%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU523^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:22 AM UTC 2026
% Result : Theorem 0.25s 0.30s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU523^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:48:49 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.26 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p
% 0.25/0.30 % Version: 3.5.1-ho
% 0.25/0.30 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.25/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.30 % Starting sh5l with 300s (1) cores
% 0.25/0.30 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.30 % Starting new_bool_2 with 300s (1) cores
% 0.25/0.30 % new_bool_1 with pid 1078616 completed with status 0
% 0.25/0.30 % Result found by new_bool_1
% 0.25/0.30 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.25/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.30 % Starting sh5l with 300s (1) cores
% 0.25/0.30 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.30 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.30 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.25/0.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.30 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.30 % SubtermCWHack with pid 1078618 completed with status 0
% 0.25/0.30 % Result found by SubtermCWHack
% 0.25/0.30 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.25/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.30 % Starting sh5l with 300s (1) cores
% 0.25/0.30 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.30 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.30 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.30 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.25/0.30 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.30 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.30 % Preprocessing time : 0.003 s
% 0.25/0.30
% 0.25/0.30 % Proof found!
% 0.25/0.30 % SZS status Theorem
% 0.25/0.30 % SZS output start CNFRefutation
% 0.25/0.30 thf(decl_23, type, in: $i > $i > $o).
% 0.25/0.30 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.25/0.30 thf(decl_25, type, setextAx: $o).
% 0.25/0.30 thf(decl_26, type, emptyset: $i).
% 0.25/0.30 thf(decl_27, type, emptysetAx: $o).
% 0.25/0.30 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.25/0.30 thf(decl_29, type, setadjoinAx: $o).
% 0.25/0.30 thf(decl_30, type, powerset: $i > $i).
% 0.25/0.30 thf(decl_31, type, powersetAx: $o).
% 0.25/0.30 thf(decl_32, type, setunion: $i > $i).
% 0.25/0.30 thf(decl_33, type, setunionAx: $o).
% 0.25/0.30 thf(decl_34, type, omega: $i).
% 0.25/0.30 thf(decl_35, type, omega0Ax: $o).
% 0.25/0.30 thf(decl_36, type, omegaSAx: $o).
% 0.25/0.30 thf(decl_37, type, omegaIndAx: $o).
% 0.25/0.30 thf(decl_38, type, replAx: $o).
% 0.25/0.30 thf(decl_39, type, foundationAx: $o).
% 0.25/0.30 thf(decl_40, type, wellorderingAx: $o).
% 0.25/0.30 thf(decl_42, type, descrp: $o).
% 0.25/0.30 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.25/0.30 thf(decl_44, type, dsetconstrI: $o).
% 0.25/0.30 thf(decl_45, type, dsetconstrEL: $o).
% 0.25/0.30 thf(decl_46, type, dsetconstrER: $o).
% 0.25/0.30 thf(decl_47, type, exuE1: $o).
% 0.25/0.30 thf(decl_48, type, prop2set: $o > $i).
% 0.25/0.30 thf(decl_49, type, prop2setE: $o).
% 0.25/0.30 thf(decl_50, type, emptysetE: $o).
% 0.25/0.30 thf(decl_51, type, emptysetimpfalse: $o).
% 0.25/0.30 thf(decl_52, type, notinemptyset: $o).
% 0.25/0.30 thf(decl_53, type, exuE3e: $o).
% 0.25/0.30 thf(decl_54, type, setext: $o).
% 0.25/0.30 thf(decl_55, type, emptyI: $o).
% 0.25/0.30 thf(decl_56, type, noeltsimpempty: $o).
% 0.25/0.30 thf(decl_57, type, setbeta: $o).
% 0.25/0.30 thf(decl_58, type, nonempty: $i > $o).
% 0.25/0.30 thf(decl_59, type, nonemptyE1: $o).
% 0.25/0.30 thf(decl_60, type, nonemptyI: $o).
% 0.25/0.30 thf(decl_61, type, nonemptyI1: $o).
% 0.25/0.30 thf(decl_62, type, setadjoinIL: $o).
% 0.25/0.30 thf(decl_63, type, emptyinunitempty: $o).
% 0.25/0.30 thf(decl_64, type, setadjoinIR: $o).
% 0.25/0.30 thf(decl_65, type, setadjoinE: $o).
% 0.25/0.30 thf(decl_66, type, setadjoinOr: $o).
% 0.25/0.30 thf(decl_67, type, setoftrueEq: $o).
% 0.25/0.30 thf(decl_68, type, powersetI: $o).
