%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU506^1 : 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 : n012.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 08:24:18 AM UTC 2026
% Result : Theorem 0.08s 0.16s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU506^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 13:46:33 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.14 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.xXi1lCd1l7/E---3.1_124695.p
% 0.08/0.16 % Version: 3.5.1-ho
% 0.08/0.16 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.16 % Starting sh5l with 300s (1) cores
% 0.08/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.16 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.16 % new_bool_1 with pid 124710 completed with status 0
% 0.08/0.16 % Result found by new_bool_1
% 0.08/0.16 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.16 % Starting sh5l with 300s (1) cores
% 0.08/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.16 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.16 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.16 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.08/0.16 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.08/0.16 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.16 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.16 % SubtermCWHack with pid 124713 completed with status 0
% 0.08/0.16 % Result found by SubtermCWHack
% 0.08/0.16 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.08/0.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.16 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.16 % Starting sh5l with 300s (1) cores
% 0.08/0.16 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.16 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.08/0.16 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.08/0.16 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.08/0.16 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.08/0.16 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.16 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.16 % Preprocessing time : 0.001 s
% 0.08/0.16
% 0.08/0.16 % Proof found!
% 0.08/0.16 % SZS status Theorem
% 0.08/0.16 % SZS output start CNFRefutation
% 0.08/0.16 thf(decl_23, type, in: $i > $i > $o).
% 0.08/0.16 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.08/0.16 thf(decl_25, type, setextAx: $o).
% 0.08/0.16 thf(decl_26, type, emptyset: $i).
% 0.08/0.16 thf(decl_27, type, emptysetAx: $o).
% 0.08/0.16 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.08/0.16 thf(decl_29, type, setadjoinAx: $o).
% 0.08/0.16 thf(decl_30, type, powerset: $i > $i).
% 0.08/0.16 thf(decl_31, type, powersetAx: $o).
% 0.08/0.16 thf(decl_33, type, setunionAx: $o).
% 0.08/0.16 thf(decl_34, type, omega: $i).
% 0.08/0.16 thf(decl_35, type, omega0Ax: $o).
% 0.08/0.16 thf(decl_36, type, omegaSAx: $o).
% 0.08/0.16 thf(decl_37, type, omegaIndAx: $o).
% 0.08/0.16 thf(decl_38, type, replAx: $o).
% 0.08/0.16 thf(decl_39, type, foundationAx: $o).
% 0.08/0.16 thf(decl_40, type, wellorderingAx: $o).
% 0.08/0.16 thf(decl_42, type, descrp: $o).
% 0.08/0.16 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.08/0.16 thf(decl_44, type, dsetconstrI: $o).
% 0.08/0.16 thf(decl_45, type, dsetconstrEL: $o).
% 0.08/0.16 thf(decl_46, type, dsetconstrER: $o).
% 0.08/0.16 thf(decl_47, type, exuE1: $o).
% 0.08/0.16 thf(decl_48, type, prop2set: $o > $i).
% 0.08/0.16 thf(decl_49, type, prop2setE: $o).
% 0.08/0.16 thf(decl_50, type, emptysetE: $o).
% 0.08/0.16 thf(decl_51, type, emptysetimpfalse: $o).
% 0.08/0.16 thf(decl_52, type, notinemptyset: $o).
% 0.08/0.16 thf(decl_53, type, exuE3e: $o).
% 0.08/0.16 thf(decl_54, type, setext: $o).
% 0.08/0.16 thf(decl_55, type, epred1_0: $o).
% 0.08/0.16 thf(decl_56, type, esk1_2: $i > $i > $i).
% 0.08/0.16 thf(decl_57, type, esk2_2: $i > $i > $i).
% 0.08/0.16 thf(decl_58, type, esk3_1: $i > $i).
% 0.08/0.16 thf(decl_59, type, esk4_2: ($i > $i > $o) > $i > $i).
% 0.08/0.16 thf(decl_60, type, esk5_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.16 thf(decl_61, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.08/0.16 thf(decl_62, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.08/0.16 thf(decl_63, type, esk8_1: $i > $i).
% 0.08/0.16 thf(decl_64, type, esk9_2: ($i > $o) > $i > $i).
% 0.08/0.16 thf(decl_65, type, esk10_1: ($i > $o) > $i).
% 0.08/0.16 thf(decl_66, type, esk11_2: ($i > $o) > $i > $i).
