%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU522^1 : 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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:21 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU522^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.15 % Computer : n017.cluster.edu
% 0.08/0.15 % Model : x86_64 x86_64
% 0.08/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.15 % Memory : 8046.5625MB
% 0.08/0.15 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Sep 29 13:43:21 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.21 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.qs2vgl3VnA/E---3.1_358802.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting sh5l with 300s (1) cores
% 0.08/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.25 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.25 % new_bool_1 with pid 358817 completed with status 0
% 0.08/0.25 % Result found by new_bool_1
% 0.08/0.25 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting sh5l with 300s (1) cores
% 0.08/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.25 % Search class: HGHSM-FFMM31-SHFSMSBN
% 0.08/0.25 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.08/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 358819 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting sh5l with 300s (1) cores
% 0.08/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.25 % Search class: HGHSM-FFMM31-SHFSMSBN
% 0.08/0.25 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.08/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.25 % Preprocessing time : 0.003 s
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% 0.08/0.25 thf(decl_23, type, in: $i > $i > $o).
% 0.08/0.25 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.08/0.25 thf(decl_25, type, setextAx: $o).
% 0.08/0.25 thf(decl_26, type, emptyset: $i).
% 0.08/0.25 thf(decl_27, type, emptysetAx: $o).
% 0.08/0.25 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.08/0.25 thf(decl_29, type, setadjoinAx: $o).
% 0.08/0.25 thf(decl_30, type, powerset: $i > $i).
% 0.08/0.25 thf(decl_31, type, powersetAx: $o).
% 0.08/0.25 thf(decl_32, type, setunion: $i > $i).
% 0.08/0.25 thf(decl_33, type, setunionAx: $o).
% 0.08/0.25 thf(decl_34, type, omega: $i).
% 0.08/0.25 thf(decl_35, type, omega0Ax: $o).
% 0.08/0.25 thf(decl_36, type, omegaSAx: $o).
% 0.08/0.25 thf(decl_37, type, omegaIndAx: $o).
% 0.08/0.25 thf(decl_38, type, replAx: $o).
% 0.08/0.25 thf(decl_39, type, foundationAx: $o).
% 0.08/0.25 thf(decl_40, type, wellorderingAx: $o).
% 0.08/0.25 thf(decl_42, type, descrp: $o).
% 0.08/0.25 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.08/0.25 thf(decl_44, type, dsetconstrI: $o).
% 0.08/0.25 thf(decl_45, type, dsetconstrEL: $o).
% 0.08/0.25 thf(decl_46, type, dsetconstrER: $o).
% 0.08/0.25 thf(decl_47, type, exuE1: $o).
% 0.08/0.25 thf(decl_48, type, prop2set: $o > $i).
% 0.08/0.25 thf(decl_49, type, prop2setE: $o).
% 0.08/0.25 thf(decl_50, type, emptysetE: $o).
% 0.08/0.25 thf(decl_51, type, emptysetimpfalse: $o).
% 0.08/0.25 thf(decl_52, type, notinemptyset: $o).
% 0.08/0.25 thf(decl_53, type, exuE3e: $o).
% 0.08/0.25 thf(decl_54, type, setext: $o).
% 0.08/0.25 thf(decl_55, type, emptyI: $o).
% 0.08/0.25 thf(decl_56, type, noeltsimpempty: $o).
% 0.08/0.25 thf(decl_57, type, setbeta: $o).
% 0.08/0.25 thf(decl_58, type, nonempty: $i > $o).
% 0.08/0.25 thf(decl_59, type, nonemptyE1: $o).
% 0.08/0.25 thf(decl_60, type, nonemptyI: $o).
% 0.08/0.25 thf(decl_61, type, nonemptyI1: $o).
% 0.08/0.25 thf(decl_62, type, setadjoinIL: $o).
% 0.08/0.25 thf(decl_63, type, emptyinunitempty: $o).
% 0.08/0.25 thf(decl_64, type, setadjoinIR: $o).
% 0.08/0.25 thf(decl_65, type, setadjoinE: $o).