% 0.25/0.30 thf(decl_69, type, emptyinPowerset: $o).
% 0.25/0.30 thf(decl_70, type, emptyInPowerset: $o).
% 0.25/0.30 thf(decl_71, type, powersetE: $o).
% 0.25/0.30 thf(decl_72, type, setunionI: $o).
% 0.25/0.30 thf(decl_73, type, epred1_0: $o).
% 0.25/0.30 thf(decl_74, type, esk1_2: $i > $i > $i).
% 0.25/0.30 thf(decl_75, type, esk2_2: $i > $i > $i).
% 0.25/0.30 thf(decl_76, type, esk3_2: $i > $i > $i).
% 0.25/0.30 thf(decl_77, type, esk4_1: $i > $i).
% 0.25/0.30 thf(decl_78, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.25/0.30 thf(decl_79, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.25/0.30 thf(decl_80, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.25/0.30 thf(decl_81, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.25/0.30 thf(decl_82, type, esk9_1: $i > $i).
% 0.25/0.30 thf(decl_83, type, esk10_2: ($i > $o) > $i > $i).
% 0.25/0.30 thf(decl_84, type, esk11_1: ($i > $o) > $i).
% 0.25/0.30 thf(decl_85, type, esk12_2: ($i > $o) > $i > $i).
% 0.25/0.30 thf(decl_86, type, esk13_1: ($i > $o) > $i).
% 0.25/0.30 thf(decl_87, type, esk14_2: $i > $i > $i).
% 0.25/0.30 thf(decl_88, type, esk15_2: $i > $i > $i).
% 0.25/0.30 thf(decl_89, type, esk16_1: $i > $i).
% 0.25/0.30 thf(decl_90, type, esk17_1: $i > $i).
% 0.25/0.30 thf(decl_91, type, esk18_1: $i > $i).
% 0.25/0.30 thf(decl_92, type, esk19_2: $i > $i > $i).
% 0.25/0.30 thf(decl_93, type, esk20_0: $i).
% 0.25/0.30 thf(decl_94, type, esk21_0: $i).
% 0.25/0.30 thf(decl_95, type, epred2_0: $o).
% 0.25/0.30 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', replAx)).
% 0.25/0.30 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', exu)).
% 0.25/0.30 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', prop2set)).
% 0.25/0.30 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', exuE1)).
% 0.25/0.30 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', exuE3e)).
% 0.25/0.30 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', nonemptyI)).
% 0.25/0.30 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', nonempty)).
% 0.25/0.30 thf(setunionE, 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)=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14)))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', setunionE)).
% 0.25/0.30 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', setoftrueEq)).
% 0.25/0.30 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', prop2setE)).
% 0.25/0.30 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', dsetconstrER)).
% 0.25/0.30 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', dsetconstrEL)).
% 0.25/0.30 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', dsetconstrI)).
% 0.25/0.30 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', setbeta)).
% 0.25/0.30 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', nonemptyI1)).
% 0.25/0.30 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', nonemptyE1)).
% 0.25/0.30 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', emptysetAx)).
% 0.25/0.30 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', setadjoinIR)).
% 0.25/0.30 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', setadjoinE)).
% 0.25/0.30 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', setadjoinOr)).
% 0.25/0.30 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', powersetI)).
% 0.25/0.30 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', emptyinPowerset)).
% 0.25/0.30 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', emptyInPowerset)).
% 0.25/0.30 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', powersetE)).
% 0.25/0.30 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', setunionI)).
% 0.25/0.30 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', setunionAx)).
% 0.25/0.30 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', omegaIndAx)).
% 0.25/0.30 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', omegaSAx)).
% 0.25/0.30 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', omega0Ax)).
% 0.25/0.30 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', powersetAx)).
% 0.25/0.30 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', setadjoinAx)).
% 0.25/0.30 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', setextAx)).
% 0.25/0.30 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', wellorderingAx)).
% 0.25/0.30 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', foundationAx)).
% 0.25/0.30 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', emptysetE)).
% 0.25/0.30 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', noeltsimpempty)).
% 0.25/0.30 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', emptyI)).
% 0.25/0.30 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', setext)).
% 0.25/0.30 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', notinemptyset)).
% 0.25/0.30 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', emptysetimpfalse)).
% 0.25/0.30 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', setadjoinIL)).
% 0.25/0.30 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.T4NanQ55wH/E---3.1_1078601.p', emptyinunitempty)).