% 0.08/0.16 thf(decl_67, type, esk12_1: ($i > $o) > $i).
% 0.08/0.16 thf(decl_68, type, esk13_2: $i > $i > $i).
% 0.08/0.16 thf(decl_69, type, esk14_2: $i > $i > $i).
% 0.08/0.16 thf(decl_70, type, esk15_0: $i).
% 0.08/0.16 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', exuE1)).
% 0.08/0.16 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', exu)).
% 0.08/0.16 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', prop2set)).
% 0.08/0.16 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', exuE3e)).
% 0.08/0.16 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', replAx)).
% 0.08/0.16 thf(emptyI, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset)))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', emptyI)).
% 0.08/0.16 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', dsetconstrI)).
% 0.08/0.16 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', dsetconstrEL)).
% 0.08/0.16 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', dsetconstrER)).
% 0.08/0.16 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', prop2setE)).
% 0.08/0.16 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', foundationAx)).
% 0.08/0.16 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.xXi1lCd1l7/E---3.1_124695.p', wellorderingAx)).
% 0.08/0.16 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', emptysetE)).
% 0.08/0.16 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', emptysetimpfalse)).
% 0.08/0.16 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', notinemptyset)).
% 0.08/0.16 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', setext)).
% 0.08/0.16 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', setadjoinAx)).
% 0.08/0.16 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', emptysetAx)).
% 0.08/0.16 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', setextAx)).
% 0.08/0.16 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', omega0Ax)).
% 0.08/0.16 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', omegaSAx)).
% 0.08/0.16 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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.xXi1lCd1l7/E---3.1_124695.p', omegaIndAx)).
% 0.08/0.16 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.xXi1lCd1l7/E---3.1_124695.p', powersetAx)).
% 0.08/0.16 thf(c_0_23, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.08/0.16 thf(c_0_24, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.08/0.16 thf(c_0_25, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.08/0.16 thf(c_0_26, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.08/0.16 thf(c_0_27, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.08/0.16 thf(c_0_28, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[emptyI])).
% 0.08/0.16 thf(c_0_29, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.08/0.16 thf(c_0_30, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.08/0.16 thf(c_0_31, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.08/0.16 thf(c_0_32, plain, ((exuE1)=(![X1:$i > $o]:((((?[X84:$i]:(((((X1 @ X84)))&(![X85:$i]:(((((X1 @ X85)))=>(((X84)=(X85))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_23, c_0_24])).
% 0.08/0.16 thf(c_0_33, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_25])).
% 0.08/0.16 thf(c_0_34, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X86:$i]:(((((X1 @ X86)))&(![X87:$i]:(((((X1 @ X87)))=>(((X86)=(X87))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_26, c_0_24])).
% 0.08/0.16 thf(c_0_35, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X82:$i]:(((((X6 @ X2 @ X82)))&(![X83:$i]:(((((X6 @ X2 @ X83)))=>(((X82)=(X83)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_27, c_0_24])).
% 0.08/0.16 thf(c_0_36, plain, ((epred1_0)<=>![X114:$i]:(?[X115:$i]:((((![X116:$i]:(((in @ X116 @ X115)=>![X117:$i]:(((in @ X117 @ X116)=>(in @ X117 @ X114)))))&![X118:$i, X119:$i]:((((in @ X118 @ X114)&(in @ X119 @ X114))=>(![X120:$i]:(((in @ X120 @ X115)=>((in @ X118 @ X120)<=>(in @ X119 @ X120))))=>((X118)=(X119))))))&![X121:$i, X122:$i]:((((in @ X121 @ X115)&(in @ X122 @ X115))=>(![X123:$i]:(((in @ X123 @ X121)=>(in @ X123 @ X122)))|![X124:$i]:(((in @ X124 @ X122)=>(in @ X124 @ X121)))))))&![X125:$i]:(((![X126:$i]:(((in @ X126 @ X125)=>(in @ X126 @ X114)))&?[X127:$i]:((in @ X127 @ X125)))=>?[X128:$i, X129:$i]:(((((in @ X128 @ X115)&(in @ X129 @ X125))&~(?[X130:$i]:(((in @ X130 @ X128)&(in @ X130 @ X125)))))&![X131:$i]:(((in @ X131 @ X115)=>(![X132:$i]:(((in @ X132 @ X131)=>(in @ X132 @ X128)))|(in @ X129 @ X131)))))))))))), introduced(definition)).
