf(decl_119, type, esk29_0: $i).
% 0.23/0.29 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', replAx)).
% 0.23/0.29 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', exu)).
% 0.23/0.29 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', exuE2)).
% 0.23/0.29 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', prop2set)).
% 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.NPJUoKqEn0/E---3.1_2689923.p', exuE1)).
% 0.23/0.29 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', descrp)).
% 0.23/0.29 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', nonempty)).
% 0.23/0.29 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', exuE3e)).
% 0.23/0.29 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', nonemptyI)).
% 0.23/0.29 thf(quantDeMorgan4, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', quantDeMorgan4)).
% 0.23/0.29 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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.NPJUoKqEn0/E---3.1_2689923.p', emptyE1)).
% 0.23/0.29 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', prop2setE)).
% 0.23/0.29 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', dsetconstrER)).
% 0.23/0.29 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', dsetconstrEL)).
% 0.23/0.29 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', dsetconstrI)).
% 0.23/0.29 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', nonemptyE1)).
% 0.23/0.29 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', setbeta)).
% 0.23/0.29 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.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.NPJUoKqEn0/E---3.1_2689923.p', nonemptyI1)).
% 0.23/0.29 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', nonemptyImpWitness)).
% 0.23/0.29 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X15:$i]:(((in @ X15 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X15)=(X2))|((X15)=(X3)))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', upairsetE)).
% 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.NPJUoKqEn0/E---3.1_2689923.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.NPJUoKqEn0/E---3.1_2689923.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.NPJUoKqEn0/E---3.1_2689923.p', eqinunit)).
% 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.NPJUoKqEn0/E---3.1_2689923.p', upairsetIL)).
% 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.NPJUoKqEn0/E---3.1_2689923.p', upairsetIR)).
% 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.NPJUoKqEn0/E---3.1_2689923.p', foundationAx)).
% 0.23/0.29 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', vacuousDall)).
% 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:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', omegaIndAx)).
% 0.23/0.29 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', quantDeMorgan1)).
% 0.23/0.29 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', omegaSAx)).
% 0.23/0.29 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', quantDeMorgan2)).
% 0.23/0.29 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.NPJUoKqEn0/E---3.1_2689923.p', wellorderingAx)).
% 0.23/0.29 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', quantDeMorgan3)).
% 0.23/0.29 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', powersetI)).
% 0.23/0.29 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', emptysetE)).
% 0.23/0.29 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.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.NPJUoKqEn0/E---3.1_2689923.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.NPJUoKqEn0/E---3.1_2689923.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.NPJUoKqEn0/E---3.1_2689923.p', setext)).
% 0.23/0.29 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', notinemptyset)).
% 0.23/0.29 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', setadjoinOr)).
% 0.23/0.29 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', setadjoinE)).
% 0.23/0.29 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', setadjoinIR)).
% 0.23/0.29 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', emptyinunitempty)).
% 0.23/0.29 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', setadjoinIL)).
% 0.23/0.29 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', subPowSU)).
% 0.23/0.29 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14)))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', setunionE)).
% 0.23/0.29 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', setunionI)).
% 0.23/0.29 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', powersetE)).
% 0.23/0.29 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', emptyInPowerset)).
% 0.23/0.29 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', emptyinPowerset)).
% 0.23/0.29 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', singletonsswitch)).
% 0.23/0.29 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', omega0Ax)).
% 0.23/0.29 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', setunionAx)).
% 0.23/0.29 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', powersetAx)).
% 0.23/0.29 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', setadjoinAx)).
% 0.23/0.29 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', emptysetAx)).
% 0.23/0.29 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.NPJUoKqEn0/E---3.1_2689923.p', setextAx)).
% 0.23/0.29 thf(c_0_59, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.23/0.29 thf(c_0_60, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.23/0.29 thf(c_0_61, plain, ((exuE2)<=>![X1:$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_62, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.23/0.29 thf(c_0_63, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.23/0.29 thf(c_0_64, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.23/0.29 thf(c_0_65, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.23/0.29 thf(c_0_66, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.23/0.29 thf(c_0_67, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.23/0.29 thf(c_0_68, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[quantDeMorgan4])).
