%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU524^1 : 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 : n003.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 0.21s 0.29s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU524^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n003.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 13:49:58 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.23 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.zd5KXSFP22/E---3.1_2528258.p
% 0.21/0.29 % Version: 3.5.1-ho
% 0.21/0.29 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.29 % Starting sh5l with 300s (1) cores
% 0.21/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.29 % new_bool_2 with pid 2528274 completed with status 0
% 0.21/0.29 % Result found by new_bool_2
% 0.21/0.29 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.29 % Starting sh5l with 300s (1) cores
% 0.21/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.29 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.29 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.21/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.29 % SubtermCWHack with pid 2528280 completed with status 0
% 0.21/0.29 % Result found by SubtermCWHack
% 0.21/0.29 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.29 % Starting sh5l with 300s (1) cores
% 0.21/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.21/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.21/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.29 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.29 % Search class: HGHSM-FFMS31-SHFSMSBN
% 0.21/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.29 % Preprocessing time : 0.003 s
% 0.21/0.29
% 0.21/0.29 % Proof found!
% 0.21/0.29 % SZS status Theorem
% 0.21/0.29 % SZS output start CNFRefutation
% 0.21/0.29 thf(decl_23, type, in: $i > $i > $o).
% 0.21/0.29 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.21/0.29 thf(decl_25, type, setextAx: $o).
% 0.21/0.29 thf(decl_26, type, emptyset: $i).
% 0.21/0.29 thf(decl_27, type, emptysetAx: $o).
% 0.21/0.29 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.21/0.29 thf(decl_29, type, setadjoinAx: $o).
% 0.21/0.29 thf(decl_30, type, powerset: $i > $i).
% 0.21/0.29 thf(decl_31, type, powersetAx: $o).
% 0.21/0.29 thf(decl_32, type, setunion: $i > $i).
% 0.21/0.29 thf(decl_33, type, setunionAx: $o).
% 0.21/0.29 thf(decl_34, type, omega: $i).
% 0.21/0.29 thf(decl_35, type, omega0Ax: $o).
% 0.21/0.29 thf(decl_36, type, omegaSAx: $o).
% 0.21/0.29 thf(decl_37, type, omegaIndAx: $o).
% 0.21/0.29 thf(decl_38, type, replAx: $o).
% 0.21/0.29 thf(decl_39, type, foundationAx: $o).
% 0.21/0.29 thf(decl_40, type, wellorderingAx: $o).
% 0.21/0.29 thf(decl_42, type, descrp: $o).
% 0.21/0.29 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.29 thf(decl_44, type, dsetconstrI: $o).
% 0.21/0.29 thf(decl_45, type, dsetconstrEL: $o).
% 0.21/0.29 thf(decl_46, type, dsetconstrER: $o).
% 0.21/0.29 thf(decl_47, type, exuE1: $o).
% 0.21/0.29 thf(decl_48, type, prop2set: $o > $i).
% 0.21/0.29 thf(decl_49, type, prop2setE: $o).
% 0.21/0.29 thf(decl_50, type, emptysetE: $o).
% 0.21/0.29 thf(decl_51, type, emptysetimpfalse: $o).
% 0.21/0.29 thf(decl_52, type, notinemptyset: $o).
% 0.21/0.29 thf(decl_53, type, exuE3e: $o).
% 0.21/0.29 thf(decl_54, type, setext: $o).
% 0.21/0.29 thf(decl_55, type, emptyI: $o).
% 0.21/0.29 thf(decl_56, type, noeltsimpempty: $o).
% 0.21/0.29 thf(decl_57, type, setbeta: $o).
% 0.21/0.29 thf(decl_58, type, nonempty: $i > $o).
% 0.21/0.29 thf(decl_59, type, nonemptyE1: $o).
% 0.21/0.29 thf(decl_60, type, nonemptyI: $o).
% 0.21/0.29 thf(decl_61, type, nonemptyI1: $o).
% 0.21/0.29 thf(decl_62, type, setadjoinIL: $o).
% 0.21/0.29 thf(decl_63, type, emptyinunitempty: $o).
% 0.21/0.29 thf(decl_64, type, setadjoinIR: $o).
% 0.21/0.29 thf(decl_65, type, setadjoinE: $o).
% 0.21/0.29 thf(decl_66, type, setadjoinOr: $o).
% 0.21/0.29 thf(decl_67, type, setoftrueEq: $o).
% 0.21/0.29 thf(decl_68, type, powersetI: $o).
% 0.21/0.29 thf(decl_69, type, emptyinPowerset: $o).
% 0.21/0.29 thf(decl_70, type, emptyInPowerset: $o).
% 0.21/0.29 thf(decl_71, type, powersetE: $o).