% 0.08/0.25 thf(decl_66, type, setadjoinOr: $o).
% 0.08/0.25 thf(decl_67, type, setoftrueEq: $o).
% 0.08/0.25 thf(decl_68, type, powersetI: $o).
% 0.08/0.25 thf(decl_69, type, emptyinPowerset: $o).
% 0.08/0.25 thf(decl_70, type, emptyInPowerset: $o).
% 0.08/0.25 thf(decl_71, type, powersetE: $o).
% 0.08/0.25 thf(decl_72, type, epred1_0: $o).
% 0.08/0.25 thf(decl_73, type, esk1_2: $i > $i > $i).
% 0.08/0.25 thf(decl_74, type, esk2_2: $i > $i > $i).
% 0.08/0.25 thf(decl_75, type, esk3_2: $i > $i > $i).
% 0.08/0.25 thf(decl_76, type, esk4_1: $i > $i).
% 0.08/0.25 thf(decl_77, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.08/0.25 thf(decl_78, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.25 thf(decl_79, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.08/0.25 thf(decl_80, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.25 thf(decl_81, type, esk9_1: $i > $i).
% 0.08/0.25 thf(decl_82, type, esk10_2: ($i > $o) > $i > $i).
% 0.08/0.25 thf(decl_83, type, esk11_1: ($i > $o) > $i).
% 0.08/0.25 thf(decl_84, type, esk12_2: ($i > $o) > $i > $i).
% 0.08/0.25 thf(decl_85, type, esk13_1: ($i > $o) > $i).
% 0.08/0.25 thf(decl_86, type, esk14_2: $i > $i > $i).
% 0.08/0.25 thf(decl_87, type, esk15_2: $i > $i > $i).
% 0.08/0.25 thf(decl_88, type, esk16_1: $i > $i).
% 0.08/0.25 thf(decl_89, type, esk17_1: $i > $i).
% 0.08/0.25 thf(decl_90, type, esk18_1: $i > $i).
% 0.08/0.25 thf(decl_91, type, esk19_2: $i > $i > $i).
% 0.08/0.25 thf(decl_92, type, esk20_0: $i).
% 0.08/0.25 thf(decl_93, type, esk21_0: $i).
% 0.08/0.25 thf(decl_94, type, esk22_0: $i).
% 0.08/0.25 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', exuE1)).
% 0.08/0.25 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', exu)).
% 0.08/0.25 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', replAx)).
% 0.08/0.25 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', prop2set)).
% 0.08/0.25 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', exuE3e)).
% 0.08/0.25 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', nonempty)).
% 0.08/0.25 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', nonemptyI)).
% 0.08/0.25 thf(setunionI, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', setunionI)).
% 0.08/0.25 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', setoftrueEq)).
% 0.08/0.25 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', dsetconstrER)).
% 0.08/0.25 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', dsetconstrEL)).
% 0.08/0.25 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', dsetconstrI)).
% 0.08/0.25 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', prop2setE)).
% 0.08/0.25 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', nonemptyE1)).
% 0.08/0.25 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', nonemptyI1)).
% 0.08/0.25 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', setbeta)).
% 0.08/0.25 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', emptyinunitempty)).
% 0.08/0.25 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', setadjoinIR)).
% 0.08/0.25 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.qs2vgl3VnA/E---3.1_358802.p', setadjoinE)).
% 0.08/0.25 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', setadjoinOr)).
% 0.08/0.25 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', powersetI)).
% 0.08/0.25 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', emptyinPowerset)).
% 0.08/0.25 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', emptyInPowerset)).
% 0.08/0.25 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', powersetE)).
% 0.08/0.25 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', setunionAx)).
% 0.08/0.25 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', omegaSAx)).
% 0.08/0.25 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', omega0Ax)).
% 0.08/0.25 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', powersetAx)).
% 0.08/0.25 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', setadjoinAx)).
% 0.08/0.25 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', emptysetAx)).
% 0.08/0.25 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', setextAx)).
