%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU507^1 : 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 : n026.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 08:26:31 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU507^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n026.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 13:49:57 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
% 0.07/0.23 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.Ye2d1MiwNT/E---3.1_616828.p
% 0.07/0.26 % Version: 3.5.1-ho
% 0.07/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting sh5l with 300s (1) cores
% 0.07/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.26 % new_bool_2 with pid 616861 completed with status 0
% 0.07/0.26 % Result found by new_bool_2
% 0.07/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting sh5l with 300s (1) cores
% 0.07/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.26 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.26 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.07/0.26 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.07/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.26 % SubtermCWHack with pid 616862 completed with status 0
% 0.07/0.26 % Result found by SubtermCWHack
% 0.07/0.26 % Preprocessing class: HSMSSLSSMLLCHFA.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting sh5l with 300s (1) cores
% 0.07/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.07/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.26 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.26 % Search class: HGHSF-FFMS31-SHFSMSBN
% 0.07/0.26 % partial match(1): HGHSM-FFMS31-SHFSMSBN
% 0.07/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.26 % Preprocessing time : 0.001 s
% 0.07/0.26
% 0.07/0.26 % Proof found!
% 0.07/0.26 % SZS status Theorem
% 0.07/0.26 % SZS output start CNFRefutation
% 0.07/0.26 thf(decl_23, type, in: $i > $i > $o).
% 0.07/0.26 thf(decl_24, type, exu: ($i > $o) > $o).
% 0.07/0.26 thf(decl_25, type, setextAx: $o).
% 0.07/0.26 thf(decl_26, type, emptyset: $i).
% 0.07/0.26 thf(decl_27, type, emptysetAx: $o).
% 0.07/0.26 thf(decl_28, type, setadjoin: $i > $i > $i).
% 0.07/0.26 thf(decl_29, type, setadjoinAx: $o).
% 0.07/0.26 thf(decl_30, type, powerset: $i > $i).
% 0.07/0.26 thf(decl_31, type, powersetAx: $o).
% 0.07/0.26 thf(decl_33, type, setunionAx: $o).
% 0.07/0.26 thf(decl_34, type, omega: $i).
% 0.07/0.26 thf(decl_35, type, omega0Ax: $o).
% 0.07/0.26 thf(decl_36, type, omegaSAx: $o).
% 0.07/0.26 thf(decl_37, type, omegaIndAx: $o).
% 0.07/0.26 thf(decl_38, type, replAx: $o).
% 0.07/0.26 thf(decl_39, type, foundationAx: $o).
% 0.07/0.26 thf(decl_40, type, wellorderingAx: $o).
% 0.07/0.26 thf(decl_42, type, descrp: $o).
% 0.07/0.26 thf(decl_43, type, dsetconstr: $i > ($i > $o) > $i).
% 0.07/0.26 thf(decl_44, type, dsetconstrI: $o).
% 0.07/0.26 thf(decl_45, type, dsetconstrEL: $o).
% 0.07/0.26 thf(decl_46, type, dsetconstrER: $o).
% 0.07/0.26 thf(decl_47, type, exuE1: $o).
% 0.07/0.26 thf(decl_48, type, prop2set: $o > $i).
% 0.07/0.26 thf(decl_49, type, prop2setE: $o).
% 0.07/0.26 thf(decl_50, type, emptysetE: $o).
% 0.07/0.26 thf(decl_51, type, emptysetimpfalse: $o).
% 0.07/0.26 thf(decl_52, type, notinemptyset: $o).
% 0.07/0.26 thf(decl_53, type, exuE3e: $o).
% 0.07/0.26 thf(decl_54, type, setext: $o).
% 0.07/0.26 thf(decl_55, type, emptyI: $o).
% 0.07/0.26 thf(decl_56, type, epred1_0: $o).
% 0.07/0.26 thf(decl_57, type, esk1_2: $i > $i > $i).
% 0.07/0.26 thf(decl_58, type, esk2_2: $i > $i > $i).
% 0.07/0.26 thf(decl_59, type, esk3_1: $i > $i).
% 0.07/0.26 thf(decl_60, type, esk4_2: ($i > $i > $o) > $i > $i).