% 0.25/0.30 thf(c_0_42, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.25/0.30 thf(c_0_43, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.25/0.30 thf(c_0_44, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.25/0.30 thf(c_0_45, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.25/0.30 thf(c_0_46, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.25/0.30 thf(c_0_47, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.25/0.30 thf(c_0_48, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.25/0.30 thf(c_0_49, 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)=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[setunionE])).
% 0.25/0.30 thf(c_0_50, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.25/0.30 thf(c_0_51, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X127:$i]:(((((X6 @ X2 @ X127)))&(![X128:$i]:(((((X6 @ X2 @ X128)))=>(((X127)=(X128)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_42, c_0_43])).
% 0.25/0.30 thf(c_0_52, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_44])).
% 0.25/0.30 thf(c_0_53, plain, ((exuE1)=(![X1:$i > $o]:((((?[X129:$i]:(((((X1 @ X129)))&(![X130:$i]:(((((X1 @ X130)))=>(((X129)=(X130))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_45, c_0_43])).
% 0.25/0.30 thf(c_0_54, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.25/0.30 thf(c_0_55, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.25/0.30 thf(c_0_56, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.25/0.30 thf(c_0_57, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.25/0.30 thf(c_0_58, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X131:$i]:(((((X1 @ X131)))&(![X132:$i]:(((((X1 @ X132)))=>(((X131)=(X132))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_46, c_0_43])).
% 0.25/0.30 thf(c_0_59, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_47, c_0_48])).
% 0.25/0.30 thf(c_0_60, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_48])).
% 0.25/0.30 thf(c_0_61, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_48])).
% 0.25/0.30 thf(c_0_62, plain, ((epred1_0)<=>![X162:$i]:(?[X163:$i]:((((![X164:$i]:(((in @ X164 @ X163)=>![X165:$i]:(((in @ X165 @ X164)=>(in @ X165 @ X162)))))&![X166:$i, X167:$i]:((((in @ X166 @ X162)&(in @ X167 @ X162))=>(![X168:$i]:(((in @ X168 @ X163)=>((in @ X166 @ X168)<=>(in @ X167 @ X168))))=>((X166)=(X167))))))&![X169:$i, X170:$i]:((((in @ X169 @ X163)&(in @ X170 @ X163))=>(![X171:$i]:(((in @ X171 @ X169)=>(in @ X171 @ X170)))|![X172:$i]:(((in @ X172 @ X170)=>(in @ X172 @ X169)))))))&![X173:$i]:(((![X174:$i]:(((in @ X174 @ X173)=>(in @ X174 @ X162)))&?[X175:$i]:((in @ X175 @ X173)))=>?[X176:$i, X177:$i]:(((((in @ X176 @ X163)&(in @ X177 @ X173))&~(?[X178:$i]:(((in @ X178 @ X176)&(in @ X178 @ X173)))))&![X179:$i]:(((in @ X179 @ X163)=>(![X180:$i]:(((in @ X180 @ X179)=>(in @ X180 @ X176)))|(in @ X177 @ X179)))))))))))), introduced(definition)).
% 0.25/0.30 thf(c_0_63, negated_conjecture, ~((![X133:$i, X134:$i]:((![X135:$i]:(((in @ X135 @ X133)<=>(in @ X135 @ X134)))=>((X133)=(X134))))=>(![X136:$i]:(~(in @ X136 @ emptyset))=>(![X137:$i, X138:$i, X139:$i]:(((in @ X139 @ (setadjoin @ X137 @ X138))<=>(((X139)=(X137))|(in @ X139 @ X138))))=>(![X140:$i, X141:$i]:(((in @ X141 @ (powerset @ X140))<=>![X142:$i]:(((in @ X142 @ X141)=>(in @ X142 @ X140)))))=>(![X143:$i, X144:$i]:(((in @ X144 @ (setunion @ X143))<=>?[X145:$i]:(((in @ X144 @ X145)&(in @ X145 @ X143)))))=>((in @ emptyset @ omega)=>(![X146:$i]:(((in @ X146 @ omega)=>(in @ (setadjoin @ X146 @ X146) @ omega)))=>(![X147:$i]:((((in @ emptyset @ X147)&![X148:$i]:((((in @ X148 @ omega)&(in @ X148 @ X147))=>(in @ (setadjoin @ X148 @ X148) @ X147))))=>![X149:$i]:(((in @ X149 @ omega)=>(in @ X149 @ X147)))))=>(![X150:$i > $i > $o, X151:$i]:((![X152:$i]:(((in @ X152 @ X151)=>?