% 0.08/0.25 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.qs2vgl3VnA/E---3.1_358802.p', omegaIndAx)).
% 0.08/0.25 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', wellorderingAx)).
% 0.08/0.25 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', foundationAx)).
% 0.08/0.25 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', noeltsimpempty)).
% 0.08/0.25 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', emptyI)).
% 0.08/0.25 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', setext)).
% 0.08/0.25 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', notinemptyset)).
% 0.08/0.25 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', emptysetimpfalse)).
% 0.08/0.25 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', emptysetE)).
% 0.08/0.25 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.qs2vgl3VnA/E---3.1_358802.p', setadjoinIL)).
% 0.08/0.25 thf(c_0_41, 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])).
% 0.08/0.25 thf(c_0_42, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.08/0.25 thf(c_0_43, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.08/0.25 thf(c_0_44, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.08/0.25 thf(c_0_45, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.08/0.25 thf(c_0_46, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.08/0.25 thf(c_0_47, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.08/0.25 thf(c_0_48, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setunionI])).
% 0.08/0.25 thf(c_0_49, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.08/0.25 thf(c_0_50, plain, ((exuE1)=(![X1:$i > $o]:((((?[X124:$i]:(((((X1 @ X124)))&(![X125:$i]:(((((X1 @ X125)))=>(((X124)=(X125))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_41, c_0_42])).
% 0.08/0.25 thf(c_0_51, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.08/0.25 thf(c_0_52, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.08/0.25 thf(c_0_53, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.08/0.25 thf(c_0_54, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X122:$i]:(((((X6 @ X2 @ X122)))&(![X123:$i]:(((((X6 @ X2 @ X123)))=>(((X122)=(X123)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_43, c_0_42])).
% 0.08/0.25 thf(c_0_55, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_44])).
% 0.08/0.25 thf(c_0_56, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X126:$i]:(((((X1 @ X126)))&(![X127:$i]:(((((X1 @ X127)))=>(((X126)=(X127))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_45, c_0_42])).
% 0.08/0.25 thf(c_0_57, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_46])).
% 0.08/0.25 thf(c_0_58, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_47, c_0_46])).
% 0.08/0.25 thf(c_0_59, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_46])).
% 0.08/0.25 thf(c_0_60, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.08/0.25 thf(c_0_61, plain, ((epred1_0)<=>![X157:$i]:(?[X158:$i]:((((![X159:$i]:(((in @ X159 @ X158)=>![X160:$i]:(((in @ X160 @ X159)=>(in @ X160 @ X157)))))&![X161:$i, X162:$i]:((((in @ X161 @ X157)&(in @ X162 @ X157))=>(![X163:$i]:(((in @ X163 @ X158)=>((in @ X161 @ X163)<=>(in @ X162 @ X163))))=>((X161)=(X162))))))&![X164:$i, X165:$i]:((((in @ X164 @ X158)&(in @ X165 @ X158))=>(![X166:$i]:(((in @ X166 @ X164)=>(in @ X166 @ X165)))|![X167:$i]:(((in @ X167 @ X165)=>(in @ X167 @ X164)))))))&![X168:$i]:(((![X169:$i]:(((in @ X169 @ X168)=>(in @ X169 @ X157)))&?[X170:$i]:((in @ X170 @ X168)))=>?[X171:$i, X172:$i]:(((((in @ X171 @ X158)&(in @ X172 @ X168))&~(?[X173:$i]:(((in @ X173 @ X171)&(in @ X173 @ X168)))))&![X174:$i]:(((in @ X174 @ X158)=>(![X175:$i]:(((in @ X175 @ X174)=>(in @ X175 @ X171)))|(in @ X172 @ X174)))))))))))), introduced(definition)).
