%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU525^1 : 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 : n015.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 0.20s 0.28s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU525^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:52:02 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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.8T0qYUF7NO/E---3.1_3554827.p
% 0.20/0.28 % Version: 3.5.1-ho
% 0.20/0.28 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.28 % Starting sh5l with 300s (1) cores
% 0.20/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.20/0.28 % new_bool_2 with pid 3554843 completed with status 0
% 0.20/0.28 % Result found by new_bool_2
% 0.20/0.28 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.28 % Starting sh5l with 300s (1) cores
% 0.20/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.20/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.28 % Search class: HGHSM-FFMS31-SHSSMSBN
% 0.20/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.28 % SubtermCWHack with pid 3554844 completed with status 0
% 0.20/0.28 % Result found by SubtermCWHack
% 0.20/0.28 % Preprocessing class: HSMSSLSSMLLCHSA.
% 0.20/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.28 % Starting sh5l with 300s (1) cores
% 0.20/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.28 % Starting new_bool_2 with 300s (1) cores
% 0.20/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.28 % Search class: HGHSM-FFMS31-SHSSMSBN
% 0.20/0.28 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.28 % Preprocessing time : 0.003 s
% 0.20/0.28
% 0.20/0.28 % Proof found!
% 0.20/0.28 % SZS status Theorem
% 0.20/0.28 % SZS output start CNFRefutation
% 0.20/0.28 thf(decl_23, type, in: $i > $i > $o).
% 0.20/0.28 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.20/0.28 thf(decl_25, type, setextAx: $o).
% 0.20/0.28 thf(decl_26, type, emptyset: $i).
% 0.20/0.28 thf(decl_27, type, emptysetAx: $o).
% 0.20/0.28 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.20/0.28 thf(decl_29, type, setadjoinAx: $o).
% 0.20/0.28 thf(decl_30, type, powerset: $i > $i).
% 0.20/0.28 thf(decl_31, type, powersetAx: $o).
% 0.20/0.28 thf(decl_32, type, setunion: $i > $i).
% 0.20/0.28 thf(decl_33, type, setunionAx: $o).
% 0.20/0.28 thf(decl_34, type, omega: $i).
% 0.20/0.28 thf(decl_35, type, omega0Ax: $o).
% 0.20/0.28 thf(decl_36, type, omegaSAx: $o).
% 0.20/0.28 thf(decl_37, type, omegaIndAx: $o).
% 0.20/0.28 thf(decl_38, type, replAx: $o).
% 0.20/0.28 thf(decl_39, type, foundationAx: $o).
% 0.20/0.28 thf(decl_40, type, wellorderingAx: $o).
% 0.20/0.28 thf(decl_42, type, descrp: $o).
% 0.20/0.28 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.20/0.28 thf(decl_44, type, dsetconstrI: $o).
% 0.20/0.28 thf(decl_45, type, dsetconstrEL: $o).
% 0.20/0.28 thf(decl_46, type, dsetconstrER: $o).
% 0.20/0.28 thf(decl_47, type, exuE1: $o).
% 0.20/0.28 thf(decl_48, type, prop2set: $o > $i).
% 0.20/0.28 thf(decl_49, type, prop2setE: $o).
% 0.20/0.28 thf(decl_50, type, emptysetE: $o).
% 0.20/0.28 thf(decl_51, type, emptysetimpfalse: $o).
% 0.20/0.28 thf(decl_52, type, notinemptyset: $o).
% 0.20/0.28 thf(decl_53, type, exuE3e: $o).
% 0.20/0.28 thf(decl_54, type, setext: $o).
% 0.20/0.28 thf(decl_55, type, emptyI: $o).
% 0.20/0.28 thf(decl_56, type, noeltsimpempty: $o).
% 0.20/0.28 thf(decl_57, type, setbeta: $o).
% 0.20/0.28 thf(decl_58, type, nonempty: $i > $o).
% 0.20/0.28 thf(decl_59, type, nonemptyE1: $o).
% 0.20/0.28 thf(decl_60, type, nonemptyI: $o).
% 0.20/0.28 thf(decl_61, type, nonemptyI1: $o).
% 0.20/0.28 thf(decl_62, type, setadjoinIL: $o).
% 0.20/0.28 thf(decl_63, type, emptyinunitempty: $o).
% 0.20/0.28 thf(decl_64, type, setadjoinIR: $o).
% 0.20/0.28 thf(decl_65, type, setadjoinE: $o).
% 0.20/0.28 thf(decl_66, type, setadjoinOr: $o).
% 0.20/0.28 thf(decl_67, type, setoftrueEq: $o).
% 0.20/0.28 thf(decl_68, type, powersetI: $o).
% 0.20/0.28 thf(decl_69, type, emptyinPowerset: $o).
% 0.20/0.28 thf(decl_70, type, emptyInPowerset: $o).