% 0.21/0.29 thf(decl_72, type, setunionI: $o).
% 0.21/0.29 thf(decl_73, type, setunionE: $o).
% 0.21/0.29 thf(decl_74, type, epred1_0: $o).
% 0.21/0.29 thf(decl_75, type, esk1_2: $i > $i > $i).
% 0.21/0.29 thf(decl_76, type, esk2_2: $i > $i > $i).
% 0.21/0.29 thf(decl_77, type, esk3_2: $i > $i > $i).
% 0.21/0.29 thf(decl_78, type, esk4_1: $i > $i).
% 0.21/0.29 thf(decl_79, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.21/0.29 thf(decl_80, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.29 thf(decl_81, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.21/0.29 thf(decl_82, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.21/0.29 thf(decl_83, type, esk9_1: $i > $i).
% 0.21/0.29 thf(decl_84, type, esk10_2: ($i > $o) > $i > $i).
% 0.21/0.29 thf(decl_85, type, esk11_1: ($i > $o) > $i).
% 0.21/0.29 thf(decl_86, type, esk12_2: ($i > $o) > $i > $i).
% 0.21/0.29 thf(decl_87, type, esk13_1: ($i > $o) > $i).
% 0.21/0.29 thf(decl_88, type, esk14_2: $i > $i > $i).
% 0.21/0.29 thf(decl_89, type, esk15_2: $i > $i > $i).
% 0.21/0.29 thf(decl_90, type, esk16_1: $i > $i).
% 0.21/0.29 thf(decl_91, type, esk17_1: $i > $i).
% 0.21/0.29 thf(decl_92, type, esk18_1: $i > $i).
% 0.21/0.29 thf(decl_93, type, esk19_2: $i > $i > $i).
% 0.21/0.29 thf(decl_94, type, esk20_3: $i > $i > $o > $i).
% 0.21/0.29 thf(decl_95, type, esk21_0: $i).
% 0.21/0.29 thf(decl_96, type, esk22_0: $i).
% 0.21/0.29 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', replAx)).
% 0.21/0.29 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', exu)).
% 0.21/0.29 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', prop2set)).
% 0.21/0.29 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', exuE1)).
% 0.21/0.29 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', exuE3e)).
% 0.21/0.29 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', nonemptyI)).
% 0.21/0.29 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', nonempty)).
% 0.21/0.29 thf(subPowSU, 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)=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', subPowSU)).
% 0.21/0.29 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', setoftrueEq)).
% 0.21/0.29 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', prop2setE)).
% 0.21/0.29 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', dsetconstrER)).
% 0.21/0.29 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', dsetconstrEL)).
% 0.21/0.29 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', dsetconstrI)).
% 0.21/0.29 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', setbeta)).
% 0.21/0.29 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', nonemptyI1)).
% 0.21/0.29 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', nonemptyE1)).
% 0.21/0.29 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', powersetAx)).
% 0.21/0.29 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', setadjoinIR)).
% 0.21/0.29 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X13:$o]:(((((X3)=(X2))=>(X13))=>(((in @ X3 @ X4)=>(X13))=>(X13))))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', setadjoinE)).
% 0.21/0.29 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', setadjoinOr)).
% 0.21/0.29 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', powersetI)).
% 0.21/0.29 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', emptyinPowerset)).
% 0.21/0.29 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', emptyInPowerset)).
% 0.21/0.29 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', powersetE)).
% 0.21/0.29 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', setunionI)).
% 0.21/0.29 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14)))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', setunionE)).
% 0.21/0.29 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.zd5KXSFP22/E---3.1_2528258.p', omegaIndAx)).
% 0.21/0.29 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', omegaSAx)).
% 0.21/0.29 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', omega0Ax)).
% 0.21/0.29 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', setunionAx)).
% 0.21/0.29 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', setadjoinAx)).
% 0.21/0.29 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', emptysetAx)).
% 0.21/0.29 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', wellorderingAx)).
% 0.21/0.29 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', foundationAx)).
% 0.21/0.29 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', emptysetE)).
% 0.21/0.29 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', setextAx)).
% 0.21/0.29 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', noeltsimpempty)).
% 0.21/0.29 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', emptyI)).
% 0.21/0.29 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.zd5KXSFP22/E---3.1_2528258.p', setext)).
% 0.21/0.29 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', notinemptyset)).
% 0.21/0.29 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', setadjoinIL)).
% 0.21/0.29 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', emptyinunitempty)).
% 0.21/0.29 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.zd5KXSFP22/E---3.1_2528258.p', emptysetimpfalse)).