% 0.08/0.25 thf(c_0_62, negated_conjecture, ~((![X128:$i, X129:$i]:((![X130:$i]:(((in @ X130 @ X128)<=>(in @ X130 @ X129)))=>((X128)=(X129))))=>(![X131:$i]:(~(in @ X131 @ emptyset))=>(![X132:$i, X133:$i, X134:$i]:(((in @ X134 @ (setadjoin @ X132 @ X133))<=>(((X134)=(X132))|(in @ X134 @ X133))))=>(![X135:$i, X136:$i]:(((in @ X136 @ (powerset @ X135))<=>![X137:$i]:(((in @ X137 @ X136)=>(in @ X137 @ X135)))))=>(![X138:$i, X139:$i]:(((in @ X139 @ (setunion @ X138))<=>?[X140:$i]:(((in @ X139 @ X140)&(in @ X140 @ X138)))))=>((in @ emptyset @ omega)=>(![X141:$i]:(((in @ X141 @ omega)=>(in @ (setadjoin @ X141 @ X141) @ omega)))=>(![X142:$i]:((((in @ emptyset @ X142)&![X143:$i]:((((in @ X143 @ omega)&(in @ X143 @ X142))=>(in @ (setadjoin @ X143 @ X143) @ X142))))=>![X144:$i]:(((in @ X144 @ omega)=>(in @ X144 @ X142)))))=>(![X145:$i > $i > $o, X146:$i]:((![X147:$i]:(((in @ X147 @ X146)=>?[X148:$i]:(((X145 @ X147 @ X148)&![X149:$i]:(((X145 @ X147 @ X149)=>((X148)=(X149))))))))=>?[X150:$i]:(![X151:$i]:(((in @ X151 @ X150)<=>?[X152:$i]:(((in @ X152 @ X146)&(X145 @ X152 @ X151))))))))=>(![X153:$i]:((?[X154:$i]:((in @ X154 @ X153))=>?[X155:$i]:(((in @ X155 @ X153)&~(?[X156:$i]:(((in @ X156 @ X155)&(in @ X156 @ X153))))))))=>((epred1_0)=>((descrp)=>(![X176:$i, X177:$i > $o, X178:$i]:(((in @ X178 @ X176)=>((X177 @ X178)=>(in @ X178 @ (dsetconstr @ X176 @ X177)))))=>(![X179:$i, X180:$i > $o, X181:$i]:(((in @ X181 @ (dsetconstr @ X179 @ X180))=>(in @ X181 @ X179)))=>(![X182:$i, X183:$i > $o, X184:$i]:(((in @ X184 @ (dsetconstr @ X182 @ X183))=>(X183 @ X184)))=>(![X185:$i > $o]:((?[X186:$i]:(((X185 @ X186)&![X187:$i]:(((X185 @ X187)=>((X186)=(X187))))))=>?[X188:$i]:(((X185 @ X188)&![X189:$i]:(((X185 @ X189)=>((X188)=(X189))))))))=>(![X190:$o, X191:$i]:(((in @ X191 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X190)))))=>(X190)))=>(![X192:$i]:(((in @ X192 @ emptyset)=>![X193:$o]:((X193))))=>(![X194:$i]:(((in @ X194 @ emptyset)=>~($true)))=>(![X195:$i]:(~(in @ X195 @ emptyset))=>(![X196:$i > $o]:((?[X197:$i]:(((X196 @ X197)&![X198:$i]:(((X196 @ X198)=>((X197)=(X198))))))=>?[X199:$i]:((X196 @ X199))))=>(![X200:$i, X201:$i]:((![X202:$i]:(((in @ X202 @ X200)=>(in @ X202 @ X201)))=>(![X203:$i]:(((in @ X203 @ X201)=>(in @ X203 @ X200)))=>((X200)=(X201)))))=>(![X204:$i]:((![X205:$i]:(~(in @ X205 @ X204))=>((X204)=(emptyset))))=>(![X206:$i]:((![X207:$i]:(~(in @ X207 @ X206))=>((X206)=(emptyset))))=>(![X208:$i, X209:$i > $o, X210:$i]:(((in @ X210 @ X208)=>((in @ X210 @ (dsetconstr @ X208 @ X209))<=>(X209 @ X210))))=>(![X211:$i]:((((X211)!=(emptyset))=>?[X212:$i]:((in @ X212 @ X211))))=>(![X213:$i, X214:$i > $o, X215:$i]:(((in @ X215 @ X213)=>((X214 @ X215)=>((dsetconstr @ X213 @ X214)!