% 0.08/0.16 thf(c_0_37, negated_conjecture, ~((![X88:$i, X89:$i]:((![X90:$i]:(((in @ X90 @ X88)<=>(in @ X90 @ X89)))=>((X88)=(X89))))=>(![X91:$i]:(~(in @ X91 @ emptyset))=>(![X92:$i, X93:$i, X94:$i]:(((in @ X94 @ (setadjoin @ X92 @ X93))<=>(((X94)=(X92))|(in @ X94 @ X93))))=>(![X95:$i, X96:$i]:(((in @ X96 @ (powerset @ X95))<=>![X97:$i]:(((in @ X97 @ X96)=>(in @ X97 @ X95)))))=>((setunionAx)=>((in @ emptyset @ omega)=>(![X98:$i]:(((in @ X98 @ omega)=>(in @ (setadjoin @ X98 @ X98) @ omega)))=>(![X99:$i]:((((in @ emptyset @ X99)&![X100:$i]:((((in @ X100 @ omega)&(in @ X100 @ X99))=>(in @ (setadjoin @ X100 @ X100) @ X99))))=>![X101:$i]:(((in @ X101 @ omega)=>(in @ X101 @ X99)))))=>(![X102:$i > $i > $o, X103:$i]:((![X104:$i]:(((in @ X104 @ X103)=>?[X105:$i]:(((X102 @ X104 @ X105)&![X106:$i]:(((X102 @ X104 @ X106)=>((X105)=(X106))))))))=>?[X107:$i]:(![X108:$i]:(((in @ X108 @ X107)<=>?[X109:$i]:(((in @ X109 @ X103)&(X102 @ X109 @ X108))))))))=>(![X110:$i]:((?[X111:$i]:((in @ X111 @ X110))=>?[X112:$i]:(((in @ X112 @ X110)&~(?[X113:$i]:(((in @ X113 @ X112)&(in @ X113 @ X110))))))))=>((epred1_0)=>((descrp)=>(![X133:$i, X134:$i > $o, X135:$i]:(((in @ X135 @ X133)=>((X134 @ X135)=>(in @ X135 @ (dsetconstr @ X133 @ X134)))))=>(![X136:$i, X137:$i > $o, X138:$i]:(((in @ X138 @ (dsetconstr @ X136 @ X137))=>(in @ X138 @ X136)))=>(![X139:$i, X140:$i > $o, X141:$i]:(((in @ X141 @ (dsetconstr @ X139 @ X140))=>(X140 @ X141)))=>(![X142:$i > $o]:((?[X143:$i]:(((X142 @ X143)&![X144:$i]:(((X142 @ X144)=>((X143)=(X144))))))=>?[X145:$i]:(((X142 @ X145)&![X146:$i]:(((X142 @ X146)=>((X145)=(X146))))))))=>(![X147:$o, X148:$i]:(((in @ X148 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X147)))))=>(X147)))=>(![X149:$i]:(((in @ X149 @ emptyset)=>![X150:$o]:((X150))))=>(![X151:$i]:(((in @ X151 @ emptyset)=>~($true)))=>(![X152:$i]:(~(in @ X152 @ emptyset))=>(![X153:$i > $o]:((?[X154:$i]:(((X153 @ X154)&![X155:$i]:(((X153 @ X155)=>((X154)=(X155))))))=>?[X156:$i]:((X153 @ X156))))=>(![X157:$i, X158:$i]:((![X159:$i]:(((in @ X159 @ X157)=>(in @ X159 @ X158)))=>(![X160:$i]:(((in @ X160 @ X158)=>(in @ X160 @ X157)))=>((X157)=(X158)))))=>![X4:$i]:((![X2:$i]:(~(in @ X2 @ X4))=>((X4)=(emptyset))))))))))))))))))))))))))), 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)],[c_0_28, foundationAx]), wellorderingAx]), c_0_29]), c_0_30]), c_0_31]), c_0_32]), c_0_33]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_34]), setext]), setadjoinAx]), emptysetAx]), setextAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_35]), powersetAx])])]), c_0_36])).