% 0.23/0.29 thf(c_0_69, plain, ((emptyE1)<=>![X4:$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, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X172:$i]:(((((X6 @ X2 @ X172)))&(![X173:$i]:(((((X6 @ X2 @ X173)))=>(((X172)=(X173)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_59, c_0_60])).
% 0.23/0.29 thf(c_0_71, plain, ((exuE2)=(![X1:$i > $o]:((((?[X180:$i]:(((((X1 @ X180)))&(![X181:$i]:(((((X1 @ X181)))=>(((X180)=(X181))))))))))=>(?[X2:$i]:(![X3:$i]:((((X1 @ X3))<=>(((X3)=(X2))))))))))), inference(apply_def,[status(thm)],[c_0_61, c_0_60])).
% 0.23/0.29 thf(c_0_72, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_62])).
% 0.23/0.29 thf(c_0_73, plain, ((exuE1)=(![X1:$i > $o]:((((?[X176:$i]:(((((X1 @ X176)))&(![X177:$i]:(((((X1 @ X177)))=>(((X176)=(X177))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_63, c_0_60])).
% 0.23/0.29 thf(c_0_74, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.23/0.29 thf(c_0_75, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.23/0.29 thf(c_0_76, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.23/0.29 thf(c_0_77, plain, ((descrp)=(![X1:$i > $o]:((((?[X174:$i]:(((((X1 @ X174)))&(![X175:$i]:(((((X1 @ X175)))=>(((X174)=(X175))))))))))=>((X1 @ (descr @ (^[Z0:$i]:((X1 @ Z0)))))))))), inference(apply_def,[status(thm)],[c_0_64, c_0_60])).
% 0.23/0.29 thf(c_0_78, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_65])).
% 0.23/0.29 thf(c_0_79, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.23/0.29 thf(c_0_80, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X178:$i]:(((((X1 @ X178)))&(![X179:$i]:(((((X1 @ X179)))=>(((X178)=(X179))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_66, c_0_60])).
% 0.23/0.29 thf(c_0_81, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_67, c_0_65])).
% 0.23/0.29 thf(c_0_82, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.23/0.29 thf(c_0_83, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_65])).
% 0.23/0.29 thf(c_0_84, axiom, ((nonemptyImpWitness)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((((in @ X2 @ X4))&(($true))))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_65])).