% 0.21/0.29 thf(c_0_43, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.21/0.29 thf(c_0_44, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.21/0.29 thf(c_0_45, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.21/0.29 thf(c_0_46, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.21/0.29 thf(c_0_47, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.21/0.29 thf(c_0_48, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.21/0.29 thf(c_0_49, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.21/0.29 thf(c_0_50, 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)=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[subPowSU])).
% 0.21/0.29 thf(c_0_51, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.21/0.29 thf(c_0_52, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X129:$i]:(((((X6 @ X2 @ X129)))&(![X130:$i]:(((((X6 @ X2 @ X130)))=>(((X129)=(X130)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_43, c_0_44])).
% 0.21/0.29 thf(c_0_53, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_45])).
% 0.21/0.29 thf(c_0_54, plain, ((exuE1)=(![X1:$i > $o]:((((?[X131:$i]:(((((X1 @ X131)))&(![X132:$i]:(((((X1 @ X132)))=>(((X131)=(X132))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_46, c_0_44])).
% 0.21/0.29 thf(c_0_55, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.21/0.29 thf(c_0_56, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.21/0.29 thf(c_0_57, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.21/0.29 thf(c_0_58, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.21/0.29 thf(c_0_59, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X133:$i]:(((((X1 @ X133)))&(![X134:$i]:(((((X1 @ X134)))=>(((X133)=(X134))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_47, c_0_44])).
% 0.21/0.29 thf(c_0_60, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_48, c_0_49])).
% 0.21/0.29 thf(c_0_61, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_49])).
% 0.21/0.29 thf(c_0_62, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_49])).
% 0.21/0.29 thf(c_0_63, plain, ((epred1_0)<=>![X164:$i]:(?[X165:$i]:((((![X166:$i]:(((in @ X166 @ X165)=>![X167:$i]:(((in @ X167 @ X166)=>(in @ X167 @ X164)))))&![X168:$i, X169:$i]:((((in @ X168 @ X164)&(in @ X169 @ X164))=>(![X170:$i]:(((in @ X170 @ X165)=>((in @ X168 @ X170)<=>(in @ X169 @ X170))))=>((X168)=(X169))))))&![X171:$i, X172:$i]:((((in @ X171 @ X165)&(in @ X172 @ X165))=>(![X173:$i]:(((in @ X173 @ X171)=>(in @ X173 @ X172)))|![X174:$i]:(((in @ X174 @ X172)=>(in @ X174 @ X171)))))))&![X175:$i]:(((![X176:$i]:(((in @ X176 @ X175)=>(in @ X176 @ X164)))&?[X177:$i]:((in @ X177 @ X175)))=>?[X178:$i, X179:$i]:(((((in @ X178 @ X165)&(in @ X179 @ X175))&~(?[X180:$i]:(((in @ X180 @ X178)&(in @ X180 @ X175)))))&![X181:$i]:(((in @ X181 @ X165)=>(![X182:$i]:(((in @ X182 @ X181)=>(in @ X182 @ X178)))|(in @ X179 @ X181)))))))))))), introduced(definition)).
% 0.21/0.29 thf(c_0_64, negated_conjecture, ~((![X135:$i, X136:$i]:((![X137:$i]:(((in @ X137 @ X135)<=>(in @ X137 @ X136)))=>((X135)=(X136))))=>(![X138:$i]:(~(in @ X138 @ emptyset))=>(![X139:$i, X140:$i, X141:$i]:(((in @ X141 @ (setadjoin @ X139 @ X140))<=>(((X141)=(X139))|(in @ X141 @ X140))))=>(![X142:$i, X143:$i]:(((in @ X143 @ (powerset @ X142))<=>![X144:$i]:(((in @ X144 @ X143)=>(in @ X144 @ X142)))))=>(![X145:$i, X146:$i]:(((in @ X146 @ (setunion @ X145))<=>?[X147:$i]:(((in @ X146 @ X147)&(in @ X147 @ X145)))))=>((in @ emptyset @ omega)=>(![X148:$i]:(((in @ X148 @ omega)=>(in @ (setadjoin @ X148 @ X148) @ omega)))=>(![X149:$i]:((((in @ emptyset @ X149)&![X150:$i]:((((in @ X150 @ omega)&(in @ X150 @ X149))=>(in @ (setadjoin @ X150 @ X150) @ X149))))=>![X151:$i]:(((in @ X151 @ omega)=>(in @ X151 @ X149)))))=>(![X152:$i > $i > $o, X153:$i]:((![X154:$i]:(((in @ X154 @ X153)=>?