[X153:$i]:(((X150 @ X152 @ X153)&![X154:$i]:(((X150 @ X152 @ X154)=>((X153)=(X154))))))))=>?[X155:$i]:(![X156:$i]:(((in @ X156 @ X155)<=>?[X157:$i]:(((in @ X157 @ X151)&(X150 @ X157 @ X156))))))))=>(![X158:$i]:((?[X159:$i]:((in @ X159 @ X158))=>?[X160:$i]:(((in @ X160 @ X158)&~(?[X161:$i]:(((in @ X161 @ X160)&(in @ X161 @ X158))))))))=>((epred1_0)=>((descrp)=>(![X181:$i, X182:$i > $o, X183:$i]:(((in @ X183 @ X181)=>((X182 @ X183)=>(in @ X183 @ (dsetconstr @ X181 @ X182)))))=>(![X184:$i, X185:$i > $o, X186:$i]:(((in @ X186 @ (dsetconstr @ X184 @ X185))=>(in @ X186 @ X184)))=>(![X187:$i, X188:$i > $o, X189:$i]:(((in @ X189 @ (dsetconstr @ X187 @ X188))=>(X188 @ X189)))=>(![X190:$i > $o]:((?[X191:$i]:(((X190 @ X191)&![X192:$i]:(((X190 @ X192)=>((X191)=(X192))))))=>?[X193:$i]:(((X190 @ X193)&![X194:$i]:(((X190 @ X194)=>((X193)=(X194))))))))=>(![X195:$o, X196:$i]:(((in @ X196 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X195)))))=>(X195)))=>(![X197:$i]:(((in @ X197 @ emptyset)=>![X198:$o]:((X198))))=>(![X199:$i]:(((in @ X199 @ emptyset)=>~($true)))=>(![X200:$i]:(~(in @ X200 @ emptyset))=>(![X201:$i > $o]:((?[X202:$i]:(((X201 @ X202)&![X203:$i]:(((X201 @ X203)=>((X202)=(X203))))))=>?[X204:$i]:((X201 @ X204))))=>(![X205:$i, X206:$i]:((![X207:$i]:(((in @ X207 @ X205)=>(in @ X207 @ X206)))=>(![X208:$i]:(((in @ X208 @ X206)=>(in @ X208 @ X205)))=>((X205)=(X206)))))=>(![X209:$i]:((![X210:$i]:(~(in @ X210 @ X209))=>((X209)=(emptyset))))=>(![X211:$i]:((![X212:$i]:(~(in @ X212 @ X211))=>((X211)=(emptyset))))=>(![X213:$i, X214:$i > $o, X215:$i]:(((in @ X215 @ X213)=>((in @ X215 @ (dsetconstr @ X213 @ X214))<=>(X214 @ X215))))=>(![X216:$i]:((((X216)!=(emptyset))=>?[X217:$i]:((in @ X217 @ X216))))=>(![X218:$i, X219:$i > $o, X220:$i]:(((in @ X220 @ X218)=>((X219 @ X220)=>((dsetconstr @ X218 @ X219)!=(emptyset)))))=>(![X221:$i]:((?[X222:$i]:((in @ X222 @ X221))=>((X221)!=(emptyset))))=>(![X223:$i, X224:$i]:((in @ X223 @ (setadjoin @ X223 @ X224)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X225:$i, X226:$i, X227:$i]:(((in @ X227 @ X226)=>(in @ X227 @ (setadjoin @ X225 @ X226))))=>(![X228:$i, X229:$i, X230:$i]:(((in @ X230 @ (setadjoin @ X228 @ X229))=>![X231:$o]:(((((X230)=(X228))=>(X231))=>(((in @ X230 @ X229)=>(X231))=>(X231))))))=>(![X232:$i, X233:$i, X234:$i]:(((in @ X234 @ (setadjoin @ X232 @ X233))=>(((X234)=(X232))|(in @ X234 @ X233))))=>(![X235:$i]:(((dsetconstr @ X235 @ (^[Z0:$i]:($true)))=(X235)))=>(![X236:$i, X237:$i]:((![X238:$i]:(((in @ X238 @ X237)=>(in @ X238 @ X236)))=>(in @ X237 @ (powerset @ X236))))=>(![X239:$i]:((in @ emptyset @ (powerset @ X239)))=>(![X240:$i]:((in @ emptyset @ (powerset @ X240)))=>(![X241:$i, X242:$i, X243:$i]:(((in @ X242 @ (powerset @ X241))=>((in @ X243 @ X242)=>(in @ X243 @ X241))))=>(![X244:$i, X245:$i, X246:$i]:(((in @ X245 @ X246)=>((in @ X246 @ X244)=>(in @ X245 @ (setunion @ X244)))))=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14))))))))))))))))))))))))))))))))))))))))))))), 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)],[c_0_49, emptysetAx]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_50]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionAx]), omegaIndAx]), omegaSAx]), omega0Ax]), powersetAx]), setadjoinAx]), setextAx]), c_0_51]), c_0_52]), c_0_53]), c_0_54]), c_0_55]), c_0_56]), wellorderingAx]), foundationAx]), emptysetE]), c_0_57]), noeltsimpempty]), emptyI]), setext]), c_0_58]), notinemptyset]), emptysetimpfalse]), c_0_59]), c_0_60]), setadjoinIL]), emptyinunitempty]), c_0_61])])]), c_0_62])).