% 0.23/0.29 thf(c_0_85, plain, ((epred1_0)<=>![X211:$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_86, 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)=>(![X230:$i > $o]:((?[X231:$i]:(((X230 @ X231)&![X232:$i]:(((X230 @ X232)=>((X231)=(X232))))))=>(X230 @ (descr @ (^[Z0:$i]:(X230 @ Z0))))))=>(![X233:$i, X234:$i > $o, X235:$i]:(((in @ X235 @ X233)=>((X234 @ X235)=>(in @ X235 @ (dsetconstr @ X233 @ X234)))))=>(![X236:$i, X237:$i > $o, X238:$i]:(((in @ X238 @ (dsetconstr @ X236 @ X237))=>(in @ X238 @ X236)))=>(![X239:$i, X240:$i > $o, X241:$i]:(((in @ X241 @ (dsetconstr @ X239 @ X240))=>(X240 @ X241)))=>(![X242:$i > $o]:((?[X243:$i]:(((X242 @ X243)&![X244:$i]:(((X242 @ X244)=>((X243)=(X244))))))=>?[X245:$i]:(((X242 @ X245)&![X246:$i]:(((X242 @ X246)=>((X245)=(X246))))))))=>(![X247:$o, X248:$i]:(((in @ X248 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X247)))))=>(X247)))=>(![X249:$i]:(((in @ X249 @ emptyset)=>![X250:$o]:((X250))))=>(![X251:$i]:(((in @ X251 @ emptyset)=>~($true)))=>(![X252:$i]:(~(in @ X252 @ emptyset))=>(![X253:$i > $o]:((?[X254:$i]:(((X253 @ X254)&![X255:$i]:(((X253 @ X255)=>((X254)=(X255))))))=>?[X256:$i]:((X253 @ X256))))=>(![X257:$i, X258:$i]:((![X259:$i]:(((in @ X259 @ X257)=>(in @ X259 @ X258)))=>(![X260:$i]:(((in @ X260 @ X258)=>(in @ X260 @ X257)))=>((X257)=(X258)))))=>(![X261:$i]:((![X262:$i]:(~(in @ X262 @ X261))=>((X261)=(emptyset))))=>(![X263:$i]:((![X264:$i]:(~(in @ X264 @ X263))=>((X263)=(emptyset))))=>(![X265:$i, X266:$i > $o, X267:$i]:(((in @ X267 @ X265)=>((in @ X267 @ (dsetconstr @ X265 @ X266))<=>(X266 @ X267))))=>(![X268:$i]:((((X268)!=(emptyset))=>?[X269:$i]:((in @ X269 @ X268))))=>(![X270:$i, X271:$i > $o, X272:$i]:(((in @ X272 @ X270)=>((X271 @ X272)=>((dsetconstr @ X270 @ X271)!=(emptyset)))))=>(![X273:$i]:((?[X274:$i]:((in @ X274 @ X273))=>((X273)!=(emptyset))))=>(![X275:$i, X276:$i]:((in @ X275 @ (setadjoin @ X275 @ X276)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X277:$i, X278:$i, X279:$i]:(((in @ X279 @ X278)=>(in @ X279 @ (setadjoin @ X277 @ X278))))=>(![X280:$i, X281:$i, X282:$i]:(((in @ X282 @ (setadjoin @ X280 @ X281))=>![X283:$o]:(((((X282)=(X280))=>(X283))=>(((in @ X282 @ X281)=>(X283))=>(X283))))))=>(![X284:$i, X285:$i, X286:$i]:(((in @ X286 @ (setadjoin @ X284 @ X285))=>(((X286)=(X284))|(in @ X286 @ X285))))=>(![X287:$i]:(((dsetconstr @ X287 @ (^[Z0:$i]:($true)))=(X287)))=>(![X288:$i, X289:$i]:((![X290:$i]:(((in @ X290 @ X289)=>(in @ X290 @ X288)))=>(in @ X289 @ (powerset @ X288))))=>(![X291:$i]:((in @ emptyset @ (powerset @ X291)))=>(![X292:$i]:((in @ emptyset @ (powerset @ X292)))=>(![X293:$i, X294:$i, X295:$i]:(((in @ X294 @ (powerset @ X293))=>((in @ X295 @ X294)=>(in @ X295 @ X293))))=>(![X296:$i, X297:$i, X298:$i]:(((in @ X297 @ X298)=>((in @ X298 @ X296)=>(in @ X297 @ (setunion @ X296)))))=>(![X299:$i, X300:$i]:(((in @ X300 @ (setunion @ X299))=>![X301:$o]:((![X302:$i]:(((in @ X300 @ X302)=>((in @ X302 @ X299)=>(X301))))=>(X301)))))=>(![X303:$i, X304:$i]:(((in @ X304 @ X303)=>(in @ X304 @ (powerset @ (setunion @ X303)))))=>(![X305:$i > $o]:((?