% 0.20/0.28 thf(decl_71, type, powersetE: $o).
% 0.20/0.28 thf(decl_72, type, setunionI: $o).
% 0.20/0.28 thf(decl_73, type, setunionE: $o).
% 0.20/0.28 thf(decl_74, type, subPowSU: $o).
% 0.20/0.28 thf(decl_75, type, epred1_0: $o).
% 0.20/0.28 thf(decl_76, type, esk1_2: $i > $i > $i).
% 0.20/0.28 thf(decl_77, type, esk2_2: $i > $i > $i).
% 0.20/0.28 thf(decl_78, type, esk3_2: $i > $i > $i).
% 0.20/0.28 thf(decl_79, type, esk4_1: $i > $i).
% 0.20/0.28 thf(decl_80, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.20/0.28 thf(decl_81, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.28 thf(decl_82, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.20/0.28 thf(decl_83, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.20/0.28 thf(decl_84, type, esk9_1: $i > $i).
% 0.20/0.28 thf(decl_85, type, esk10_2: ($i > $o) > $i > $i).
% 0.20/0.28 thf(decl_86, type, esk11_1: ($i > $o) > $i).
% 0.20/0.28 thf(decl_87, type, esk12_2: ($i > $o) > $i > $i).
% 0.20/0.28 thf(decl_88, type, esk13_1: ($i > $o) > $i).
% 0.20/0.28 thf(decl_89, type, esk14_2: $i > $i > $i).
% 0.20/0.28 thf(decl_90, type, esk15_2: $i > $i > $i).
% 0.20/0.28 thf(decl_91, type, esk16_1: $i > $i).
% 0.20/0.28 thf(decl_92, type, esk17_1: $i > $i).
% 0.20/0.28 thf(decl_93, type, esk18_1: $i > $i).
% 0.20/0.28 thf(decl_94, type, esk19_2: $i > $i > $i).
% 0.20/0.28 thf(decl_95, type, esk20_3: $i > $i > $o > $i).
% 0.20/0.28 thf(decl_96, type, epred2_0: $i > $o).
% 0.20/0.28 thf(decl_97, type, esk21_0: $i).
% 0.20/0.28 thf(decl_98, type, esk22_1: $i > $i).
% 0.20/0.28 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', replAx)).
% 0.20/0.28 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', exu)).
% 0.20/0.28 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', prop2set)).
% 0.20/0.28 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', exuE1)).
% 0.20/0.28 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', nonemptyI)).
% 0.20/0.28 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', nonempty)).
% 0.20/0.28 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', exuE3e)).
% 0.20/0.28 thf(exuE2, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', exuE2)).
% 0.20/0.28 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', setoftrueEq)).
% 0.20/0.28 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', prop2setE)).
% 0.20/0.28 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', dsetconstrER)).
% 0.20/0.28 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', dsetconstrEL)).
% 0.20/0.28 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', dsetconstrI)).
% 0.20/0.28 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', nonemptyE1)).
% 0.20/0.28 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', setbeta)).
% 0.20/0.28 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', nonemptyI1)).
% 0.20/0.28 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.8T0qYUF7NO/E---3.1_3554827.p', omegaIndAx)).
% 0.20/0.28 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', setadjoinOr)).
% 0.20/0.28 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', powersetI)).
% 0.20/0.28 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', setadjoinAx)).
% 0.20/0.28 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', emptyinPowerset)).
% 0.20/0.28 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', emptyInPowerset)).
% 0.20/0.28 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', powersetE)).
% 0.20/0.28 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', setunionI)).
% 0.20/0.28 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X14:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X14))))=>(X14)))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', setunionE)).
% 0.20/0.28 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', subPowSU)).
% 0.20/0.28 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', emptysetAx)).
% 0.20/0.28 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.8T0qYUF7NO/E---3.1_3554827.p', foundationAx)).
% 0.20/0.28 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', omegaSAx)).
% 0.20/0.28 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', omega0Ax)).
% 0.20/0.28 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', setunionAx)).
% 0.20/0.28 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', powersetAx)).
% 0.20/0.28 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.8T0qYUF7NO/E---3.1_3554827.p', wellorderingAx)).
% 0.20/0.28 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', emptysetimpfalse)).
% 0.20/0.28 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', emptysetE)).
% 0.20/0.28 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', notinemptyset)).
% 0.20/0.28 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', noeltsimpempty)).
% 0.20/0.28 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', emptyI)).
% 0.20/0.28 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', setext)).
% 0.20/0.28 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', setadjoinIL)).
% 0.20/0.28 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', emptyinunitempty)).
% 0.20/0.28 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', setadjoinIR)).
% 0.20/0.28 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.8T0qYUF7NO/E---3.1_3554827.p', setadjoinE)).