=(emptyset)))))=>(![X216:$i]:((?[X217:$i]:((in @ X217 @ X216))=>((X216)!=(emptyset))))=>(![X218:$i, X219:$i]:((in @ X218 @ (setadjoin @ X218 @ X219)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X220:$i, X221:$i, X222:$i]:(((in @ X222 @ X221)=>(in @ X222 @ (setadjoin @ X220 @ X221))))=>(![X223:$i, X224:$i, X225:$i]:(((in @ X225 @ (setadjoin @ X223 @ X224))=>![X226:$o]:(((((X225)=(X223))=>(X226))=>(((in @ X225 @ X224)=>(X226))=>(X226))))))=>(![X227:$i, X228:$i, X229:$i]:(((in @ X229 @ (setadjoin @ X227 @ X228))=>(((X229)=(X227))|(in @ X229 @ X228))))=>(![X230:$i]:(((dsetconstr @ X230 @ (^[Z0:$i]:($true)))=(X230)))=>(![X231:$i, X232:$i]:((![X233:$i]:(((in @ X233 @ X232)=>(in @ X233 @ X231)))=>(in @ X232 @ (powerset @ X231))))=>(![X234:$i]:((in @ emptyset @ (powerset @ X234)))=>(![X235:$i]:((in @ emptyset @ (powerset @ X235)))=>(![X236:$i, X237:$i, X238:$i]:(((in @ X237 @ (powerset @ X236))=>((in @ X238 @ X237)=>(in @ X238 @ X236))))=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_48, emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_49]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionAx]), omegaSAx]), omega0Ax]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx]), omegaIndAx]), c_0_50]), c_0_51]), c_0_52]), c_0_53]), wellorderingAx]), foundationAx]), c_0_54]), c_0_55]), noeltsimpempty]), emptyI]), setext]), c_0_56]), notinemptyset]), emptysetimpfalse]), emptysetE]), c_0_57]), c_0_58]), c_0_59]), setadjoinIL]), c_0_60])])]), c_0_61])).
% 0.08/0.25 thf(c_0_63, negated_conjecture, ![X239:$i, X240:$i, X242:$i, X243:$i, X244:$i, X245:$i, X246:$i, X247:$i, X248:$i, X249:$i, X250:$i, X252:$i, X253:$i, X255:$i, X256:$i, X257:$i, X258:$i, X259:$i, X261:$i, X262:$i > $i > $o, X263:$i, X265:$i, X268:$i, X270:$i, X271:$i, X272:$i, X273:$i, X275:$i, X276:$i, X277:$i > $o, X278:$i, X279:$i, X280:$i > $o, X281:$i, X282:$i, X283:$i > $o, X284:$i, X285:$i > $o, X286:$i, X289:$i, X290:$o, X291:$i, X292:$i, X293:$o, X294:$i, X295:$i, X296:$i > $o, X297:$i, X300:$i, X301:$i, X304:$i, X306:$i, X308:$i, X309:$i > $o, X310:$i, X311:$i, X313:$i, X314:$i > $o, X315:$i, X316:$i, X317:$i, X318:$i, X319:$i, X320:$i, X321:$i, X322:$i, X323:$i, X324:$i, X325:$i, X326:$o, X327:$i, X328:$i, X329:$i, X330:$i, X331:$i, X332:$i, X334:$i, X335:$i, X336:$i, X337:$i, X338:$i]:((((~(in @ (esk1_2 @ X239 @ X240) @ X239)|~(in @ (esk1_2 @ X239 @ X240) @ X240)|((X239)=(X240)))&((in @ (esk1_2 @ X239 @ X240) @ X239)|(in @ (esk1_2 @ X239 @ X240) @ X240)|((X239)=(X240))))&(~(in @ X242 @ emptyset)&(((~(in @ X245 @ (setadjoin @ X243 @ X244))|(((X245)=(X243))|(in @ X245 @ X244)))&((((X245)!