% 0.08/0.16 thf(c_0_38, negated_conjecture, ![X161:$i, X162:$i, X164:$i, X165:$i, X166:$i, X167:$i, X168:$i, X169:$i, X170:$i, X171:$i, X172:$i, X174:$i, X175:$i, X177:$i, X178:$i > $i > $o, X179:$i, X181:$i, X184:$i, X186:$i, X187:$i, X188:$i, X189:$i, X191:$i, X192:$i, X193:$i > $o, X194:$i, X195:$i, X196:$i > $o, X197:$i, X198:$i, X199:$i > $o, X200:$i, X201:$i > $o, X202:$i, X205:$i, X206:$o, X207:$i, X208:$i, X209:$o, X210:$i, X211:$i, X212:$i > $o, X213:$i, X216:$i, X217:$i, X221:$i]:((((~(in @ (esk1_2 @ X161 @ X162) @ X161)|~(in @ (esk1_2 @ X161 @ X162) @ X162)|((X161)=(X162)))&((in @ (esk1_2 @ X161 @ X162) @ X161)|(in @ (esk1_2 @ X161 @ X162) @ X162)|((X161)=(X162))))&(~(in @ X164 @ emptyset)&(((~(in @ X167 @ (setadjoin @ X165 @ X166))|(((X167)=(X165))|(in @ X167 @ X166)))&((((X167)!=(X165))|(in @ X167 @ (setadjoin @ X165 @ X166)))&(~(in @ X167 @ X166)|(in @ X167 @ (setadjoin @ X165 @ X166)))))&(((~(in @ X169 @ (powerset @ X168))|(~(in @ X170 @ X169)|(in @ X170 @ X168)))&(((in @ (esk2_2 @ X171 @ X172) @ X172)|(in @ X172 @ (powerset @ X171)))&(~(in @ (esk2_2 @ X171 @ X172) @ X171)|(in @ X172 @ (powerset @ X171)))))&((setunionAx)&((in @ emptyset @ omega)&((~(in @ X174 @ omega)|(in @ (setadjoin @ X174 @ X174) @ omega))&(((((in @ (esk3_1 @ X175) @ omega)|~(in @ emptyset @ X175)|(~(in @ X177 @ omega)|(in @ X177 @ X175)))&((in @ (esk3_1 @ X175) @ X175)|~(in @ emptyset @ X175)|(~(in @ X177 @ omega)|(in @ X177 @ X175))))&(~(in @ (setadjoin @ (esk3_1 @ X175) @ (esk3_1 @ X175)) @ X175)|~(in @ emptyset @ X175)|(~(in @ X177 @ omega)|(in @ X177 @ X175))))&((((((in @ (esk7_3 @ X178 @ X179 @ X184) @ X179)|~(in @ X184 @ (esk6_2 @ X178 @ X179))|(in @ (esk4_2 @ X178 @ X179) @ X179))&((X178 @ (esk7_3 @ X178 @ X179 @ X184) @ X184)|~(in @ X184 @ (esk6_2 @ X178 @ X179))|(in @ (esk4_2 @ X178 @ X179) @ X179)))&(~(in @ X187 @ X179)|~(X178 @ X187 @ X186)|(in @ X186 @ (esk6_2 @ X178 @ X179))|(in @ (esk4_2 @ X178 @ X179) @ X179)))&(((((in @ (esk7_3 @ X178 @ X179 @ X184) @ X179)|~(in @ X184 @ (esk6_2 @ X178 @ X179))|((X178 @ (esk4_2 @ X178 @ X179) @ (esk5_3 @ X178 @ X179 @ X181))|~(X178 @ (esk4_2 @ X178 @ X179) @ X181)))&((X178 @ (esk7_3 @ X178 @ X179 @ X184) @ X184)|~(in @ X184 @ (esk6_2 @ X178 @ X179))|((X178 @ (esk4_2 @ X178 @ X179) @ (esk5_3 @ X178 @ X179 @ X181))|~(X178 @ (esk4_2 @ X178 @ X179) @ X181))))&(~(in @ X187 @ X179)|~(X178 @ X187 @ X186)|(in @ X186 @ (esk6_2 @ X178 @ X179))|((X178 @ (esk4_2 @ X178 @ X179) @ (esk5_3 @ X178 @ X179 @ X181))|~(X178 @ (esk4_2 @ X178 @ X179) @ X181))))&((((in @ (esk7_3 @ X178 @ X179 @ X184) @ X179)|~(in @ X184 @ (esk6_2 @ X178 @ X179))|(((X181)!