% 0.20/0.28 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.8T0qYUF7NO/E---3.1_3554827.p', setextAx)).
% 0.20/0.28 thf(c_0_44, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.20/0.28 thf(c_0_45, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.20/0.28 thf(c_0_46, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.20/0.28 thf(c_0_47, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.20/0.28 thf(c_0_48, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.20/0.28 thf(c_0_49, plain, ((nonempty)=(^[Z0:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.20/0.28 thf(c_0_50, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.20/0.28 thf(c_0_51, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[exuE2])).
% 0.20/0.28 thf(c_0_52, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.20/0.28 thf(c_0_53, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X132:$i]:(((((X6 @ X2 @ X132)))&(![X133:$i]:(((((X6 @ X2 @ X133)))=>(((X132)=(X133)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_44, c_0_45])).
% 0.20/0.28 thf(c_0_54, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_46])).
% 0.20/0.28 thf(c_0_55, plain, ((exuE1)=(![X1:$i > $o]:((((?[X134:$i]:(((((X1 @ X134)))&(![X135:$i]:(((((X1 @ X135)))=>(((X134)=(X135))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_47, c_0_45])).
% 0.20/0.28 thf(c_0_56, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.20/0.28 thf(c_0_57, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.20/0.28 thf(c_0_58, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.20/0.28 thf(c_0_59, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:((((in @ X2 @ X4))=>((((X1 @ X2))=>((((dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))!=(emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_48, c_0_49])).
% 0.20/0.28 thf(c_0_60, axiom, ((nonemptyE1)=(![X4:$i]:((((((X4)!=(emptyset))))=>(?[X2:$i]:((in @ X2 @ X4))))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_49])).
% 0.20/0.28 thf(c_0_61, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.20/0.28 thf(c_0_62, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X136:$i]:(((((X1 @ X136)))&(![X137:$i]:(((((X1 @ X137)))=>(((X136)=(X137))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_50, c_0_45])).
% 0.20/0.28 thf(c_0_63, axiom, ((nonemptyI1)=(![X4:$i]:(((?[X2:$i]:((in @ X2 @ X4)))=>((((X4)!=(emptyset)))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_49])).
% 0.20/0.28 thf(c_0_64, plain, ((epred1_0)<=>![X167:$i]:(?[X168:$i]:((((![X169:$i]:(((in @ X169 @ X168)=>![X170:$i]:(((in @ X170 @ X169)=>(in @ X170 @ X167)))))&![X171:$i, X172:$i]:((((in @ X171 @ X167)&(in @ X172 @ X167))=>(![X173:$i]:(((in @ X173 @ X168)=>((in @ X171 @ X173)<=>(in @ X172 @ X173))))=>((X171)=(X172))))))&![X174:$i, X175:$i]:((((in @ X174 @ X168)&(in @ X175 @ X168))=>(![X176:$i]:(((in @ X176 @ X174)=>(in @ X176 @ X175)))|![X177:$i]:(((in @ X177 @ X175)=>(in @ X177 @ X174)))))))&![X178:$i]:(((![X179:$i]:(((in @ X179 @ X178)=>(in @ X179 @ X167)))&?[X180:$i]:((in @ X180 @ X178)))=>?[X181:$i, X182:$i]:(((((in @ X181 @ X168)&(in @ X182 @ X178))&~(?[X183:$i]:(((in @ X183 @ X181)&(in @ X183 @ X178)))))&![X184:$i]:(((in @ X184 @ X168)=>(![X185:$i]:(((in @ X185 @ X184)=>(in @ X185 @ X181)))|(in @ X182 @ X184)))))))))))), introduced(definition)).