[X155:$i]:(((X152 @ X154 @ X155)&![X156:$i]:(((X152 @ X154 @ X156)=>((X155)=(X156))))))))=>?[X157:$i]:(![X158:$i]:(((in @ X158 @ X157)<=>?[X159:$i]:(((in @ X159 @ X153)&(X152 @ X159 @ X158))))))))=>(![X160:$i]:((?[X161:$i]:((in @ X161 @ X160))=>?[X162:$i]:(((in @ X162 @ X160)&~(?[X163:$i]:(((in @ X163 @ X162)&(in @ X163 @ X160))))))))=>((epred1_0)=>((descrp)=>(![X183:$i, X184:$i > $o, X185:$i]:(((in @ X185 @ X183)=>((X184 @ X185)=>(in @ X185 @ (dsetconstr @ X183 @ (^[Z0:$i]:((X184 @ Z0))))))))=>(![X186:$i, X187:$i > $o, X188:$i]:(((in @ X188 @ (dsetconstr @ X186 @ (^[Z0:$i]:((X187 @ Z0)))))=>(in @ X188 @ X186)))=>(![X189:$i, X190:$i > $o, X191:$i]:(((in @ X191 @ (dsetconstr @ X189 @ (^[Z0:$i]:((X190 @ Z0)))))=>(X190 @ X191)))=>(![X192:$i > $o]:((?[X193:$i]:(((X192 @ X193)&![X194:$i]:(((X192 @ X194)=>((X193)=(X194))))))=>?[X195:$i]:(((X192 @ X195)&![X196:$i]:(((X192 @ X196)=>((X195)=(X196))))))))=>(![X197:$o, X198:$i]:(((in @ X198 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X197)))))=>(X197)))=>(![X199:$i]:(((in @ X199 @ emptyset)=>![X200:$o]:((X200))))=>(![X201:$i]:(~(in @ X201 @ emptyset))=>(![X202:$i]:(~(in @ X202 @ emptyset))=>(![X203:$i > $o]:((?[X204:$i]:(((X203 @ X204)&![X205:$i]:(((X203 @ X205)=>((X204)=(X205))))))=>?[X206:$i]:((X203 @ X206))))=>(![X207:$i, X208:$i]:((![X209:$i]:(((in @ X209 @ X207)=>(in @ X209 @ X208)))=>(![X210:$i]:(((in @ X210 @ X208)=>(in @ X210 @ X207)))=>((X207)=(X208)))))=>(![X211:$i]:((![X212:$i]:(~(in @ X212 @ X211))=>((X211)=(emptyset))))=>(![X213:$i]:((![X214:$i]:(~(in @ X214 @ X213))=>((X213)=(emptyset))))=>(![X215:$i, X216:$i > $o, X217:$i]:(((in @ X217 @ X215)=>((in @ X217 @ (dsetconstr @ X215 @ (^[Z0:$i]:((X216 @ Z0)))))<=>(X216 @ X217))))=>(![X218:$i]:((((X218)!=(emptyset))=>?[X219:$i]:((in @ X219 @ X218))))=>(![X220:$i, X221:$i > $o, X222:$i]:(((in @ X222 @ X220)=>((X221 @ X222)=>((dsetconstr @ X220 @ (^[Z0:$i]:((X221 @ Z0))))!=(emptyset)))))=>(![X223:$i]:((?[X224:$i]:((in @ X224 @ X223))=>((X223)!=(emptyset))))=>(![X225:$i, X226:$i]:((in @ X225 @ (setadjoin @ X225 @ X226)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X227:$i, X228:$i, X229:$i]:(((in @ X229 @ X228)=>(in @ X229 @ (setadjoin @ X227 @ X228))))=>(![X230:$i, X231:$i, X232:$i]:(((in @ X232 @ (setadjoin @ X230 @ X231))=>![X233:$o]:(((((X232)=(X230))=>(X233))=>(((in @ X232 @ X231)=>(X233))=>(X233))))))=>(![X234:$i, X235:$i, X236:$i]:(((in @ X236 @ (setadjoin @ X234 @ X235))=>(((X236)=(X234))|(in @ X236 @ X235))))=>(![X237:$i]:(((dsetconstr @ X237 @ (^[Z0:$i]:(($true))))=(X237)))=>(![X238:$i, X239:$i]:((![X240:$i]:(((in @ X240 @ X239)=>(in @ X240 @ X238)))=>(in @ X239 @ (powerset @ X238))))=>(![X241:$i]:((in @ emptyset @ (powerset @ X241)))=>(![X242:$i]:((in @ emptyset @ (powerset @ X242)))=>(![X243:$i, X244:$i, X245:$i]:(((in @ X244 @ (powerset @ X243))=>((in @ X245 @ X244)=>(in @ X245 @ X243))))=>(![X246:$i, X247:$i, X248:$i]:(((in @ X247 @ X248)=>((in @ X248 @ X246)=>(in @ X247 @ (setunion @ X246)))))=>(![X249:$i, X250:$i]:(((in @ X250 @ (setunion @ X249))=>![X251:$o]:((![X252:$i]:(((in @ X250 @ X252)=>((in @ X252 @ X249)=>(X251))))=>(X251)))))=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_50, powersetAx]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_51]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), omegaIndAx]), omegaSAx]), omega0Ax]), setunionAx]), setadjoinAx]), emptysetAx]), c_0_52]), c_0_53]), c_0_54]), c_0_55]), c_0_56]), c_0_57]), wellorderingAx]), foundationAx]), emptysetE]), setextAx]), c_0_58]), noeltsimpempty]), emptyI]), setext]), c_0_59]), notinemptyset]), c_0_60]), c_0_61]), setadjoinIL]), emptyinunitempty]), emptysetimpfalse]), c_0_62])]), c_0_63])).