=(X243))|(in @ X245 @ (setadjoin @ X243 @ X244)))&(~(in @ X245 @ X244)|(in @ X245 @ (setadjoin @ X243 @ X244)))))&(((~(in @ X247 @ (powerset @ X246))|(~(in @ X248 @ X247)|(in @ X248 @ X246)))&(((in @ (esk2_2 @ X249 @ X250) @ X250)|(in @ X250 @ (powerset @ X249)))&(~(in @ (esk2_2 @ X249 @ X250) @ X249)|(in @ X250 @ (powerset @ X249)))))&(((((in @ X253 @ (esk3_2 @ X252 @ X253))|~(in @ X253 @ (setunion @ X252)))&((in @ (esk3_2 @ X252 @ X253) @ X252)|~(in @ X253 @ (setunion @ X252))))&(~(in @ X256 @ X257)|~(in @ X257 @ X255)|(in @ X256 @ (setunion @ X255))))&((in @ emptyset @ omega)&((~(in @ X258 @ omega)|(in @ (setadjoin @ X258 @ X258) @ omega))&(((((in @ (esk4_1 @ X259) @ omega)|~(in @ emptyset @ X259)|(~(in @ X261 @ omega)|(in @ X261 @ X259)))&((in @ (esk4_1 @ X259) @ X259)|~(in @ emptyset @ X259)|(~(in @ X261 @ omega)|(in @ X261 @ X259))))&(~(in @ (setadjoin @ (esk4_1 @ X259) @ (esk4_1 @ X259)) @ X259)|~(in @ emptyset @ X259)|(~(in @ X261 @ omega)|(in @ X261 @ X259))))&((((((in @ (esk8_3 @ X262 @ X263 @ X268) @ X263)|~(in @ X268 @ (esk7_2 @ X262 @ X263))|(in @ (esk5_2 @ X262 @ X263) @ X263))&((X262 @ (esk8_3 @ X262 @ X263 @ X268) @ X268)|~(in @ X268 @ (esk7_2 @ X262 @ X263))|(in @ (esk5_2 @ X262 @ X263) @ X263)))&(~(in @ X271 @ X263)|~(X262 @ X271 @ X270)|(in @ X270 @ (esk7_2 @ X262 @ X263))|(in @ (esk5_2 @ X262 @ X263) @ X263)))&(((((in @ (esk8_3 @ X262 @ X263 @ X268) @ X263)|~(in @ X268 @ (esk7_2 @ X262 @ X263))|((X262 @ (esk5_2 @ X262 @ X263) @ (esk6_3 @ X262 @ X263 @ X265))|~(X262 @ (esk5_2 @ X262 @ X263) @ X265)))&((X262 @ (esk8_3 @ X262 @ X263 @ X268) @ X268)|~(in @ X268 @ (esk7_2 @ X262 @ X263))|((X262 @ (esk5_2 @ X262 @ X263) @ (esk6_3 @ X262 @ X263 @ X265))|~(X262 @ (esk5_2 @ X262 @ X263) @ X265))))&(~(in @ X271 @ X263)|~(X262 @ X271 @ X270)|(in @ X270 @ (esk7_2 @ X262 @ X263))|((X262 @ (esk5_2 @ X262 @ X263) @ (esk6_3 @ X262 @ X263 @ X265))|~(X262 @ (esk5_2 @ X262 @ X263) @ X265))))&((((in @ (esk8_3 @ X262 @ X263 @ X268) @ X263)|~(in @ X268 @ (esk7_2 @ X262 @ X263))|(((X265)!=(esk6_3 @ X262 @ X263 @ X265))|~(X262 @ (esk5_2 @ X262 @ X263) @ X265)))&((X262 @ (esk8_3 @ X262 @ X263 @ X268) @ X268)|~(in @ X268 @ (esk7_2 @ X262 @ X263))|(((X265)!=(esk6_3 @ X262 @ X263 @ X265))|~(X262 @ (esk5_2 @ X262 @ X263) @ X265))))&(~(in @ X271 @ X263)|~(X262 @ X271 @ X270)|(in @ X270 @ (esk7_2 @ X262 @ X263))|(((X265)!=(esk6_3 @ X262 @ X263 @ X265))|~(X262 @ (esk5_2 @ X262 @ X263) @ X265))))))&((((in @ (esk9_1 @ X272) @ X272)|~(in @ X273 @ X272))&(~(in @ X275 @ (esk9_1 @ X272))|~(in @ X275 @ X272)|~(in @ X273 @ X272)))&((epred1_0)&((descrp)&((~(in @ X278 @ X276)|(~(X277 @ X278)|(in @ X278 @ (dsetconstr @ X276 @ X277))))&((~(in @ X281 @ (dsetconstr @ X279 @ X280))|(in @ X281 @ X279))&((~(in @ X284 @ (dsetconstr @ X282 @ X283))|(X283 @ X284))&(((((X285 @ (esk11_1 @ X285))|((X285 @ (esk10_2 @ X285 @ X286))|~(X285 @ X286)))&(~(X285 @ X289)|((esk11_1 @ X285)=(X289))|((X285 @ (esk10_2 @ X285 @ X286))|~(X285 @ X286))))&(((X285 @ (esk11_1 @ X285))|(((X286)!