% 0.20/0.28 thf(c_0_65, negated_conjecture, ~((![X138:$i, X139:$i]:((![X140:$i]:(((in @ X140 @ X138)<=>(in @ X140 @ X139)))=>((X138)=(X139))))=>(![X141:$i]:(~(in @ X141 @ emptyset))=>(![X142:$i, X143:$i, X144:$i]:(((in @ X144 @ (setadjoin @ X142 @ X143))<=>(((X144)=(X142))|(in @ X144 @ X143))))=>(![X145:$i, X146:$i]:(((in @ X146 @ (powerset @ X145))<=>![X147:$i]:(((in @ X147 @ X146)=>(in @ X147 @ X145)))))=>(![X148:$i, X149:$i]:(((in @ X149 @ (setunion @ X148))<=>?[X150:$i]:(((in @ X149 @ X150)&(in @ X150 @ X148)))))=>((in @ emptyset @ omega)=>(![X151:$i]:(((in @ X151 @ omega)=>(in @ (setadjoin @ X151 @ X151) @ omega)))=>(![X152:$i]:((((in @ emptyset @ X152)&![X153:$i]:((((in @ X153 @ omega)&(in @ X153 @ X152))=>(in @ (setadjoin @ X153 @ X153) @ X152))))=>![X154:$i]:(((in @ X154 @ omega)=>(in @ X154 @ X152)))))=>(![X155:$i > $i > $o, X156:$i]:((![X157:$i]:(((in @ X157 @ X156)=>?[X158:$i]:(((X155 @ X157 @ X158)&![X159:$i]:(((X155 @ X157 @ X159)=>((X158)=(X159))))))))=>?[X160:$i]:(![X161:$i]:(((in @ X161 @ X160)<=>?[X162:$i]:(((in @ X162 @ X156)&(X155 @ X162 @ X161))))))))=>(![X163:$i]:((?[X164:$i]:((in @ X164 @ X163))=>?[X165:$i]:(((in @ X165 @ X163)&~(?[X166:$i]:(((in @ X166 @ X165)&(in @ X166 @ X163))))))))=>((epred1_0)=>((descrp)=>(![X186:$i, X187:$i > $o, X188:$i]:(((in @ X188 @ X186)=>((X187 @ X188)=>(in @ X188 @ (dsetconstr @ X186 @ (^[Z0:$i]:((X187 @ Z0))))))))=>(![X189:$i, X190:$i > $o, X191:$i]:(((in @ X191 @ (dsetconstr @ X189 @ (^[Z0:$i]:((X190 @ Z0)))))=>(in @ X191 @ X189)))=>(![X192:$i, X193:$i > $o, X194:$i]:(((in @ X194 @ (dsetconstr @ X192 @ (^[Z0:$i]:((X193 @ Z0)))))=>(X193 @ X194)))=>(![X195:$i > $o]:((?[X196:$i]:(((X195 @ X196)&![X197:$i]:(((X195 @ X197)=>((X196)=(X197))))))=>?[X198:$i]:(((X195 @ X198)&![X199:$i]:(((X195 @ X199)=>((X198)=(X199))))))))=>(![X200:$o, X201:$i]:(((in @ X201 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X200)))))=>(X200)))=>(![X202:$i]:(((in @ X202 @ emptyset)=>![X203:$o]:((X203))))=>(![X204:$i]:(~(in @ X204 @ emptyset))=>(![X205:$i]:(~(in @ X205 @ emptyset))=>(![X206:$i > $o]:((?[X207:$i]:(((X206 @ X207)&![X208:$i]:(((X206 @ X208)=>((X207)=(X208))))))=>?[X209:$i]:((X206 @ X209))))=>(![X210:$i, X211:$i]:((![X212:$i]:(((in @ X212 @ X210)=>(in @ X212 @ X211)))=>(![X213:$i]:(((in @ X213 @ X211)=>(in @ X213 @ X210)))=>((X210)=(X211)))))=>(![X214:$i]:((![X215:$i]:(~(in @ X215 @ X214))=>((X214)=(emptyset))))=>(![X216:$i]:((![X217:$i]:(~(in @ X217 @ X216))=>((X216)=(emptyset))))=>(![X218:$i, X219:$i > $o, X220:$i]:(((in @ X220 @ X218)=>((in @ X220 @ (dsetconstr @ X218 @ (^[Z0:$i]:((X219 @ Z0)))))<=>(X219 @ X220))))=>(![X221:$i]:((((X221)!=(emptyset))=>?[X222:$i]:((in @ X222 @ X221))))=>(![X223:$i, X224:$i > $o, X225:$i]:(((in @ X225 @ X223)=>((X224 @ X225)=>((dsetconstr @ X223 @ (^[Z0:$i]:((X224 @ Z0))))!=(emptyset)))))=>(![X226:$i]:((?[X227:$i]:((in @ X227 @ X226))=>((X226)!