% 0.07/0.26 thf(decl_61, type, esk5_3: ($i > $i > $o) > $i > $i > $i).
% 0.07/0.26 thf(decl_62, type, esk6_2: ($i > $i > $o) > $i > $i).
% 0.07/0.26 thf(decl_63, type, esk7_3: ($i > $i > $o) > $i > $i > $i).
% 0.07/0.26 thf(decl_64, type, esk8_1: $i > $i).
% 0.07/0.26 thf(decl_65, type, esk9_2: ($i > $o) > $i > $i).
% 0.07/0.26 thf(decl_66, type, esk10_1: ($i > $o) > $i).
% 0.07/0.26 thf(decl_67, type, esk11_2: ($i > $o) > $i > $i).
% 0.07/0.26 thf(decl_68, type, esk12_1: ($i > $o) > $i).
% 0.07/0.26 thf(decl_69, type, esk13_2: $i > $i > $i).
% 0.07/0.26 thf(decl_70, type, esk14_2: $i > $i > $i).
% 0.07/0.26 thf(decl_71, type, esk15_1: $i > $i).
% 0.07/0.26 thf(decl_72, type, esk16_0: $i).
% 0.07/0.26 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', exuE1)).
% 0.07/0.26 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', exu)).
% 0.07/0.26 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', prop2set)).
% 0.07/0.26 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', exuE3e)).
% 0.07/0.26 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', replAx)).
% 0.07/0.26 thf(noeltsimpempty, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))))))))))))))))))))))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', noeltsimpempty)).
% 0.07/0.26 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', dsetconstrI)).
% 0.07/0.26 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', dsetconstrEL)).
% 0.07/0.26 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', dsetconstrER)).
% 0.07/0.26 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', prop2setE)).
% 0.07/0.26 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$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.Ye2d1MiwNT/E---3.1_616828.p', wellorderingAx)).
% 0.07/0.26 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', emptysetE)).
% 0.07/0.26 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', emptysetimpfalse)).
% 0.07/0.26 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', notinemptyset)).
% 0.07/0.26 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', setext)).
% 0.07/0.26 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', emptyI)).
% 0.07/0.26 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', powersetAx)).
% 0.07/0.26 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', setadjoinAx)).
% 0.07/0.26 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', emptysetAx)).
% 0.07/0.26 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', setextAx)).
% 0.07/0.26 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', omegaSAx)).
% 0.07/0.26 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', omegaIndAx)).
% 0.07/0.26 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', foundationAx)).
% 0.07/0.26 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.Ye2d1MiwNT/E---3.1_616828.p', omega0Ax)).
% 0.07/0.26 thf(c_0_24, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.07/0.26 thf(c_0_25, plain, ((exu)=(^[Z0:$i > $o]:(?[X2:$i]:((((Z0 @ X2))&(![X3:$i]:((((Z0 @ X3))=>(((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.07/0.26 thf(c_0_26, plain, ((prop2set)=(^[Z0:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])).
% 0.07/0.26 thf(c_0_27, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.07/0.26 thf(c_0_28, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.07/0.26 thf(c_0_29, negated_conjecture, ~(((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset)))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[noeltsimpempty])).
% 0.07/0.26 thf(c_0_30, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.07/0.26 thf(c_0_31, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.07/0.26 thf(c_0_32, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.07/0.26 thf(c_0_33, plain, ((exuE1)=(![X1:$i > $o]:((((?[X86:$i]:(((((X1 @ X86)))&(![X87:$i]:(((((X1 @ X87)))=>(((X86)=(X87))))))))))=>(?[X2:$i]:((((X1 @ X2))&(![X3:$i]:((((X1 @ X3))=>(((X2)=(X3))))))))))))), inference(apply_def,[status(thm)],[c_0_24, c_0_25])).
% 0.07/0.26 thf(c_0_34, axiom, ((prop2setE)=(![X11:$o, X2:$i]:((((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:(((X11)))))))=>((X11)))))), inference(apply_def,[status(thm)],[prop2setE, c_0_26])).
% 0.07/0.26 thf(c_0_35, plain, ((exuE3e)=(![X1:$i > $o]:((((?[X88:$i]:(((((X1 @ X88)))&(![X89:$i]:(((((X1 @ X89)))=>(((X88)=(X89))))))))))=>(?[X2:$i]:((X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_27, c_0_25])).