=(esk5_3 @ X178 @ X179 @ X181))|~(X178 @ (esk4_2 @ X178 @ X179) @ X181)))&((X178 @ (esk7_3 @ X178 @ X179 @ X184) @ X184)|~(in @ X184 @ (esk6_2 @ X178 @ X179))|(((X181)!=(esk5_3 @ X178 @ X179 @ X181))|~(X178 @ (esk4_2 @ X178 @ X179) @ X181))))&(~(in @ X187 @ X179)|~(X178 @ X187 @ X186)|(in @ X186 @ (esk6_2 @ X178 @ X179))|(((X181)!=(esk5_3 @ X178 @ X179 @ X181))|~(X178 @ (esk4_2 @ X178 @ X179) @ X181))))))&((((in @ (esk8_1 @ X188) @ X188)|~(in @ X189 @ X188))&(~(in @ X191 @ (esk8_1 @ X188))|~(in @ X191 @ X188)|~(in @ X189 @ X188)))&((epred1_0)&((descrp)&((~(in @ X194 @ X192)|(~(X193 @ X194)|(in @ X194 @ (dsetconstr @ X192 @ X193))))&((~(in @ X197 @ (dsetconstr @ X195 @ X196))|(in @ X197 @ X195))&((~(in @ X200 @ (dsetconstr @ X198 @ X199))|(X199 @ X200))&(((((X201 @ (esk10_1 @ X201))|((X201 @ (esk9_2 @ X201 @ X202))|~(X201 @ X202)))&(~(X201 @ X205)|((esk10_1 @ X201)=(X205))|((X201 @ (esk9_2 @ X201 @ X202))|~(X201 @ X202))))&(((X201 @ (esk10_1 @ X201))|(((X202)!=(esk9_2 @ X201 @ X202))|~(X201 @ X202)))&(~(X201 @ X205)|((esk10_1 @ X201)=(X205))|(((X202)!=(esk9_2 @ X201 @ X202))|~(X201 @ X202)))))&((~(in @ X207 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X206)))))|(X206))&((~(in @ X208 @ emptyset)|(X209))&((~(in @ X210 @ emptyset)|~($true))&(~(in @ X211 @ emptyset)&((((X212 @ (esk11_2 @ X212 @ X213))|~(X212 @ X213)|(X212 @ (esk12_1 @ X212)))&(((X213)!=(esk11_2 @ X212 @ X213))|~(X212 @ X213)|(X212 @ (esk12_1 @ X212))))&(((((in @ (esk14_2 @ X216 @ X217) @ X217)|((X216)=(X217))|(in @ (esk13_2 @ X216 @ X217) @ X216))&(~(in @ (esk14_2 @ X216 @ X217) @ X216)|((X216)=(X217))|(in @ (esk13_2 @ X216 @ X217) @ X216)))&(((in @ (esk14_2 @ X216 @ X217) @ X217)|((X216)=(X217))|~(in @ (esk13_2 @ X216 @ X217) @ X217))&(~(in @ (esk14_2 @ X216 @ X217) @ X216)|((X216)=(X217))|~(in @ (esk13_2 @ X216 @ X217) @ X217))))&(~(in @ X221 @ esk15_0)&((esk15_0)!=(emptyset)))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])])])])])).
% 0.08/0.16 thf(c_0_39, negated_conjecture, ![X2:$i]:(~((in @ X2 @ esk15_0))), inference(split_conjunct,[status(thm)],[c_0_38])).
% 0.08/0.16 thf(c_0_40, negated_conjecture, ![X2:$i, X3:$i]:(((in @ (esk1_2 @ X2 @ X3) @ X2)|(in @ (esk1_2 @ X2 @ X3) @ X3)|((X2)=(X3)))), inference(split_conjunct,[status(thm)],[c_0_38])).
% 0.08/0.16 thf(c_0_41, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_38])).
% 0.08/0.16 thf(c_0_42, negated_conjecture, ![X2:$i]:((((X2)=(esk15_0))|(in @ (esk1_2 @ X2 @ esk15_0) @ X2))), inference(spm,[status(thm)],[c_0_39, c_0_40])).
% 0.08/0.16 thf(c_0_43, negated_conjecture, ((esk15_0)!=(emptyset)), inference(split_conjunct,[status(thm)],[c_0_38])).