=(emptyset))))=>(![X228:$i, X229:$i]:((in @ X228 @ (setadjoin @ X228 @ X229)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X230:$i, X231:$i, X232:$i]:(((in @ X232 @ X231)=>(in @ X232 @ (setadjoin @ X230 @ X231))))=>(![X233:$i, X234:$i, X235:$i]:(((in @ X235 @ (setadjoin @ X233 @ X234))=>![X236:$o]:(((((X235)=(X233))=>(X236))=>(((in @ X235 @ X234)=>(X236))=>(X236))))))=>(![X237:$i, X238:$i, X239:$i]:(((in @ X239 @ (setadjoin @ X237 @ X238))=>(((X239)=(X237))|(in @ X239 @ X238))))=>(![X240:$i]:(((dsetconstr @ X240 @ (^[Z0:$i]:(($true))))=(X240)))=>(![X241:$i, X242:$i]:((![X243:$i]:(((in @ X243 @ X242)=>(in @ X243 @ X241)))=>(in @ X242 @ (powerset @ X241))))=>(![X244:$i]:((in @ emptyset @ (powerset @ X244)))=>(![X245:$i]:((in @ emptyset @ (powerset @ X245)))=>(![X246:$i, X247:$i, X248:$i]:(((in @ X247 @ (powerset @ X246))=>((in @ X248 @ X247)=>(in @ X248 @ X246))))=>(![X249:$i, X250:$i, X251:$i]:(((in @ X250 @ X251)=>((in @ X251 @ X249)=>(in @ X250 @ (setunion @ X249)))))=>(![X252:$i, X253:$i]:(((in @ X253 @ (setunion @ X252))=>![X254:$o]:((![X255:$i]:(((in @ X253 @ X255)=>((in @ X255 @ X252)=>(X254))))=>(X254)))))=>(![X256:$i, X257:$i]:(((in @ X257 @ X256)=>(in @ X257 @ (powerset @ (setunion @ X256)))))=>![X1:$i > $o]:((?[X258:$i]:(((X1 @ X258)&![X259:$i]:(((X1 @ X259)=>((X258)=(X259))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_51]), omegaIndAx]), setadjoinOr]), c_0_52]), powersetI]), setadjoinAx]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_45]), emptysetAx]), foundationAx]), c_0_53]), omegaSAx]), omega0Ax]), setunionAx]), powersetAx]), wellorderingAx]), emptysetimpfalse]), emptysetE]), c_0_54]), c_0_55]), c_0_56]), c_0_57]), c_0_58]), notinemptyset]), c_0_59]), c_0_60]), c_0_61]), noeltsimpempty]), emptyI]), setext]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), c_0_62]), c_0_63]), setextAx])]), c_0_64])).
% 0.20/0.28 thf(c_0_66, negated_conjecture, ![X260:$i, X261:$i, X263:$i, X264:$i, X265:$i, X266:$i, X267:$i, X268:$i, X269:$i, X270:$i, X271:$i, X273:$i, X274:$i, X276:$i, X277:$i, X278:$i, X279:$i, X280:$i, X282:$i, X283:$i > $i > $o, X284:$i, X286:$i, X289:$i, X291:$i, X292:$i, X293:$i, X294:$i, X296:$i, X297:$i, X298:$i > $o, X299:$i, X300:$i, X301:$i > $o, X302:$i, X303:$i, X304:$i > $o, X305:$i, X306:$i > $o, X307:$i, X310:$i, X311:$o, X312:$i, X313:$i, X314:$o, X315:$i, X316:$i, X317:$i > $o, X318:$i, X321:$i, X322:$i, X325:$i, X327:$i, X329:$i, X330:$i > $o, X331:$i, X332:$i, X334:$i, X335:$i > $o, X336:$i, X337:$i, X338:$i, X339:$i, X340:$i, X341:$i, X342:$i, X343:$i, X344:$i, X345:$i, X346:$i, X347:$o, X348:$i, X349:$i, X350:$i, X351:$i, X352:$i, X353:$i, X355:$i, X356:$i, X357:$i, X358:$i, X359:$i, X360:$i, X361:$i, X362:$i, X363:$i, X364:$i, X365:$o, X367:$i, X368:$i, X371:$i, X372:$i]:((((~(in @ (esk1_2 @ X260 @ X261) @ X260)|~(in @ (esk1_2 @ X260 @ X261) @ X261)|((X260)=(X261)))&((in @ (esk1_2 @ X260 @ X261) @ X260)|(in @ (esk1_2 @ X260 @ X261) @ X261)|((X260)=(X261))))&(~(in @ X263 @ emptyset)&(((~(in @ X266 @ (setadjoin @ X264 @ X265))|(((X266)=(X264))|(in @ X266 @ X265)))&((((X266)!