% 0.21/0.29 thf(c_0_65, negated_conjecture, ![X253:$i, X254:$i, X256:$i, X257:$i, X258:$i, X259:$i, X260:$i, X261:$i, X262:$i, X263:$i, X264:$i, X266:$i, X267:$i, X269:$i, X270:$i, X271:$i, X272:$i, X273:$i, X275:$i, X276:$i > $i > $o, X277:$i, X279:$i, X282:$i, X284:$i, X285:$i, X286:$i, X287:$i, X289:$i, X290:$i, X291:$i > $o, X292:$i, X293:$i, X294:$i > $o, X295:$i, X296:$i, X297:$i > $o, X298:$i, X299:$i > $o, X300:$i, X303:$i, X304:$o, X305:$i, X306:$i, X307:$o, X308:$i, X309:$i, X310:$i > $o, X311:$i, X314:$i, X315:$i, X318:$i, X320:$i, X322:$i, X323:$i > $o, X324:$i, X325:$i, X327:$i, X328:$i > $o, X329:$i, X330:$i, X331:$i, X332:$i, X333:$i, X334:$i, X335:$i, X336:$i, X337:$i, X338:$i, X339:$i, X340:$o, X341:$i, X342:$i, X343:$i, X344:$i, X345:$i, X346:$i, X348:$i, X349:$i, X350:$i, X351:$i, X352:$i, X353:$i, X354:$i, X355:$i, X356:$i, X357:$i, X358:$o]:((((~(in @ (esk1_2 @ X253 @ X254) @ X253)|~(in @ (esk1_2 @ X253 @ X254) @ X254)|((X253)=(X254)))&((in @ (esk1_2 @ X253 @ X254) @ X253)|(in @ (esk1_2 @ X253 @ X254) @ X254)|((X253)=(X254))))&(~(in @ X256 @ emptyset)&(((~(in @ X259 @ (setadjoin @ X257 @ X258))|(((X259)=(X257))|(in @ X259 @ X258)))&((((X259)!=(X257))|(in @ X259 @ (setadjoin @ X257 @ X258)))&(~(in @ X259 @ X258)|(in @ X259 @ (setadjoin @ X257 @ X258)))))&(((~(in @ X261 @ (powerset @ X260))|(~(in @ X262 @ X261)|(in @ X262 @ X260)))&(((in @ (esk2_2 @ X263 @ X264) @ X264)|(in @ X264 @ (powerset @ X263)))&(~(in @ (esk2_2 @ X263 @ X264) @ X263)|(in @ X264 @ (powerset @ X263)))))&(((((in @ X267 @ (esk3_2 @ X266 @ X267))|~(in @ X267 @ (setunion @ X266)))&((in @ (esk3_2 @ X266 @ X267) @ X266)|~(in @ X267 @ (setunion @ X266))))&(~(in @ X270 @ X271)|~(in @ X271 @ X269)|(in @ X270 @ (setunion @ X269))))&((in @ emptyset @ omega)&((~(in @ X272 @ omega)|(in @ (setadjoin @ X272 @ X272) @ omega))&(((((in @ (esk4_1 @ X273) @ omega)|~(in @ emptyset @ X273)|(~(in @ X275 @ omega)|(in @ X275 @ X273)))&((in @ (esk4_1 @ X273) @ X273)|~(in @ emptyset @ X273)|(~(in @ X275 @ omega)|(in @ X275 @ X273))))&(~(in @ (setadjoin @ (esk4_1 @ X273) @ (esk4_1 @ X273)) @ X273)|~(in @ emptyset @ X273)|(~(in @ X275 @ omega)|(in @ X275 @ X273))))&((((((in @ (esk8_3 @ X276 @ X277 @ X282) @ X277)|~(in @ X282 @ (esk7_2 @ X276 @ X277))|(in @ (esk5_2 @ X276 @ X277) @ X277))&((X276 @ (esk8_3 @ X276 @ X277 @ X282) @ X282)|~(in @ X282 @ (esk7_2 @ X276 @ X277))|(in @ (esk5_2 @ X276 @ X277) @ X277)))&(~(in @ X285 @ X277)|~(X276 @ X285 @ X284)|(in @ X284 @ (esk7_2 @ X276 @ X277))|(in @ (esk5_2 @ X276 @ X277) @ X277)))&(((((in @ (esk8_3 @ X276 @ X277 @ X282) @ X277)|~(in @ X282 @ (esk7_2 @ X276 @ X277))|((X276 @ (esk5_2 @ X276 @ X277) @ (esk6_3 @ X276 @ X277 @ X279))|~(X276 @ (esk5_2 @ X276 @ X277) @ X279)))&((X276 @ (esk8_3 @ X276 @ X277 @ X282) @ X282)|~(in @ X282 @ (esk7_2 @ X276 @ X277))|((X276 @ (esk5_2 @ X276 @ X277) @ (esk6_3 @ X276 @ X277 @ X279))|~(X276 @ (esk5_2 @ X276 @ X277) @ X279))))&(~(in @ X285 @ X277)|~(X276 @ X285 @ X284)|(in @ X284 @ (esk7_2 @ X276 @ X277))|((X276 @ (esk5_2 @ X276 @ X277) @ (esk6_3 @ X276 @ X277 @ X279))|~(X276 @ (esk5_2 @ X276 @ X277) @ X279))))&((((in @ (esk8_3 @ X276 @ X277 @ X282) @ X277)|~(in @ X282 @ (esk7_2 @ X276 @ X277))|(((X279)!=(esk6_3 @ X276 @ X277 @ X279))|~(X276 @ (esk5_2 @ X276 @ X277) @ X279)))&((X276 @ (esk8_3 @ X276 @ X277 @ X282) @ X282)|~(in @ X282 @ (esk7_2 @ X276 @ X277))|(((X279)!=(esk6_3 @ X276 @ X277 @ X279))|~(X276 @ (esk5_2 @ X276 @ X277) @ X279))))&(~(in @ X285 @ X277)|~(X276 @ X285 @ X284)|(in @ X284 @ (esk7_2 @ X276 @ X277))|(((X279)!=(esk6_3 @ X276 @ X277 @ X279))|~(X276 @ (esk5_2 @ X276 @ X277) @ X279))))))&((((in @ (esk9_1 @ X286) @ X286)|~(in @ X287 @ X286))&(~(in @ X289 @ (esk9_1 @ X286))|~(in @ X289 @ X286)|~(in @ X287 @ X286)))&((epred1_0)&((descrp)&((~(in @ X292 @ X290)|(~(X291 @ X292)|(in @ X292 @ (dsetconstr @ X290 @ (^[Z0:$i]:((X291 @ Z0)))))))&((~(in @ X295 @ (dsetconstr @ X293 @ (^[Z0:$i]:((X294 @ Z0)))))|(in @ X295 @ X293))&((~(in @ X298 @ (dsetconstr @ X296 @ (^[Z0:$i]:((X297 @ Z0)))))|(X297 @ X298))&(((((X299 @ (esk11_1 @ X299))|((X299 @ (esk10_2 @ X299 @ X300))|~(X299 @ X300)))&(~(X299 @ X303)|((esk11_1 @ X299)=(X303))|((X299 @ (esk10_2 @ X299 @ X300))|~(X299 @ X300))))&(((X299 @ (esk11_1 @ X299))|(((X300)!=(esk10_2 @ X299 @ X300))|~(X299 @ X300)))&(~(X299 @ X303)|((esk11_1 @ X299)=(X303))|(((X300)!=(esk10_2 @ X299 @ X300))|~(X299 @ X300)))))&((~(in @ X305 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X304)))))|(X304))&((~(in @ X306 @ emptyset)|(X307))&(~(in @ X308 @ emptyset)&(~(in @ X309 @ emptyset)&((((X310 @ (esk12_2 @ X310 @ X311))|~(X310 @ X311)|(X310 @ (esk13_1 @ X310)))&(((X311)!=(esk12_2 @ X310 @ X311))|~(X310 @ X311)|(X310 @ (esk13_1 @ X310))))&(((((in @ (esk15_2 @ X314 @ X315) @ X315)|((X314)=(X315))|(in @ (esk14_2 @ X314 @ X315) @ X314))&(~(in @ (esk15_2 @ X314 @ X315) @ X314)|((X314)=(X315))|(in @ (esk14_2 @ X314 @ X315) @ X314)))&(((in @ (esk15_2 @ X314 @ X315) @ X315)|((X314)=(X315))|~(in @ (esk14_2 @ X314 @ X315) @ X315))&(~(in @ (esk15_2 @ X314 @ X315) @ X314)|((X314)=(X315))|~(in @ (esk14_2 @ X314 @ X315) @ X315))))&(((in @ (esk16_1 @ X318) @ X318)|((X318)=(emptyset)))&(((in @ (esk17_1 @ X320) @ X320)|((X320)=(emptyset)))&(((~(in @ X324 @ (dsetconstr @ X322 @ (^[Z0:$i]:((X323 @ Z0)))))|(X323 @ X324)|~(in @ X324 @ X322))&(~(X323 @ X324)|(in @ X324 @ (dsetconstr @ X322 @ (^[Z0:$i]:((X323 @ Z0)))))|~(in @ X324 @ X322)))&((((X325)=(emptyset))|(in @ (esk18_1 @ X325) @ X325))&((~(in @ X329 @ X327)|(~(X328 @ X329)|((dsetconstr @ X327 @ (^[Z0:$i]:((X328 @ Z0))))!