[X306:$i]:(((X305 @ X306)&![X307:$i]:(((X305 @ X307)=>((X306)=(X307))))))=>?[X308:$i]:(![X309:$i]:(((X305 @ X309)<=>((X309)=(X308)))))))=>(![X310:$i]:((((X310)!=(emptyset))=>?[X311:$i]:(((in @ X311 @ X310)&$true))))=>(![X312:$i, X313:$i]:(((in @ X312 @ (setadjoin @ X313 @ emptyset))=>((X312)=(X313))))=>(![X314:$i, X315:$i]:((((X314)!=(X315))=>~(in @ X315 @ (setadjoin @ X314 @ emptyset))))=>(![X316:$i, X317:$i]:((((X316)=(X317))=>(in @ X316 @ (setadjoin @ X317 @ emptyset))))=>(![X318:$i, X319:$i]:(((in @ X318 @ (setadjoin @ X319 @ emptyset))=>(in @ X319 @ (setadjoin @ X318 @ emptyset))))=>(![X320:$i, X321:$i, X322:$i]:(((in @ X322 @ (setadjoin @ X320 @ (setadjoin @ X321 @ emptyset)))=>(((X322)=(X320))|((X322)=(X321)))))=>(![X323:$i, X324:$i]:((in @ X323 @ (setadjoin @ X323 @ (setadjoin @ X324 @ emptyset))))=>(![X325:$i, X326:$i]:((in @ X326 @ (setadjoin @ X325 @ (setadjoin @ X326 @ emptyset))))=>(![X327:$i, X328:$i > $o]:((?[X329:$i]:(((in @ X329 @ X327)&(X328 @ X329)))=>(((dsetconstr @ X327 @ X328)=(emptyset))=>~($true))))=>(![X330:$i > $o, X331:$i]:(((in @ X331 @ emptyset)=>(X330 @ X331)))=>(![X332:$i, X333:$i > $o]:((~(![X334:$i]:(((in @ X334 @ X332)=>(X333 @ X334))))=>?[X335:$i]:(((in @ X335 @ X332)&~((X333 @ X335))))))=>(![X336:$i, X337:$i > $o]:((![X338:$i]:(((in @ X338 @ X336)=>~((X337 @ X338))))=>~(?[X339:$i]:(((in @ X339 @ X336)&(X337 @ X339))))))=>(![X340:$i, X341:$i > $o]:((~(?[X342:$i]:(((in @ X342 @ X340)&(X341 @ X342))))=>![X343:$i]:(((in @ X343 @ X340)=>~((X341 @ X343))))))=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_68, upairsetE]), uniqinunit]), notinsingleton]), eqinunit]), upairsetIL]), upairsetIR]), foundationAx]), c_0_69]), c_0_70]), vacuousDall]), omegaIndAx]), quantDeMorgan1]), omegaSAx]), quantDeMorgan2]), wellorderingAx]), quantDeMorgan3]), powersetI]), c_0_71]), emptysetE]), c_0_72]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), emptysetimpfalse]), c_0_78]), c_0_79]), noeltsimpempty]), emptyI]), setext]), c_0_80]), notinemptyset]), c_0_81]), c_0_82]), setadjoinOr]), setadjoinE]), setadjoinIR]), emptyinunitempty]), setadjoinIL]), c_0_83]), subPowSU]), setunionE]), setunionI]), powersetE]), emptyInPowerset]), emptyinPowerset]), singletonsswitch]), c_0_84]), omega0Ax]), setunionAx]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx])])]), c_0_85])).