=(X264))|(in @ X266 @ (setadjoin @ X264 @ X265)))&(~(in @ X266 @ X265)|(in @ X266 @ (setadjoin @ X264 @ X265)))))&(((~(in @ X268 @ (powerset @ X267))|(~(in @ X269 @ X268)|(in @ X269 @ X267)))&(((in @ (esk2_2 @ X270 @ X271) @ X271)|(in @ X271 @ (powerset @ X270)))&(~(in @ (esk2_2 @ X270 @ X271) @ X270)|(in @ X271 @ (powerset @ X270)))))&(((((in @ X274 @ (esk3_2 @ X273 @ X274))|~(in @ X274 @ (setunion @ X273)))&((in @ (esk3_2 @ X273 @ X274) @ X273)|~(in @ X274 @ (setunion @ X273))))&(~(in @ X277 @ X278)|~(in @ X278 @ X276)|(in @ X277 @ (setunion @ X276))))&((in @ emptyset @ omega)&((~(in @ X279 @ omega)|(in @ (setadjoin @ X279 @ X279) @ omega))&(((((in @ (esk4_1 @ X280) @ omega)|~(in @ emptyset @ X280)|(~(in @ X282 @ omega)|(in @ X282 @ X280)))&((in @ (esk4_1 @ X280) @ X280)|~(in @ emptyset @ X280)|(~(in @ X282 @ omega)|(in @ X282 @ X280))))&(~(in @ (setadjoin @ (esk4_1 @ X280) @ (esk4_1 @ X280)) @ X280)|~(in @ emptyset @ X280)|(~(in @ X282 @ omega)|(in @ X282 @ X280))))&((((((in @ (esk8_3 @ X283 @ X284 @ X289) @ X284)|~(in @ X289 @ (esk7_2 @ X283 @ X284))|(in @ (esk5_2 @ X283 @ X284) @ X284))&((X283 @ (esk8_3 @ X283 @ X284 @ X289) @ X289)|~(in @ X289 @ (esk7_2 @ X283 @ X284))|(in @ (esk5_2 @ X283 @ X284) @ X284)))&(~(in @ X292 @ X284)|~(X283 @ X292 @ X291)|(in @ X291 @ (esk7_2 @ X283 @ X284))|(in @ (esk5_2 @ X283 @ X284) @ X284)))&(((((in @ (esk8_3 @ X283 @ X284 @ X289) @ X284)|~(in @ X289 @ (esk7_2 @ X283 @ X284))|((X283 @ (esk5_2 @ X283 @ X284) @ (esk6_3 @ X283 @ X284 @ X286))|~(X283 @ (esk5_2 @ X283 @ X284) @ X286)))&((X283 @ (esk8_3 @ X283 @ X284 @ X289) @ X289)|~(in @ X289 @ (esk7_2 @ X283 @ X284))|((X283 @ (esk5_2 @ X283 @ X284) @ (esk6_3 @ X283 @ X284 @ X286))|~(X283 @ (esk5_2 @ X283 @ X284) @ X286))))&(~(in @ X292 @ X284)|~(X283 @ X292 @ X291)|(in @ X291 @ (esk7_2 @ X283 @ X284))|((X283 @ (esk5_2 @ X283 @ X284) @ (esk6_3 @ X283 @ X284 @ X286))|~(X283 @ (esk5_2 @ X283 @ X284) @ X286))))&((((in @ (esk8_3 @ X283 @ X284 @ X289) @ X284)|~(in @ X289 @ (esk7_2 @ X283 @ X284))|(((X286)!=(esk6_3 @ X283 @ X284 @ X286))|~(X283 @ (esk5_2 @ X283 @ X284) @ X286)))&((X283 @ (esk8_3 @ X283 @ X284 @ X289) @ X289)|~(in @ X289 @ (esk7_2 @ X283 @ X284))|(((X286)!=(esk6_3 @ X283 @ X284 @ X286))|~(X283 @ (esk5_2 @ X283 @ X284) @ X286))))&(~(in @ X292 @ X284)|~(X283 @ X292 @ X291)|(in @ X291 @ (esk7_2 @ X283 @ X284))|(((X286)!=(esk6_3 @ X283 @ X284 @ X286))|~(X283 @ (esk5_2 @ X283 @ X284) @ X286))))))&((((in @ (esk9_1 @ X293) @ X293)|~(in @ X294 @ X293))&(~(in @ X296 @ (esk9_1 @ X293))|~(in @ X296 @ X293)|~(in @ X294 @ X293)))&((epred1_0)&((descrp)&((~(in @ X299 @ X297)|(~(X298 @ X299)|(in @ X299 @ (dsetconstr @ X297 @ (^[Z0:$i]:((X298 @ Z0)))))))&((~(in @ X302 @ (dsetconstr @ X300 @ (^[Z0:$i]:((X301 @ Z0)))))|(in @ X302 @ X300))&((~(in @ X305 @ (dsetconstr @ X303 @ (^[Z0:$i]:((X304 @ Z0)))))|(X304 @ X305))&(((((X306 @ (esk11_1 @ X306))|((X306 @ (esk10_2 @ X306 @ X307))|~(X306 @ X307)))&(~(X306 @ X310)|((esk11_1 @ X306)=(X310))|((X306 @ (esk10_2 @ X306 @ X307))|~(X306 @ X307))))&(((X306 @ (esk11_1 @ X306))|(((X307)!=(esk10_2 @ X306 @ X307))|~(X306 @ X307)))&(~(X306 @ X310)|((esk11_1 @ X306)=(X310))|(((X307)!