=(emptyset))))&((~(in @ X331 @ X330)|((X330)!=(emptyset)))&((in @ X332 @ (setadjoin @ X332 @ X333))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X336 @ X335)|(in @ X336 @ (setadjoin @ X334 @ X335)))&(((((in @ X339 @ X338)|(X340)|((X339)=(X337))|~(in @ X339 @ (setadjoin @ X337 @ X338)))&(~(X340)|(X340)|((X339)=(X337))|~(in @ X339 @ (setadjoin @ X337 @ X338))))&(((in @ X339 @ X338)|(X340)|~(X340)|~(in @ X339 @ (setadjoin @ X337 @ X338)))&(~(X340)|(X340)|~(X340)|~(in @ X339 @ (setadjoin @ X337 @ X338)))))&((~(in @ X343 @ (setadjoin @ X341 @ X342))|(((X343)=(X341))|(in @ X343 @ X342)))&(((dsetconstr @ X344 @ (^[Z0:$i]:(($true))))=(X344))&((((in @ (esk19_2 @ X345 @ X346) @ X346)|(in @ X346 @ (powerset @ X345)))&(~(in @ (esk19_2 @ X345 @ X346) @ X345)|(in @ X346 @ (powerset @ X345))))&((in @ emptyset @ (powerset @ X348))&((in @ emptyset @ (powerset @ X349))&((~(in @ X351 @ (powerset @ X350))|(~(in @ X352 @ X351)|(in @ X352 @ X350)))&((~(in @ X354 @ X355)|(~(in @ X355 @ X353)|(in @ X354 @ (setunion @ X353))))&((((in @ X357 @ (esk20_3 @ X356 @ X357 @ X358))|(X358)|~(in @ X357 @ (setunion @ X356)))&(((in @ (esk20_3 @ X356 @ X357 @ X358) @ X356)|(X358)|~(in @ X357 @ (setunion @ X356)))&(~(X358)|(X358)|~(in @ X357 @ (setunion @ X356)))))&((in @ esk22_0 @ esk21_0)&~(in @ esk22_0 @ (powerset @ (setunion @ esk21_0))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])])])])).
% 0.21/0.29 thf(c_0_66, negated_conjecture, ![X2:$i, X3:$i, X4:$i]:(((in @ X2 @ (setunion @ X4))|~((in @ X2 @ X3))|~((in @ X3 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_65])).
% 0.21/0.29 thf(c_0_67, negated_conjecture, (in @ esk22_0 @ esk21_0), inference(split_conjunct,[status(thm)],[c_0_65])).
% 0.21/0.29 thf(c_0_68, negated_conjecture, ![X3:$i, X2:$i]:(((in @ X3 @ (powerset @ X2))|~((in @ (esk2_2 @ X2 @ X3) @ X2)))), inference(split_conjunct,[status(thm)],[c_0_65])).
% 0.21/0.29 thf(c_0_69, negated_conjecture, ![X2:$i]:(((in @ X2 @ (setunion @ esk21_0))|~((in @ X2 @ esk22_0)))), inference(spm,[status(thm)],[c_0_66, c_0_67])).
% 0.21/0.29 thf(c_0_70, negated_conjecture, ![X2:$i]:(((in @ X2 @ (powerset @ (setunion @ esk21_0)))|~((in @ (esk2_2 @ (setunion @ esk21_0) @ X2) @ esk22_0)))), inference(spm,[status(thm)],[c_0_68, c_0_69])).