% 0.23/0.29 thf(c_0_87, negated_conjecture, ![X344:$i, X345:$i, X347:$i, X348:$i, X349:$i, X350:$i, X351:$i, X352:$i, X353:$i, X354:$i, X355:$i, X357:$i, X358:$i, X360:$i, X361:$i, X362:$i, X363:$i, X364:$i, X366:$i, X367:$i > $i > $o, X368:$i, X370:$i, X373:$i, X375:$i, X376:$i, X377:$i, X378:$i, X380:$i, X381:$i > $o, X382:$i, X384:$i, X385:$i > $o, X386:$i, X387:$i, X388:$i > $o, X389:$i, X390:$i, X391:$i > $o, X392:$i, X393:$i > $o, X394:$i, X397:$i, X398:$o, X399:$i, X400:$i, X401:$o, X402:$i, X403:$i, X404:$i > $o, X405:$i, X408:$i, X409:$i, X412:$i, X414:$i, X416:$i, X417:$i > $o, X418:$i, X419:$i, X421:$i, X422:$i > $o, X423:$i, X424:$i, X425:$i, X426:$i, X427:$i, X428:$i, X429:$i, X430:$i, X431:$i, X432:$i, X433:$i, X434:$o, X435:$i, X436:$i, X437:$i, X438:$i, X439:$i, X440:$i, X442:$i, X443:$i, X444:$i, X445:$i, X446:$i, X447:$i, X448:$i, X449:$i, X450:$i, X451:$i, X452:$o, X454:$i, X455:$i, X456:$i > $o, X457:$i, X460:$i, X461:$i, X462:$i, X464:$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:$i, X480:$i > $o, X481:$i, X482:$i > $o, X483:$i, X484:$i, X485:$i > $o, X486:$i, X488:$i, X489:$i > $o, X491:$i, X492:$i, X493:$i > $o, X495:$i, X499:$i]:((((~(in @ (esk1_2 @ X344 @ X345) @ X344)|~(in @ (esk1_2 @ X344 @ X345) @ X345)|((X344)=(X345)))&((in @ (esk1_2 @ X344 @ X345) @ X344)|(in @ (esk1_2 @ X344 @ X345) @ X345)|((X344)=(X345))))&(~(in @ X347 @ emptyset)&(((~(in @ X350 @ (setadjoin @ X348 @ X349))|(((X350)=(X348))|(in @ X350 @ X349)))&((((X350)!=(X348))|(in @ X350 @ (setadjoin @ X348 @ X349)))&(~(in @ X350 @ X349)|(in @ X350 @ (setadjoin @ X348 @ X349)))))&(((~(in @ X352 @ (powerset @ X351))|(~(in @ X353 @ X352)|(in @ X353 @ X351)))&(((in @ (esk2_2 @ X354 @ X355) @ X355)|(in @ X355 @ (powerset @ X354)))&(~(in @ (esk2_2 @ X354 @ X355) @ X354)|(in @ X355 @ (powerset @ X354)))))&(((((in @ X358 @ (esk3_2 @ X357 @ X358))|~(in @ X358 @ (setunion @ X357)))&((in @ (esk3_2 @ X357 @ X358) @ X357)|~(in @ X358 @ (setunion @ X357))))&(~(in @ X361 @ X362)|~(in @ X362 @ X360)|(in @ X361 @ (setunion @ X360))))&((in @ emptyset @ omega)&((~(in @ X363 @ omega)|(in @ (setadjoin @ X363 @ X363) @ omega))&(((((in @ (esk4_1 @ X364) @ omega)|~(in @ emptyset @ X364)|(~(in @ X366 @ omega)|(in @ X366 @ X364)))&((in @ (esk4_1 @ X364) @ X364)|~(in @ emptyset @ X364)|(~(in @ X366 @ omega)|(in @ X366 @ X364))))&(~(in @ (setadjoin @ (esk4_1 @ X364) @ (esk4_1 @ X364)) @ X364)|~(in @ emptyset @ X364)|(~(in @ X366 @ omega)|(in @ X366 @ X364))))&((((((in @ (esk8_3 @ X367 @ X368 @ X373) @ X368)|~(in @ X373 @ (esk7_2 @ X367 @ X368))|(in @ (esk5_2 @ X367 @ X368) @ X368))&((X367 @ (esk8_3 @ X367 @ X368 @ X373) @ X373)|~(in @ X373 @ (esk7_2 @ X367 @ X368))|(in @ (esk5_2 @ X367 @ X368) @ X368)))&(~(in @ X376 @ X368)|~(X367 @ X376 @ X375)|(in @ X375 @ (esk7_2 @ X367 @ X368))|(in @ (esk5_2 @ X367 @ X368) @ X368)))&(((((in @ (esk8_3 @ X367 @ X368 @ X373) @ X368)|~(in @ X373 @ (esk7_2 @ X367 @ X368))|((X367 @ (esk5_2 @ X367 @ X368) @ (esk6_3 @ X367 @ X368 @ X370))|~(X367 @ (esk5_2 @ X367 @ X368) @ X370)))&((X367 @ (esk8_3 @ X367 @ X368 @ X373) @ X373)|~(in @ X373 @ (esk7_2 @ X367 @ X368))|((X367 @ (esk5_2 @ X367 @ X368) @ (esk6_3 @ X367 @ X368 @ X370))|~(X367 @ (esk5_2 @ X367 @ X368) @ X370))))&(~(in @ X376 @ X368)|~(X367 @ X376 @ X375)|(in @ X375 @ (esk7_2 @ X367 @ X368))|((X367 @ (esk5_2 @ X367 @ X368) @ (esk6_3 @ X367 @ X368 @ X370))|~(X367 @ (esk5_2 @ X367 @ X368) @ X370))))&((((in @ (esk8_3 @ X367 @ X368 @ X373) @ X368)|~(in @ X373 @ (esk7_2 @ X367 @ X368))|(((X370)!=(esk6_3 @ X367 @ X368 @ X370))|~(X367 @ (esk5_2 @ X367 @ X368) @ X370)))&((X367 @ (esk8_3 @ X367 @ X368 @ X373) @ X373)|~(in @ X373 @ (esk7_2 @ X367 @ X368))|(((X370)!=(esk6_3 @ X367 @ X368 @ X370))|~(X367 @ (esk5_2 @ X367 @ X368) @ X370))))&(~(in @ X376 @ X368)|~(X367 @ X376 @ X375)|(in @ X375 @ (esk7_2 @ X367 @ X368))|(((X370)!=(esk6_3 @ X367 @ X368 @ X370))|~(X367 @ (esk5_2 @ X367 @ X368) @ X370))))))&((((in @ (esk9_1 @ X377) @ X377)|~(in @ X378 @ X377))&(~(in @ X380 @ (esk9_1 @ X377))|~(in @ X380 @ X377)|~(in @ X378 @ X377)))&((epred1_0)&((((X381 @ (esk10_2 @ X381 @ X382))|~(X381 @ X382)|(X381 @ (descr @ X381)))&(((X382)!=(esk10_2 @ X381 @ X382))|~(X381 @ X382)|(X381 @ (descr @ X381))))&((~(in @ X386 @ X384)|(~(X385 @ X386)|(in @ X386 @ (dsetconstr @ X384 @ X385))))&((~(in @ X389 @ (dsetconstr @ X387 @ X388))|(in @ X389 @ X387))&((~(in @ X392 @ (dsetconstr @ X390 @ X391))|(X391 @ X392))&(((((X393 @ (esk12_1 @ X393))|((X393 @ (esk11_2 @ X393 @ X394))|~(X393 @ X394)))&(~(X393 @ X397)|((esk12_1 @ X393)=(X397))|((X393 @ (esk11_2 @ X393 @ X394))|~(X393 @ X394))))&(((X393 @ (esk12_1 @ X393))|(((X394)!=(esk11_2 @ X393 @ X394))|~(X393 @ X394)))&(~(X393 @ X397)|((esk12_1 @ X393)=(X397))|(((X394)!=(esk11_2 @ X393 @ X394))|~(X393 @ X394)))))&((~(in @ X399 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X398)))))|(X398))&((~(in @ X400 @ emptyset)|(X401))&((~(in @ X402 @ emptyset)|~($true))&(~(in @ X403 @ emptyset)&((((X404 @ (esk13_2 @ X404 @ X405))|~(X404 @ X405)|(X404 @ (esk14_1 @ X404)))&(((X405)!