=(esk10_2 @ X306 @ X307))|~(X306 @ X307)))))&((~(in @ X312 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X311)))))|(X311))&((~(in @ X313 @ emptyset)|(X314))&(~(in @ X315 @ emptyset)&(~(in @ X316 @ emptyset)&((((X317 @ (esk12_2 @ X317 @ X318))|~(X317 @ X318)|(X317 @ (esk13_1 @ X317)))&(((X318)!=(esk12_2 @ X317 @ X318))|~(X317 @ X318)|(X317 @ (esk13_1 @ X317))))&(((((in @ (esk15_2 @ X321 @ X322) @ X322)|((X321)=(X322))|(in @ (esk14_2 @ X321 @ X322) @ X321))&(~(in @ (esk15_2 @ X321 @ X322) @ X321)|((X321)=(X322))|(in @ (esk14_2 @ X321 @ X322) @ X321)))&(((in @ (esk15_2 @ X321 @ X322) @ X322)|((X321)=(X322))|~(in @ (esk14_2 @ X321 @ X322) @ X322))&(~(in @ (esk15_2 @ X321 @ X322) @ X321)|((X321)=(X322))|~(in @ (esk14_2 @ X321 @ X322) @ X322))))&(((in @ (esk16_1 @ X325) @ X325)|((X325)=(emptyset)))&(((in @ (esk17_1 @ X327) @ X327)|((X327)=(emptyset)))&(((~(in @ X331 @ (dsetconstr @ X329 @ (^[Z0:$i]:((X330 @ Z0)))))|(X330 @ X331)|~(in @ X331 @ X329))&(~(X330 @ X331)|(in @ X331 @ (dsetconstr @ X329 @ (^[Z0:$i]:((X330 @ Z0)))))|~(in @ X331 @ X329)))&((((X332)=(emptyset))|(in @ (esk18_1 @ X332) @ X332))&((~(in @ X336 @ X334)|(~(X335 @ X336)|((dsetconstr @ X334 @ (^[Z0:$i]:((X335 @ Z0))))!=(emptyset))))&((~(in @ X338 @ X337)|((X337)!=(emptyset)))&((in @ X339 @ (setadjoin @ X339 @ X340))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X343 @ X342)|(in @ X343 @ (setadjoin @ X341 @ X342)))&(((((in @ X346 @ X345)|(X347)|((X346)=(X344))|~(in @ X346 @ (setadjoin @ X344 @ X345)))&(~(X347)|(X347)|((X346)=(X344))|~(in @ X346 @ (setadjoin @ X344 @ X345))))&(((in @ X346 @ X345)|(X347)|~(X347)|~(in @ X346 @ (setadjoin @ X344 @ X345)))&(~(X347)|(X347)|~(X347)|~(in @ X346 @ (setadjoin @ X344 @ X345)))))&((~(in @ X350 @ (setadjoin @ X348 @ X349))|(((X350)=(X348))|(in @ X350 @ X349)))&(((dsetconstr @ X351 @ (^[Z0:$i]:(($true))))=(X351))&((((in @ (esk19_2 @ X352 @ X353) @ X353)|(in @ X353 @ (powerset @ X352)))&(~(in @ (esk19_2 @ X352 @ X353) @ X352)|(in @ X353 @ (powerset @ X352))))&((in @ emptyset @ (powerset @ X355))&((in @ emptyset @ (powerset @ X356))&((~(in @ X358 @ (powerset @ X357))|(~(in @ X359 @ X358)|(in @ X359 @ X357)))&((~(in @ X361 @ X362)|(~(in @ X362 @ X360)|(in @ X361 @ (setunion @ X360))))&((((in @ X364 @ (esk20_3 @ X363 @ X364 @ X365))|(X365)|~(in @ X364 @ (setunion @ X363)))&(((in @ (esk20_3 @ X363 @ X364 @ X365) @ X363)|(X365)|~(in @ X364 @ (setunion @ X363)))&(~(X365)|(X365)|~(in @ X364 @ (setunion @ X363)))))&((~(in @ X368 @ X367)|(in @ X368 @ (powerset @ (setunion @ X367))))&(((epred2_0 @ esk21_0)&(~(epred2_0 @ X371)|((esk21_0)=(X371))))&((~(epred2_0 @ (esk22_1 @ X372))|((esk22_1 @ X372)!=(X372)))&((epred2_0 @ (esk22_1 @ X372))|((esk22_1 @ X372)=(X372))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])])])])).
% 0.20/0.28 thf(c_0_67, negated_conjecture, ![X2:$i]:((((esk21_0)=(X2))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_66])).
% 0.20/0.28 thf(c_0_68, negated_conjecture, ![X2:$i]:(((epred2_0 @ (esk22_1 @ X2))|((esk22_1 @ X2)=(X2)))), inference(split_conjunct,[status(thm)],[c_0_66])).
% 0.20/0.28 thf(c_0_69, negated_conjecture, ![X2:$i]:((((esk22_1 @ X2)=(esk21_0))|((esk22_1 @ X2)=(X2)))), inference(spm,[status(thm)],[c_0_67, c_0_68])).