% 0.25/0.30 thf(c_0_64, negated_conjecture, ![X247:$i, X248:$i, X250:$i, X251:$i, X252:$i, X253:$i, X254:$i, X255:$i, X256:$i, X257:$i, X258:$i, X260:$i, X261:$i, X263:$i, X264:$i, X265:$i, X266:$i, X267:$i, X269:$i, X270:$i > $i > $o, X271:$i, X273:$i, X276:$i, X278:$i, X279:$i, X280:$i, X281:$i, X283:$i, X284:$i, X285:$i > $o, X286:$i, X287:$i, X288:$i > $o, X289:$i, X290:$i, X291:$i > $o, X292:$i, X293:$i > $o, X294:$i, X297:$i, X298:$o, X299:$i, X300:$i, X301:$o, X302:$i, X303:$i, X304:$i > $o, X305:$i, X308:$i, X309:$i, X312:$i, X314:$i, X316:$i, X317:$i > $o, X318:$i, X319:$i, X321:$i, X322:$i > $o, X323:$i, X324:$i, X325:$i, X326:$i, X327:$i, X328:$i, X329:$i, X330:$i, X331:$i, X332:$i, X333:$i, X334:$o, X335:$i, X336:$i, X337:$i, X338:$i, X339:$i, X340:$i, X342:$i, X343:$i, X344:$i, X345:$i, X346:$i, X347:$i, X348:$i, X349:$i, X353:$i]:((((~(in @ (esk1_2 @ X247 @ X248) @ X247)|~(in @ (esk1_2 @ X247 @ X248) @ X248)|((X247)=(X248)))&((in @ (esk1_2 @ X247 @ X248) @ X247)|(in @ (esk1_2 @ X247 @ X248) @ X248)|((X247)=(X248))))&(~(in @ X250 @ emptyset)&(((~(in @ X253 @ (setadjoin @ X251 @ X252))|(((X253)=(X251))|(in @ X253 @ X252)))&((((X253)!=(X251))|(in @ X253 @ (setadjoin @ X251 @ X252)))&(~(in @ X253 @ X252)|(in @ X253 @ (setadjoin @ X251 @ X252)))))&(((~(in @ X255 @ (powerset @ X254))|(~(in @ X256 @ X255)|(in @ X256 @ X254)))&(((in @ (esk2_2 @ X257 @ X258) @ X258)|(in @ X258 @ (powerset @ X257)))&(~(in @ (esk2_2 @ X257 @ X258) @ X257)|(in @ X258 @ (powerset @ X257)))))&(((((in @ X261 @ (esk3_2 @ X260 @ X261))|~(in @ X261 @ (setunion @ X260)))&((in @ (esk3_2 @ X260 @ X261) @ X260)|~(in @ X261 @ (setunion @ X260))))&(~(in @ X264 @ X265)|~(in @ X265 @ X263)|(in @ X264 @ (setunion @ X263))))&((in @ emptyset @ omega)&((~(in @ X266 @ omega)|(in @ (setadjoin @ X266 @ X266) @ omega))&(((((in @ (esk4_1 @ X267) @ omega)|~(in @ emptyset @ X267)|(~(in @ X269 @ omega)|(in @ X269 @ X267)))&((in @ (esk4_1 @ X267) @ X267)|~(in @ emptyset @ X267)|(~(in @ X269 @ omega)|(in @ X269 @ X267))))&(~(in @ (setadjoin @ (esk4_1 @ X267) @ (esk4_1 @ X267)) @ X267)|~(in @ emptyset @ X267)|(~(in @ X269 @ omega)|(in @ X269 @ X267))))&((((((in @ (esk8_3 @ X270 @ X271 @ X276) @ X271)|~(in @ X276 @ (esk7_2 @ X270 @ X271))|(in @ (esk5_2 @ X270 @ X271) @ X271))&((X270 @ (esk8_3 @ X270 @ X271 @ X276) @ X276)|~(in @ X276 @ (esk7_2 @ X270 @ X271))|(in @ (esk5_2 @ X270 @ X271) @ X271)))&(~(in @ X279 @ X271)|~(X270 @ X279 @ X278)|(in @ X278 @ (esk7_2 @ X270 @ X271))|(in @ (esk5_2 @ X270 @ X271) @ X271)))&(((((in @ (esk8_3 @ X270 @ X271 @ X276) @ X271)|~(in @ X276 @ (esk7_2 @ X270 @ X271))|((X270 @ (esk5_2 @ X270 @ X271) @ (esk6_3 @ X270 @ X271 @ X273))|~(X270 @ (esk5_2 @ X270 @ X271) @ X273)))&((X270 @ (esk8_3 @ X270 @ X271 @ X276) @ X276)|~(in @ X276 @ (esk7_2 @ X270 @ X271))|((X270 @ (esk5_2 @ X270 @ X271) @ (esk6_3 @ X270 @ X271 @ X273))|~(X270 @ (esk5_2 @ X270 @ X271) @ X273))))&(~(in @ X279 @ X271)|~(X270 @ X279 @ X278)|(in @ X278 @ (esk7_2 @ X270 @ X271))|((X270 @ (esk5_2 @ X270 @ X271) @ (esk6_3 @ X270 @ X271 @ X273))|~(X270 @ (esk5_2 @ X270 @ X271) @ X273))))&((((in @ (esk8_3 @ X270 @ X271 @ X276) @ X271)|~(in @ X276 @ (esk7_2 @ X270 @ X271))|(((X273)!=(esk6_3 @ X270 @ X271 @ X273))|~(X270 @ (esk5_2 @ X270 @ X271) @ X273)))&((X270 @ (esk8_3 @ X270 @ X271 @ X276) @ X276)|~(in @ X276 @ (esk7_2 @ X270 @ X271))|(((X273)!=(esk6_3 @ X270 @ X271 @ X273))|~(X270 @ (esk5_2 @ X270 @ X271) @ X273))))&(~(in @ X279 @ X271)|~(X270 @ X279 @ X278)|(in @ X278 @ (esk7_2 @ X270 @ X271))|(((X273)!=(esk6_3 @ X270 @ X271 @ X273))|~(X270 @ (esk5_2 @ X270 @ X271) @ X273))))))&((((in @ (esk9_1 @ X280) @ X280)|~(in @ X281 @ X280))&(~(in @ X283 @ (esk9_1 @ X280))|~(in @ X283 @ X280)|~(in @ X281 @ X280)))&((epred1_0)&((descrp)&((~(in @ X286 @ X284)|(~(X285 @ X286)|(in @ X286 @ (dsetconstr @ X284 @ X285))))&((~(in @ X289 @ (dsetconstr @ X287 @ X288))|(in @ X289 @ X287))&((~(in @ X292 @ (dsetconstr @ X290 @ X291))|(X291 @ X292))&(((((X293 @ (esk11_1 @ X293))|((X293 @ (esk10_2 @ X293 @ X294))|~(X293 @ X294)))&(~(X293 @ X297)|((esk11_1 @ X293)=(X297))|((X293 @ (esk10_2 @ X293 @ X294))|~(X293 @ X294))))&(((X293 @ (esk11_1 @ X293))|(((X294)!=(esk10_2 @ X293 @ X294))|~(X293 @ X294)))&(~(X293 @ X297)|((esk11_1 @ X293)=(X297))|(((X294)!=(esk10_2 @ X293 @ X294))|~(X293 @ X294)))))&((~(in @ X299 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X298)))))|(X298))&((~(in @ X300 @ emptyset)|(X301))&((~(in @ X302 @ emptyset)|~($true))&(~(in @ X303 @ emptyset)&((((X304 @ (esk12_2 @ X304 @ X305))|~(X304 @ X305)|(X304 @ (esk13_1 @ X304)))&(((X305)!=(esk12_2 @ X304 @ X305))|~(X304 @ X305)|(X304 @ (esk13_1 @ X304))))&(((((in @ (esk15_2 @ X308 @ X309) @ X309)|((X308)=(X309))|(in @ (esk14_2 @ X308 @ X309) @ X308))&(~(in @ (esk15_2 @ X308 @ X309) @ X308)|((X308)=(X309))|(in @ (esk14_2 @ X308 @ X309) @ X308)))&(((in @ (esk15_2 @ X308 @ X309) @ X309)|((X308)=(X309))|~(in @ (esk14_2 @ X308 @ X309) @ X309))&(~(in @ (esk15_2 @ X308 @ X309) @ X308)|((X308)=(X309))|~(in @ (esk14_2 @ X308 @ X309) @ X309))))&(((in @ (esk16_1 @ X312) @ X312)|((X312)=(emptyset)))&(((in @ (esk17_1 @ X314) @ X314)|((X314)=(emptyset)))&(((~(in @ X318 @ (dsetconstr @ X316 @ X317))|(X317 @ X318)|~(in @ X318 @ X316))&(~(X317 @ X318)|(in @ X318 @ (dsetconstr @ X316 @ X317))|~(in @ X318 @ X316)))&((((X319)=(emptyset))|(in @ (esk18_1 @ X319) @ X319))&((~(in @ X323 @ X321)|(~(X322 @ X323)|((dsetconstr @ X321 @ X322)!