=(esk13_2 @ X404 @ X405))|~(X404 @ X405)|(X404 @ (esk14_1 @ X404))))&(((((in @ (esk16_2 @ X408 @ X409) @ X409)|((X408)=(X409))|(in @ (esk15_2 @ X408 @ X409) @ X408))&(~(in @ (esk16_2 @ X408 @ X409) @ X408)|((X408)=(X409))|(in @ (esk15_2 @ X408 @ X409) @ X408)))&(((in @ (esk16_2 @ X408 @ X409) @ X409)|((X408)=(X409))|~(in @ (esk15_2 @ X408 @ X409) @ X409))&(~(in @ (esk16_2 @ X408 @ X409) @ X408)|((X408)=(X409))|~(in @ (esk15_2 @ X408 @ X409) @ X409))))&(((in @ (esk17_1 @ X412) @ X412)|((X412)=(emptyset)))&(((in @ (esk18_1 @ X414) @ X414)|((X414)=(emptyset)))&(((~(in @ X418 @ (dsetconstr @ X416 @ X417))|(X417 @ X418)|~(in @ X418 @ X416))&(~(X417 @ X418)|(in @ X418 @ (dsetconstr @ X416 @ X417))|~(in @ X418 @ X416)))&((((X419)=(emptyset))|(in @ (esk19_1 @ X419) @ X419))&((~(in @ X423 @ X421)|(~(X422 @ X423)|((dsetconstr @ X421 @ X422)!=(emptyset))))&((~(in @ X425 @ X424)|((X424)!=(emptyset)))&((in @ X426 @ (setadjoin @ X426 @ X427))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X430 @ X429)|(in @ X430 @ (setadjoin @ X428 @ X429)))&(((((in @ X433 @ X432)|(X434)|((X433)=(X431))|~(in @ X433 @ (setadjoin @ X431 @ X432)))&(~(X434)|(X434)|((X433)=(X431))|~(in @ X433 @ (setadjoin @ X431 @ X432))))&(((in @ X433 @ X432)|(X434)|~(X434)|~(in @ X433 @ (setadjoin @ X431 @ X432)))&(~(X434)|(X434)|~(X434)|~(in @ X433 @ (setadjoin @ X431 @ X432)))))&((~(in @ X437 @ (setadjoin @ X435 @ X436))|(((X437)=(X435))|(in @ X437 @ X436)))&(((dsetconstr @ X438 @ (^[Z0:$i]:($true)))=(X438))&((((in @ (esk20_2 @ X439 @ X440) @ X440)|(in @ X440 @ (powerset @ X439)))&(~(in @ (esk20_2 @ X439 @ X440) @ X439)|(in @ X440 @ (powerset @ X439))))&((in @ emptyset @ (powerset @ X442))&((in @ emptyset @ (powerset @ X443))&((~(in @ X445 @ (powerset @ X444))|(~(in @ X446 @ X445)|(in @ X446 @ X444)))&((~(in @ X448 @ X449)|(~(in @ X449 @ X447)|(in @ X448 @ (setunion @ X447))))&((((in @ X451 @ (esk21_3 @ X450 @ X451 @ X452))|(X452)|~(in @ X451 @ (setunion @ X450)))&(((in @ (esk21_3 @ X450 @ X451 @ X452) @ X450)|(X452)|~(in @ X451 @ (setunion @ X450)))&(~(X452)|(X452)|~(in @ X451 @ (setunion @ X450)))))&((~(in @ X455 @ X454)|(in @ X455 @ (powerset @ (setunion @ X454))))&((((~(X456 @ X460)|((X460)=(esk23_1 @ X456))|((X456 @ (esk22_2 @ X456 @ X457))|~(X456 @ X457)))&(((X461)!=(esk23_1 @ X456))|(X456 @ X461)|((X456 @ (esk22_2 @ X456 @ X457))|~(X456 @ X457))))&((~(X456 @ X460)|((X460)=(esk23_1 @ X456))|(((X457)!=(esk22_2 @ X456 @ X457))|~(X456 @ X457)))&(((X461)!=(esk23_1 @ X456))|(X456 @ X461)|(((X457)!=(esk22_2 @ X456 @ X457))|~(X456 @ X457)))))&((((in @ (esk24_1 @ X462) @ X462)|((X462)=(emptyset)))&(($true)|((X462)=(emptyset))))&((~(in @ X464 @ (setadjoin @ X465 @ emptyset))|((X464)=(X465)))&((((X466)=(X467))|~(in @ X467 @ (setadjoin @ X466 @ emptyset)))&((((X468)!=(X469))|(in @ X468 @ (setadjoin @ X469 @ emptyset)))&((~(in @ X470 @ (setadjoin @ X471 @ emptyset))|(in @ X471 @ (setadjoin @ X470 @ emptyset)))&((~(in @ X474 @ (setadjoin @ X472 @ (setadjoin @ X473 @ emptyset)))|(((X474)=(X472))|((X474)=(X473))))&((in @ X475 @ (setadjoin @ X475 @ (setadjoin @ X476 @ emptyset)))&((in @ X478 @ (setadjoin @ X477 @ (setadjoin @ X478 @ emptyset)))&((~(in @ X481 @ X479)|~(X480 @ X481)|(((dsetconstr @ X479 @ X480)!