% 0.08/0.16 thf(c_0_44, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_43]), ['proof']).
% 0.08/0.16 % SZS output end CNFRefutation
% 0.08/0.16 % Parsed axioms : 57
% 0.08/0.16 % Removed by relevancy pruning/SinE : 34
% 0.08/0.16 % Initial clauses : 60
% 0.08/0.16 % Removed in clause preprocessing : 0
% 0.08/0.16 % Initial clauses in saturation : 60
% 0.08/0.16 % Processed clauses : 80
% 0.08/0.16 % ...of these trivial : 2
% 0.08/0.16 % ...subsumed : 17
% 0.08/0.16 % ...remaining for further processing : 61
% 0.08/0.16 % Other redundant clauses eliminated : 1
% 0.08/0.16 % Clauses deleted for lack of memory : 0
% 0.08/0.16 % Backward-subsumed : 1
% 0.08/0.16 % Backward-rewritten : 0
% 0.08/0.16 % Generated clauses : 273
% 0.08/0.16 % ...of the previous two non-redundant : 231
% 0.08/0.16 % ...aggressively subsumed : 0
% 0.08/0.16 % Contextual simplify-reflections : 0
% 0.08/0.16 % Paramodulations : 270
% 0.08/0.16 % Factorizations : 2
% 0.08/0.16 % NegExts : 0
% 0.08/0.16 % Equation resolutions : 1
% 0.08/0.16 % Disequality decompositions : 0
% 0.08/0.16 % Total rewrite steps : 38
% 0.08/0.16 % ...of those cached : 20
% 0.08/0.16 % Propositional unsat checks : 0
% 0.08/0.16 % Propositional check models : 0
% 0.08/0.16 % Propositional check unsatisfiable : 0
% 0.08/0.16 % Propositional clauses : 0
% 0.08/0.16 % Propositional clauses after purity: 0
% 0.08/0.16 % Propositional unsat core size : 0
% 0.08/0.16 % Propositional preprocessing time : 0.000
% 0.08/0.16 % Propositional encoding time : 0.000
% 0.08/0.16 % Propositional solver time : 0.000
% 0.08/0.16 % Success case prop preproc time : 0.000
% 0.08/0.16 % Success case prop encoding time : 0.000
% 0.08/0.16 % Success case prop solver time : 0.000
% 0.08/0.16 % Current number of processed clauses : 59
% 0.08/0.16 % Positive orientable unit clauses : 17
% 0.08/0.16 % Positive unorientable unit clauses: 0
% 0.08/0.16 % Negative unit clauses : 4
% 0.08/0.16 % Non-unit-clauses : 38
% 0.08/0.16 % Current number of unprocessed clauses: 195
% 0.08/0.16 % ...number of literals in the above : 645
% 0.08/0.16 % Current number of archived formulas : 0
% 0.08/0.16 % Current number of archived clauses : 1
% 0.08/0.16 % Clause-clause subsumption calls (NU) : 504
% 0.08/0.16 % Rec. Clause-clause subsumption calls : 353
% 0.08/0.16 % Non-unit clause-clause subsumptions : 7
% 0.08/0.16 % Unit Clause-clause subsumption calls : 136
% 0.08/0.16 % Rewrite failures with RHS unbound : 0
% 0.08/0.16 % BW rewrite match attempts : 11
% 0.08/0.16 % BW rewrite match successes : 0
% 0.08/0.16 % Condensation attempts : 0
% 0.08/0.16 % Condensation successes : 0
% 0.08/0.16 % Termbank termtop insertions : 11461
% 0.08/0.16 % Search garbage collected termcells : 2695
% 0.08/0.16
% 0.08/0.16 % -------------------------------------------------
% 0.08/0.16 % User time : 0.009 s
% 0.08/0.16 % System time : 0.003 s
% 0.08/0.16 % Total time : 0.012 s
% 0.08/0.16 % Maximum resident set size: 4208 pages
% 0.08/0.16
% 0.08/0.16 % -------------------------------------------------
% 0.08/0.16 % User time : 0.011 s
% 0.08/0.16 % System time : 0.005 s
% 0.08/0.16 % Total time : 0.016 s
% 0.08/0.16 % Maximum resident set size: 4864 pages
% 0.08/0.16 % E exiting
%------------------------------------------------------------------------------