=(emptyset))))&((~(in @ X325 @ X324)|((X324)!=(emptyset)))&((in @ X326 @ (setadjoin @ X326 @ X327))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X330 @ X329)|(in @ X330 @ (setadjoin @ X328 @ X329)))&(((((in @ X333 @ X332)|(X334)|((X333)=(X331))|~(in @ X333 @ (setadjoin @ X331 @ X332)))&(~(X334)|(X334)|((X333)=(X331))|~(in @ X333 @ (setadjoin @ X331 @ X332))))&(((in @ X333 @ X332)|(X334)|~(X334)|~(in @ X333 @ (setadjoin @ X331 @ X332)))&(~(X334)|(X334)|~(X334)|~(in @ X333 @ (setadjoin @ X331 @ X332)))))&((~(in @ X337 @ (setadjoin @ X335 @ X336))|(((X337)=(X335))|(in @ X337 @ X336)))&(((dsetconstr @ X338 @ (^[Z0:$i]:($true)))=(X338))&((((in @ (esk19_2 @ X339 @ X340) @ X340)|(in @ X340 @ (powerset @ X339)))&(~(in @ (esk19_2 @ X339 @ X340) @ X339)|(in @ X340 @ (powerset @ X339))))&((in @ emptyset @ (powerset @ X342))&((in @ emptyset @ (powerset @ X343))&((~(in @ X345 @ (powerset @ X344))|(~(in @ X346 @ X345)|(in @ X346 @ X344)))&((~(in @ X348 @ X349)|(~(in @ X349 @ X347)|(in @ X348 @ (setunion @ X347))))&((in @ esk21_0 @ (setunion @ esk20_0))&((~(in @ esk21_0 @ X353)|(~(in @ X353 @ esk20_0)|(epred2_0)))&~(epred2_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_63])])])])])])])).
% 0.25/0.30 thf(c_0_65, negated_conjecture, ![X2:$i]:(((epred2_0)|~((in @ esk21_0 @ X2))|~((in @ X2 @ esk20_0)))), inference(split_conjunct,[status(thm)],[c_0_64])).
% 0.25/0.30 thf(c_0_66, negated_conjecture, ~((epred2_0)), inference(split_conjunct,[status(thm)],[c_0_64])).
% 0.25/0.30 thf(c_0_67, negated_conjecture, ![X2:$i]:((~((in @ X2 @ esk20_0))|~((in @ esk21_0 @ X2)))), inference(sr,[status(thm)],[c_0_65, c_0_66])).
% 0.25/0.30 thf(c_0_68, negated_conjecture, ![X3:$i, X2:$i]:(((in @ (esk3_2 @ X2 @ X3) @ X2)|~((in @ X3 @ (setunion @ X2))))), inference(split_conjunct,[status(thm)],[c_0_64])).
% 0.25/0.30 thf(c_0_69, negated_conjecture, ![X2:$i]:((~((in @ esk21_0 @ (esk3_2 @ esk20_0 @ X2)))|~((in @ X2 @ (setunion @ esk20_0))))), inference(spm,[status(thm)],[c_0_67, c_0_68])).
% 0.25/0.30 thf(c_0_70, negated_conjecture, ![X2:$i, X3:$i]:(((in @ X2 @ (esk3_2 @ X3 @ X2))|~((in @ X2 @ (setunion @ X3))))), inference(split_conjunct,[status(thm)],[c_0_64])).