% 0.21/0.29 thf(c_0_71, negated_conjecture, ![X3:$i, X2:$i]:(((in @ (esk2_2 @ X2 @ X3) @ X3)|(in @ X3 @ (powerset @ X2)))), inference(split_conjunct,[status(thm)],[c_0_65])).
% 0.21/0.29 thf(c_0_72, negated_conjecture, ~((in @ esk22_0 @ (powerset @ (setunion @ esk21_0)))), inference(split_conjunct,[status(thm)],[c_0_65])).
% 0.21/0.29 thf(c_0_73, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_72]), ['proof']).
% 0.21/0.29 % SZS output end CNFRefutation
% 0.21/0.29 % Parsed axioms : 95
% 0.21/0.29 % Removed by relevancy pruning/SinE : 52
% 0.21/0.29 % Initial clauses : 87
% 0.21/0.29 % Removed in clause preprocessing : 4
% 0.21/0.30 % Initial clauses in saturation : 83
% 0.21/0.30 % Processed clauses : 232
% 0.21/0.30 % ...of these trivial : 2
% 0.21/0.30 % ...subsumed : 104
% 0.21/0.30 % ...remaining for further processing : 126
% 0.21/0.30 % Other redundant clauses eliminated : 3
% 0.21/0.30 % Clauses deleted for lack of memory : 0
% 0.21/0.30 % Backward-subsumed : 0
% 0.21/0.30 % Backward-rewritten : 4
% 0.21/0.30 % Generated clauses : 1213
% 0.21/0.30 % ...of the previous two non-redundant : 1113
% 0.21/0.30 % ...aggressively subsumed : 0
% 0.21/0.30 % Contextual simplify-reflections : 0
% 0.21/0.30 % Paramodulations : 1208
% 0.21/0.30 % Factorizations : 2
% 0.21/0.30 % NegExts : 0
% 0.21/0.30 % Equation resolutions : 3
% 0.21/0.30 % Disequality decompositions : 0
% 0.21/0.30 % Total rewrite steps : 114
% 0.21/0.30 % ...of those cached : 99
% 0.21/0.30 % Propositional unsat checks : 0
% 0.21/0.30 % Propositional check models : 0
% 0.21/0.30 % Propositional check unsatisfiable : 0
% 0.21/0.30 % Propositional clauses : 0
% 0.21/0.30 % Propositional clauses after purity: 0
% 0.21/0.30 % Propositional unsat core size : 0
% 0.21/0.30 % Propositional preprocessing time : 0.000
% 0.21/0.30 % Propositional encoding time : 0.000
% 0.21/0.30 % Propositional solver time : 0.000
% 0.21/0.30 % Success case prop preproc time : 0.000
% 0.21/0.30 % Success case prop encoding time : 0.000
% 0.21/0.30 % Success case prop solver time : 0.000
% 0.21/0.30 % Current number of processed clauses : 120
% 0.21/0.30 % Positive orientable unit clauses : 17
% 0.21/0.30 % Positive unorientable unit clauses: 0
% 0.21/0.30 % Negative unit clauses : 2
% 0.21/0.30 % Non-unit-clauses : 101
% 0.21/0.30 % Current number of unprocessed clauses: 948
% 0.21/0.30 % ...number of literals in the above : 2856
% 0.21/0.30 % Current number of archived formulas : 0
% 0.21/0.30 % Current number of archived clauses : 4
% 0.21/0.30 % Clause-clause subsumption calls (NU) : 1954
% 0.21/0.30 % Rec. Clause-clause subsumption calls : 1251
% 0.21/0.30 % Non-unit clause-clause subsumptions : 79
% 0.21/0.30 % Unit Clause-clause subsumption calls : 48
% 0.21/0.30 % Rewrite failures with RHS unbound : 0
% 0.21/0.30 % BW rewrite match attempts : 9
% 0.21/0.30 % BW rewrite match successes : 4
% 0.21/0.30 % Condensation attempts : 0
% 0.21/0.30 % Condensation successes : 0
% 0.21/0.30 % Termbank termtop insertions : 24855
% 0.21/0.30 % Search garbage collected termcells : 3491
% 0.21/0.30
% 0.21/0.30 % -------------------------------------------------
% 0.21/0.30 % User time : 0.035 s
% 0.21/0.30 % System time : 0.006 s
% 0.21/0.30 % Total time : 0.041 s
% 0.21/0.30 % Maximum resident set size: 4700 pages
% 0.21/0.30
% 0.21/0.30 % -------------------------------------------------
% 0.21/0.30 % User time : 0.038 s
% 0.21/0.30 % System time : 0.012 s
% 0.21/0.30 % Total time : 0.050 s
% 0.21/0.30 % Maximum resident set size: 4864 pages
% 0.21/0.30 % E exiting
%------------------------------------------------------------------------------