% 0.07/0.26 thf(c_0_36, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:(((![X2:$i]:((((in @ X2 @ X4))=>((?[X84:$i]:(((((X6 @ X2 @ X84)))&(![X85:$i]:(((((X6 @ X2 @ X85)))=>(((X84)=(X85)))))))))))))=>(?[X5:$i]:(![X2:$i]:((((in @ X2 @ X5))<=>(?[X3:$i]:((((in @ X3 @ X4))&((X6 @ X3 @ X2))))))))))))), inference(apply_def,[status(thm)],[c_0_28, c_0_25])).
% 0.07/0.26 thf(c_0_37, plain, ((epred1_0)<=>![X116:$i]:(?[X117:$i]:((((![X118:$i]:(((in @ X118 @ X117)=>![X119:$i]:(((in @ X119 @ X118)=>(in @ X119 @ X116)))))&![X120:$i, X121:$i]:((((in @ X120 @ X116)&(in @ X121 @ X116))=>(![X122:$i]:(((in @ X122 @ X117)=>((in @ X120 @ X122)<=>(in @ X121 @ X122))))=>((X120)=(X121))))))&![X123:$i, X124:$i]:((((in @ X123 @ X117)&(in @ X124 @ X117))=>(![X125:$i]:(((in @ X125 @ X123)=>(in @ X125 @ X124)))|![X126:$i]:(((in @ X126 @ X124)=>(in @ X126 @ X123)))))))&![X127:$i]:(((![X128:$i]:(((in @ X128 @ X127)=>(in @ X128 @ X116)))&?[X129:$i]:((in @ X129 @ X127)))=>?[X130:$i, X131:$i]:(((((in @ X130 @ X117)&(in @ X131 @ X127))&~(?[X132:$i]:(((in @ X132 @ X130)&(in @ X132 @ X127)))))&![X133:$i]:(((in @ X133 @ X117)=>(![X134:$i]:(((in @ X134 @ X133)=>(in @ X134 @ X130)))|(in @ X131 @ X133)))))))))))), introduced(definition)).
% 0.07/0.26 thf(c_0_38, negated_conjecture, ~((![X90:$i, X91:$i]:((![X92:$i]:(((in @ X92 @ X90)<=>(in @ X92 @ X91)))=>((X90)=(X91))))=>(![X93:$i]:(~(in @ X93 @ emptyset))=>(![X94:$i, X95:$i, X96:$i]:(((in @ X96 @ (setadjoin @ X94 @ X95))<=>(((X96)=(X94))|(in @ X96 @ X95))))=>(![X97:$i, X98:$i]:(((in @ X98 @ (powerset @ X97))<=>![X99:$i]:(((in @ X99 @ X98)=>(in @ X99 @ X97)))))=>((setunionAx)=>((in @ emptyset @ omega)=>(![X100:$i]:(((in @ X100 @ omega)=>(in @ (setadjoin @ X100 @ X100) @ omega)))=>(![X101:$i]:((((in @ emptyset @ X101)&![X102:$i]:((((in @ X102 @ omega)&(in @ X102 @ X101))=>(in @ (setadjoin @ X102 @ X102) @ X101))))=>![X103:$i]:(((in @ X103 @ omega)=>(in @ X103 @ X101)))))=>(![X104:$i > $i > $o, X105:$i]:((![X106:$i]:(((in @ X106 @ X105)=>?[X107:$i]:(((X104 @ X106 @ X107)&![X108:$i]:(((X104 @ X106 @ X108)=>((X107)=(X108))))))))=>?[X109:$i]:(![X110:$i]:(((in @ X110 @ X109)<=>?[X111:$i]:(((in @ X111 @ X105)&(X104 @ X111 @ X110))))))))=>(![X112:$i]:((?[X113:$i]:((in @ X113 @ X112))=>?[X114:$i]:(((in @ X114 @ X112)&~(?[X115:$i]:(((in @ X115 @ X114)&(in @ X115 @ X112))))))))=>((epred1_0)=>((descrp)=>(![X135:$i, X136:$i > $o, X137:$i]:(((in @ X137 @ X135)=>((X136 @ X137)=>(in @ X137 @ (dsetconstr @ X135 @ (^[Z0:$i]:((X136 @ Z0))))))))=>(![X138:$i, X139:$i > $o, X140:$i]:(((in @ X140 @ (dsetconstr @ X138 @ (^[Z0:$i]:((X139 @ Z0)))))=>(in @ X140 @ X138)))=>(![X141:$i, X142:$i > $o, X143:$i]:(((in @ X143 @ (dsetconstr @ X141 @ (^[Z0:$i]:((X142 @ Z0)))))=>(X142 @ X143)))=>(![X144:$i > $o]:((?