=(emptyset))|~($true)))&((~(in @ X483 @ emptyset)|(X482 @ X483))&((((in @ (esk25_2 @ X484 @ X485) @ X484)|(~(in @ X486 @ X484)|(X485 @ X486)))&(~(X485 @ (esk25_2 @ X484 @ X485))|(~(in @ X486 @ X484)|(X485 @ X486))))&((((in @ (esk26_2 @ X488 @ X489) @ X488)|(~(in @ X491 @ X488)|~(X489 @ X491)))&((X489 @ (esk26_2 @ X488 @ X489))|(~(in @ X491 @ X488)|~(X489 @ X491))))&((((in @ (esk27_2 @ X492 @ X493) @ X492)|(~(in @ X495 @ X492)|~(X493 @ X495)))&((X493 @ (esk27_2 @ X492 @ X493))|(~(in @ X495 @ X492)|~(X493 @ X495))))&(((in @ esk29_0 @ esk28_0)&~(epred2_0 @ esk29_0))&(~(in @ X499 @ esk28_0)|(epred2_0 @ X499))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_86])])])])])])])).
% 0.23/0.29 thf(c_0_88, negated_conjecture, ![X2:$i]:(((epred2_0 @ X2)|~((in @ X2 @ esk28_0)))), inference(split_conjunct,[status(thm)],[c_0_87])).
% 0.23/0.29 thf(c_0_89, negated_conjecture, (in @ esk29_0 @ esk28_0), inference(split_conjunct,[status(thm)],[c_0_87])).
% 0.23/0.29 thf(c_0_90, negated_conjecture, ~((epred2_0 @ esk29_0)), inference(split_conjunct,[status(thm)],[c_0_87])).
% 0.23/0.29 thf(c_0_91, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_90]), ['proof']).
% 0.23/0.29 % SZS output end CNFRefutation
% 0.23/0.29 % Parsed axioms : 125
% 0.23/0.29 % Removed by relevancy pruning/SinE : 66
% 0.23/0.29 % Initial clauses : 111
% 0.23/0.29 % Removed in clause preprocessing : 5
% 0.23/0.29 % Initial clauses in saturation : 106
% 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 : 8
% 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 : 2
% 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 : 2
% 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 : 1
% 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 : 8
% 0.23/0.29 % Positive orientable unit clauses : 4
% 0.23/0.29 % Positive unorientable unit clauses: 0
% 0.23/0.29 % Negative unit clauses : 2
% 0.23/0.29 % Non-unit-clauses : 2
% 0.23/0.29 % Current number of unprocessed clauses: 94
% 0.23/0.29 % ...number of literals in the above : 292
% 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 : 14333
% 0.23/0.29 % Search garbage collected termcells : 5777
% 0.23/0.29
% 0.23/0.29 % -------------------------------------------------
% 0.23/0.29 % User time : 0.011 s
% 0.23/0.29 % System time : 0.004 s
% 0.23/0.29 % Total time : 0.015 s
% 0.23/0.29 % Maximum resident set size: 5044 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 : 0.023 s
% 0.23/0.29 % Maximum resident set size: 5120 pages
% 0.23/0.29 % E exiting
%------------------------------------------------------------------------------