% 0.25/0.30 thf(c_0_71, negated_conjecture, (in @ esk21_0 @ (setunion @ esk20_0)), inference(split_conjunct,[status(thm)],[c_0_64])).
% 0.25/0.30 thf(c_0_72, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_70]), c_0_71])]), ['proof']).
% 0.25/0.30 % SZS output end CNFRefutation
% 0.25/0.30 % Parsed axioms : 93
% 0.25/0.30 % Removed by relevancy pruning/SinE : 51
% 0.25/0.30 % Initial clauses : 85
% 0.25/0.30 % Removed in clause preprocessing : 3
% 0.25/0.30 % Initial clauses in saturation : 82
% 0.25/0.30 % Processed clauses : 83
% 0.25/0.30 % ...of these trivial : 2
% 0.25/0.30 % ...subsumed : 23
% 0.25/0.30 % ...remaining for further processing : 58
% 0.25/0.30 % Other redundant clauses eliminated : 2
% 0.25/0.30 % Clauses deleted for lack of memory : 0
% 0.25/0.30 % Backward-subsumed : 2
% 0.25/0.30 % Backward-rewritten : 3
% 0.25/0.30 % Generated clauses : 142
% 0.25/0.30 % ...of the previous two non-redundant : 126
% 0.25/0.30 % ...aggressively subsumed : 0
% 0.25/0.30 % Contextual simplify-reflections : 0
% 0.25/0.30 % Paramodulations : 140
% 0.25/0.30 % Factorizations : 0
% 0.25/0.30 % NegExts : 0
% 0.25/0.30 % Equation resolutions : 2
% 0.25/0.30 % Disequality decompositions : 0
% 0.25/0.30 % Total rewrite steps : 22
% 0.25/0.30 % ...of those cached : 10
% 0.25/0.30 % Propositional unsat checks : 0
% 0.25/0.30 % Propositional check models : 0
% 0.25/0.30 % Propositional check unsatisfiable : 0
% 0.25/0.30 % Propositional clauses : 0
% 0.25/0.30 % Propositional clauses after purity: 0
% 0.25/0.30 % Propositional unsat core size : 0
% 0.25/0.30 % Propositional preprocessing time : 0.000
% 0.25/0.30 % Propositional encoding time : 0.000
% 0.25/0.30 % Propositional solver time : 0.000
% 0.25/0.30 % Success case prop preproc time : 0.000
% 0.25/0.30 % Success case prop encoding time : 0.000
% 0.25/0.30 % Success case prop solver time : 0.000
% 0.25/0.30 % Current number of processed clauses : 51
% 0.25/0.30 % Positive orientable unit clauses : 15
% 0.25/0.30 % Positive unorientable unit clauses: 0
% 0.25/0.30 % Negative unit clauses : 3
% 0.25/0.30 % Non-unit-clauses : 33
% 0.25/0.30 % Current number of unprocessed clauses: 118
% 0.25/0.30 % ...number of literals in the above : 344
% 0.25/0.30 % Current number of archived formulas : 0
% 0.25/0.30 % Current number of archived clauses : 5
% 0.25/0.30 % Clause-clause subsumption calls (NU) : 229
% 0.25/0.30 % Rec. Clause-clause subsumption calls : 204
% 0.25/0.30 % Non-unit clause-clause subsumptions : 11
% 0.25/0.30 % Unit Clause-clause subsumption calls : 42
% 0.25/0.30 % Rewrite failures with RHS unbound : 0
% 0.25/0.30 % BW rewrite match attempts : 7
% 0.25/0.30 % BW rewrite match successes : 3
% 0.25/0.30 % Condensation attempts : 0
% 0.25/0.30 % Condensation successes : 0
% 0.25/0.30 % Termbank termtop insertions : 11965
% 0.25/0.30 % Search garbage collected termcells : 4063
% 0.25/0.30
% 0.25/0.30 % -------------------------------------------------
% 0.25/0.30 % User time : 0.013 s
% 0.25/0.30 % System time : 0.009 s
% 0.25/0.30 % Total time : 0.022 s
% 0.25/0.30 % Maximum resident set size: 4496 pages
% 0.25/0.30
% 0.25/0.30 % -------------------------------------------------
% 0.25/0.30 % User time : 0.016 s
% 0.25/0.30 % System time : 0.014 s
% 0.25/0.30 % Total time : 0.030 s
% 0.25/0.30 % Maximum resident set size: 4864 pages
% 0.25/0.30 % E exiting
%------------------------------------------------------------------------------