[X145:$i]:(((X144 @ X145)&![X146:$i]:(((X144 @ X146)=>((X145)=(X146))))))=>?[X147:$i]:(((X144 @ X147)&![X148:$i]:(((X144 @ X148)=>((X147)=(X148))))))))=>(![X149:$o, X150:$i]:(((in @ X150 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X149)))))=>(X149)))=>(![X151:$i]:(((in @ X151 @ emptyset)=>![X152:$o]:((X152))))=>(![X153:$i]:(~(in @ X153 @ emptyset))=>(![X154:$i]:(~(in @ X154 @ emptyset))=>(![X155:$i > $o]:((?[X156:$i]:(((X155 @ X156)&![X157:$i]:(((X155 @ X157)=>((X156)=(X157))))))=>?[X158:$i]:((X155 @ X158))))=>(![X159:$i, X160:$i]:((![X161:$i]:(((in @ X161 @ X159)=>(in @ X161 @ X160)))=>(![X162:$i]:(((in @ X162 @ X160)=>(in @ X162 @ X159)))=>((X159)=(X160)))))=>(![X163:$i]:((![X164:$i]:(~(in @ X164 @ X163))=>((X163)=(emptyset))))=>![X4:$i]:((![X2:$i]:(~(in @ X2 @ X4))=>((X4)=(emptyset)))))))))))))))))))))))))))), 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)],[c_0_29, wellorderingAx]), c_0_30]), c_0_31]), c_0_32]), c_0_33]), c_0_34]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_35]), setext]), emptyI]), powersetAx]), setadjoinAx]), emptysetAx]), setextAx]), omegaSAx]), omegaIndAx]), c_0_36]), foundationAx]), omega0Ax])]), c_0_37])).
% 0.07/0.26 thf(c_0_39, negated_conjecture, ![X165:$i, X166:$i, X168:$i, X169:$i, X170:$i, X171:$i, X172:$i, X173:$i, X174:$i, X175:$i, X176:$i, X178:$i, X179:$i, X181:$i, X182:$i > $i > $o, X183:$i, X185:$i, X188:$i, X190:$i, X191:$i, X192:$i, X193:$i, X195:$i, X196:$i, X197:$i > $o, X198:$i, X199:$i, X200:$i > $o, X201:$i, X202:$i, X203:$i > $o, X204:$i, X205:$i > $o, X206:$i, X209:$i, X210:$o, X211:$i, X212:$i, X213:$o, X214:$i, X215:$i, X216:$i > $o, X217:$i, X220:$i, X221:$i, X224:$i, X227:$i]:((((~(in @ (esk1_2 @ X165 @ X166) @ X165)|~(in @ (esk1_2 @ X165 @ X166) @ X166)|((X165)=(X166)))&((in @ (esk1_2 @ X165 @ X166) @ X165)|(in @ (esk1_2 @ X165 @ X166) @ X166)|((X165)=(X166))))&(~(in @ X168 @ emptyset)&(((~(in @ X171 @ (setadjoin @ X169 @ X170))|(((X171)=(X169))|(in @ X171 @ X170)))&((((X171)!