=(esk10_2 @ X285 @ X286))|~(X285 @ X286)))&(~(X285 @ X289)|((esk11_1 @ X285)=(X289))|(((X286)!=(esk10_2 @ X285 @ X286))|~(X285 @ X286)))))&((~(in @ X291 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X290)))))|(X290))&((~(in @ X292 @ emptyset)|(X293))&((~(in @ X294 @ emptyset)|~($true))&(~(in @ X295 @ emptyset)&((((X296 @ (esk12_2 @ X296 @ X297))|~(X296 @ X297)|(X296 @ (esk13_1 @ X296)))&(((X297)!=(esk12_2 @ X296 @ X297))|~(X296 @ X297)|(X296 @ (esk13_1 @ X296))))&(((((in @ (esk15_2 @ X300 @ X301) @ X301)|((X300)=(X301))|(in @ (esk14_2 @ X300 @ X301) @ X300))&(~(in @ (esk15_2 @ X300 @ X301) @ X300)|((X300)=(X301))|(in @ (esk14_2 @ X300 @ X301) @ X300)))&(((in @ (esk15_2 @ X300 @ X301) @ X301)|((X300)=(X301))|~(in @ (esk14_2 @ X300 @ X301) @ X301))&(~(in @ (esk15_2 @ X300 @ X301) @ X300)|((X300)=(X301))|~(in @ (esk14_2 @ X300 @ X301) @ X301))))&(((in @ (esk16_1 @ X304) @ X304)|((X304)=(emptyset)))&(((in @ (esk17_1 @ X306) @ X306)|((X306)=(emptyset)))&(((~(in @ X310 @ (dsetconstr @ X308 @ X309))|(X309 @ X310)|~(in @ X310 @ X308))&(~(X309 @ X310)|(in @ X310 @ (dsetconstr @ X308 @ X309))|~(in @ X310 @ X308)))&((((X311)=(emptyset))|(in @ (esk18_1 @ X311) @ X311))&((~(in @ X315 @ X313)|(~(X314 @ X315)|((dsetconstr @ X313 @ X314)!=(emptyset))))&((~(in @ X317 @ X316)|((X316)!=(emptyset)))&((in @ X318 @ (setadjoin @ X318 @ X319))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X322 @ X321)|(in @ X322 @ (setadjoin @ X320 @ X321)))&(((((in @ X325 @ X324)|(X326)|((X325)=(X323))|~(in @ X325 @ (setadjoin @ X323 @ X324)))&(~(X326)|(X326)|((X325)=(X323))|~(in @ X325 @ (setadjoin @ X323 @ X324))))&(((in @ X325 @ X324)|(X326)|~(X326)|~(in @ X325 @ (setadjoin @ X323 @ X324)))&(~(X326)|(X326)|~(X326)|~(in @ X325 @ (setadjoin @ X323 @ X324)))))&((~(in @ X329 @ (setadjoin @ X327 @ X328))|(((X329)=(X327))|(in @ X329 @ X328)))&(((dsetconstr @ X330 @ (^[Z0:$i]:($true)))=(X330))&((((in @ (esk19_2 @ X331 @ X332) @ X332)|(in @ X332 @ (powerset @ X331)))&(~(in @ (esk19_2 @ X331 @ X332) @ X331)|(in @ X332 @ (powerset @ X331))))&((in @ emptyset @ (powerset @ X334))&((in @ emptyset @ (powerset @ X335))&((~(in @ X337 @ (powerset @ X336))|(~(in @ X338 @ X337)|(in @ X338 @ X336)))&((in @ esk21_0 @ esk22_0)&((in @ esk22_0 @ esk20_0)&~(in @ esk21_0 @ (setunion @ esk20_0))))))))))))))))))))))))))))))))))))))))))), 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_62])])])])])])])).