% 0.20/0.28 thf(c_0_70, negated_conjecture, ![X2:$i]:((~((epred2_0 @ (esk22_1 @ X2)))|((esk22_1 @ X2)!=(X2)))), inference(split_conjunct,[status(thm)],[c_0_66])).
% 0.20/0.28 thf(c_0_71, negated_conjecture, ((esk22_1 @ esk21_0)=(esk21_0)), inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_69])])).
% 0.20/0.28 thf(c_0_72, negated_conjecture, (epred2_0 @ esk21_0), inference(split_conjunct,[status(thm)],[c_0_66])).
% 0.20/0.28 thf(c_0_73, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_72])]), ['proof']).
% 0.20/0.28 % SZS output end CNFRefutation
% 0.20/0.28 % Parsed axioms : 97
% 0.20/0.28 % Removed by relevancy pruning/SinE : 53
% 0.20/0.28 % Initial clauses : 90
% 0.20/0.28 % Removed in clause preprocessing : 4
% 0.20/0.28 % Initial clauses in saturation : 86
% 0.20/0.28 % Processed clauses : 42
% 0.20/0.28 % ...of these trivial : 1
% 0.20/0.28 % ...subsumed : 11
% 0.20/0.28 % ...remaining for further processing : 30
% 0.20/0.28 % Other redundant clauses eliminated : 5
% 0.20/0.28 % Clauses deleted for lack of memory : 0
% 0.20/0.28 % Backward-subsumed : 0
% 0.20/0.28 % Backward-rewritten : 2
% 0.20/0.28 % Generated clauses : 37
% 0.20/0.28 % ...of the previous two non-redundant : 26
% 0.20/0.28 % ...aggressively subsumed : 0
% 0.20/0.28 % Contextual simplify-reflections : 0
% 0.20/0.28 % Paramodulations : 30
% 0.20/0.28 % Factorizations : 2
% 0.20/0.28 % NegExts : 0
% 0.20/0.28 % Equation resolutions : 5
% 0.20/0.28 % Disequality decompositions : 0
% 0.20/0.28 % Total rewrite steps : 11
% 0.20/0.28 % ...of those cached : 3
% 0.20/0.28 % Propositional unsat checks : 0
% 0.20/0.28 % Propositional check models : 0
% 0.20/0.28 % Propositional check unsatisfiable : 0
% 0.20/0.28 % Propositional clauses : 0
% 0.20/0.28 % Propositional clauses after purity: 0
% 0.20/0.28 % Propositional unsat core size : 0
% 0.20/0.28 % Propositional preprocessing time : 0.000
% 0.20/0.28 % Propositional encoding time : 0.000
% 0.20/0.28 % Propositional solver time : 0.000
% 0.20/0.28 % Success case prop preproc time : 0.000
% 0.20/0.28 % Success case prop encoding time : 0.000
% 0.20/0.28 % Success case prop solver time : 0.000
% 0.20/0.28 % Current number of processed clauses : 26
% 0.20/0.28 % Positive orientable unit clauses : 11
% 0.20/0.28 % Positive unorientable unit clauses: 0
% 0.20/0.28 % Negative unit clauses : 1
% 0.20/0.28 % Non-unit-clauses : 14
% 0.20/0.28 % Current number of unprocessed clauses: 70
% 0.20/0.28 % ...number of literals in the above : 229
% 0.20/0.28 % Current number of archived formulas : 0
% 0.20/0.28 % Current number of archived clauses : 2
% 0.20/0.28 % Clause-clause subsumption calls (NU) : 30
% 0.20/0.28 % Rec. Clause-clause subsumption calls : 25
% 0.20/0.28 % Non-unit clause-clause subsumptions : 4
% 0.20/0.28 % Unit Clause-clause subsumption calls : 7
% 0.20/0.28 % Rewrite failures with RHS unbound : 0
% 0.20/0.28 % BW rewrite match attempts : 2
% 0.20/0.28 % BW rewrite match successes : 2
% 0.20/0.28 % Condensation attempts : 0
% 0.20/0.28 % Condensation successes : 0
% 0.20/0.28 % Termbank termtop insertions : 9997
% 0.20/0.28 % Search garbage collected termcells : 3694
% 0.20/0.28
% 0.20/0.28 % -------------------------------------------------
% 0.20/0.28 % User time : 0.010 s
% 0.20/0.28 % System time : 0.005 s
% 0.20/0.28 % Total time : 0.015 s
% 0.20/0.28 % Maximum resident set size: 5012 pages
% 0.20/0.28
% 0.20/0.28 % -------------------------------------------------
% 0.20/0.28 % User time : 0.013 s
% 0.20/0.28 % System time : 0.010 s
% 0.20/0.28 % Total time : 0.024 s
% 0.20/0.28 % Maximum resident set size: 4864 pages
% 0.20/0.28 % E exiting
%------------------------------------------------------------------------------