=(X169))|(in @ X171 @ (setadjoin @ X169 @ X170)))&(~(in @ X171 @ X170)|(in @ X171 @ (setadjoin @ X169 @ X170)))))&(((~(in @ X173 @ (powerset @ X172))|(~(in @ X174 @ X173)|(in @ X174 @ X172)))&(((in @ (esk2_2 @ X175 @ X176) @ X176)|(in @ X176 @ (powerset @ X175)))&(~(in @ (esk2_2 @ X175 @ X176) @ X175)|(in @ X176 @ (powerset @ X175)))))&((setunionAx)&((in @ emptyset @ omega)&((~(in @ X178 @ omega)|(in @ (setadjoin @ X178 @ X178) @ omega))&(((((in @ (esk3_1 @ X179) @ omega)|~(in @ emptyset @ X179)|(~(in @ X181 @ omega)|(in @ X181 @ X179)))&((in @ (esk3_1 @ X179) @ X179)|~(in @ emptyset @ X179)|(~(in @ X181 @ omega)|(in @ X181 @ X179))))&(~(in @ (setadjoin @ (esk3_1 @ X179) @ (esk3_1 @ X179)) @ X179)|~(in @ emptyset @ X179)|(~(in @ X181 @ omega)|(in @ X181 @ X179))))&((((((in @ (esk7_3 @ X182 @ X183 @ X188) @ X183)|~(in @ X188 @ (esk6_2 @ X182 @ X183))|(in @ (esk4_2 @ X182 @ X183) @ X183))&((X182 @ (esk7_3 @ X182 @ X183 @ X188) @ X188)|~(in @ X188 @ (esk6_2 @ X182 @ X183))|(in @ (esk4_2 @ X182 @ X183) @ X183)))&(~(in @ X191 @ X183)|~(X182 @ X191 @ X190)|(in @ X190 @ (esk6_2 @ X182 @ X183))|(in @ (esk4_2 @ X182 @ X183) @ X183)))&(((((in @ (esk7_3 @ X182 @ X183 @ X188) @ X183)|~(in @ X188 @ (esk6_2 @ X182 @ X183))|((X182 @ (esk4_2 @ X182 @ X183) @ (esk5_3 @ X182 @ X183 @ X185))|~(X182 @ (esk4_2 @ X182 @ X183) @ X185)))&((X182 @ (esk7_3 @ X182 @ X183 @ X188) @ X188)|~(in @ X188 @ (esk6_2 @ X182 @ X183))|((X182 @ (esk4_2 @ X182 @ X183) @ (esk5_3 @ X182 @ X183 @ X185))|~(X182 @ (esk4_2 @ X182 @ X183) @ X185))))&(~(in @ X191 @ X183)|~(X182 @ X191 @ X190)|(in @ X190 @ (esk6_2 @ X182 @ X183))|((X182 @ (esk4_2 @ X182 @ X183) @ (esk5_3 @ X182 @ X183 @ X185))|~(X182 @ (esk4_2 @ X182 @ X183) @ X185))))&((((in @ (esk7_3 @ X182 @ X183 @ X188) @ X183)|~(in @ X188 @ (esk6_2 @ X182 @ X183))|(((X185)!=(esk5_3 @ X182 @ X183 @ X185))|~(X182 @ (esk4_2 @ X182 @ X183) @ X185)))&((X182 @ (esk7_3 @ X182 @ X183 @ X188) @ X188)|~(in @ X188 @ (esk6_2 @ X182 @ X183))|(((X185)!=(esk5_3 @ X182 @ X183 @ X185))|~(X182 @ (esk4_2 @ X182 @ X183) @ X185))))&(~(in @ X191 @ X183)|~(X182 @ X191 @ X190)|(in @ X190 @ (esk6_2 @ X182 @ X183))|(((X185)!=(esk5_3 @ X182 @ X183 @ X185))|~(X182 @ (esk4_2 @ X182 @ X183) @ X185))))))&((((in @ (esk8_1 @ X192) @ X192)|~(in @ X193 @ X192))&(~(in @ X195 @ (esk8_1 @ X192))|~(in @ X195 @ X192)|~(in @ X193 @ X192)))&((epred1_0)&((descrp)&((~(in @ X198 @ X196)|(~(X197 @ X198)|(in @ X198 @ (dsetconstr @ X196 @ (^[Z0:$i]:((X197 @ Z0)))))))&((~(in @ X201 @ (dsetconstr @ X199 @ (^[Z0:$i]:((X200 @ Z0)))))|(in @ X201 @ X199))&((~(in @ X204 @ (dsetconstr @ X202 @ (^[Z0:$i]:((X203 @ Z0)))))|(X203 @ X204))&(((((X205 @ (esk10_1 @ X205))|((X205 @ (esk9_2 @ X205 @ X206))|~(X205 @ X206)))&(~(X205 @ X209)|((esk10_1 @ X205)=(X209))|((X205 @ (esk9_2 @ X205 @ X206))|~(X205 @ X206))))&(((X205 @ (esk10_1 @ X205))|(((X206)!=(esk9_2 @ X205 @ X206))|~(X205 @ X206)))&(~(X205 @ X209)|((esk10_1 @ X205)=(X209))|(((X206)!