% 0.08/0.25 thf(c_0_64, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ (setunion @ X4))|~((in @ X2 @ X3))|~((in @ X3 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_63])).
% 0.08/0.25 thf(c_0_65, negated_conjecture, (in @ esk22_0 @ esk20_0), inference(split_conjunct,[status(thm)],[c_0_63])).
% 0.08/0.25 thf(c_0_66, negated_conjecture, ~((in @ esk21_0 @ (setunion @ esk20_0))), inference(split_conjunct,[status(thm)],[c_0_63])).
% 0.08/0.25 thf(c_0_67, negated_conjecture, ![X2:$i]:(((in @ X2 @ (setunion @ esk20_0))|~((in @ X2 @ esk22_0)))), inference(spm,[status(thm)],[c_0_64, c_0_65])).
% 0.08/0.25 thf(c_0_68, negated_conjecture, (in @ esk21_0 @ esk22_0), inference(split_conjunct,[status(thm)],[c_0_63])).
% 0.08/0.25 thf(c_0_69, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67]), c_0_68])]), ['proof']).
% 0.08/0.25 % SZS output end CNFRefutation
% 0.08/0.25 % Parsed axioms : 91
% 0.08/0.25 % Removed by relevancy pruning/SinE : 50
% 0.08/0.25 % Initial clauses : 84
% 0.08/0.25 % Removed in clause preprocessing : 3
% 0.08/0.25 % Initial clauses in saturation : 81
% 0.08/0.25 % Processed clauses : 56
% 0.08/0.25 % ...of these trivial : 1
% 0.08/0.25 % ...subsumed : 15
% 0.08/0.25 % ...remaining for further processing : 40
% 0.08/0.25 % Other redundant clauses eliminated : 2
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 0
% 0.08/0.25 % Backward-rewritten : 3
% 0.08/0.25 % Generated clauses : 97
% 0.08/0.25 % ...of the previous two non-redundant : 82
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 95
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 2
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 17
% 0.08/0.25 % ...of those cached : 6
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 35
% 0.08/0.25 % Positive orientable unit clauses : 15
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 2
% 0.08/0.25 % Non-unit-clauses : 18
% 0.08/0.25 % Current number of unprocessed clauses: 100
% 0.08/0.25 % ...number of literals in the above : 303
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 3
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 62
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 48
% 0.08/0.25 % Non-unit clause-clause subsumptions : 6
% 0.08/0.25 % Unit Clause-clause subsumption calls : 5
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 3
% 0.08/0.25 % BW rewrite match successes : 3
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 11005
% 0.08/0.25 % Search garbage collected termcells : 3938
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.010 s
% 0.08/0.25 % System time : 0.005 s
% 0.08/0.25 % Total time : 0.015 s
% 0.08/0.25 % Maximum resident set size: 4492 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.013 s
% 0.08/0.25 % System time : 0.009 s
% 0.08/0.25 % Total time : 0.022 s
% 0.08/0.25 % Maximum resident set size: 4864 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------