=(esk9_2 @ X205 @ X206))|~(X205 @ X206)))))&((~(in @ X211 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0:$i]:((X210)))))|(X210))&((~(in @ X212 @ emptyset)|(X213))&(~(in @ X214 @ emptyset)&(~(in @ X215 @ emptyset)&((((X216 @ (esk11_2 @ X216 @ X217))|~(X216 @ X217)|(X216 @ (esk12_1 @ X216)))&(((X217)!=(esk11_2 @ X216 @ X217))|~(X216 @ X217)|(X216 @ (esk12_1 @ X216))))&(((((in @ (esk14_2 @ X220 @ X221) @ X221)|((X220)=(X221))|(in @ (esk13_2 @ X220 @ X221) @ X220))&(~(in @ (esk14_2 @ X220 @ X221) @ X220)|((X220)=(X221))|(in @ (esk13_2 @ X220 @ X221) @ X220)))&(((in @ (esk14_2 @ X220 @ X221) @ X221)|((X220)=(X221))|~(in @ (esk13_2 @ X220 @ X221) @ X221))&(~(in @ (esk14_2 @ X220 @ X221) @ X220)|((X220)=(X221))|~(in @ (esk13_2 @ X220 @ X221) @ X221))))&(((in @ (esk15_1 @ X224) @ X224)|((X224)=(emptyset)))&(~(in @ X227 @ esk16_0)&((esk16_0)!=(emptyset))))))))))))))))))))))))))), 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_38])])])])])])).
% 0.07/0.26 thf(c_0_40, negated_conjecture, ![X2:$i]:(~((in @ X2 @ esk16_0))), inference(split_conjunct,[status(thm)],[c_0_39])).
% 0.07/0.26 thf(c_0_41, negated_conjecture, ![X2:$i]:(((in @ (esk15_1 @ X2) @ X2)|((X2)=(emptyset)))), inference(split_conjunct,[status(thm)],[c_0_39])).
% 0.07/0.26 thf(c_0_42, negated_conjecture, ((esk16_0)!=(emptyset)), inference(split_conjunct,[status(thm)],[c_0_39])).
% 0.07/0.26 thf(c_0_43, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41]), c_0_42]), ['proof']).
% 0.07/0.26 % SZS output end CNFRefutation
% 0.07/0.26 % Parsed axioms : 59
% 0.07/0.26 % Removed by relevancy pruning/SinE : 35
% 0.07/0.26 % Initial clauses : 61
% 0.07/0.26 % Removed in clause preprocessing : 0
% 0.07/0.26 % Initial clauses in saturation : 61
% 0.07/0.26 % Processed clauses : 11
% 0.07/0.26 % ...of these trivial : 0
% 0.07/0.26 % ...subsumed : 3
% 0.07/0.26 % ...remaining for further processing : 8
% 0.07/0.26 % Other redundant clauses eliminated : 0
% 0.07/0.26 % Clauses deleted for lack of memory : 0
% 0.07/0.26 % Backward-subsumed : 0
% 0.07/0.26 % Backward-rewritten : 0
% 0.07/0.26 % Generated clauses : 1
% 0.07/0.26 % ...of the previous two non-redundant : 0
% 0.07/0.26 % ...aggressively subsumed : 0
% 0.07/0.26 % Contextual simplify-reflections : 0
% 0.07/0.26 % Paramodulations : 1
% 0.07/0.26 % Factorizations : 0
% 0.07/0.26 % NegExts : 0
% 0.07/0.26 % Equation resolutions : 0
% 0.07/0.26 % Disequality decompositions : 0
% 0.07/0.26 % Total rewrite steps : 0
% 0.07/0.26 % ...of those cached : 0
% 0.07/0.26 % Propositional unsat checks : 0
% 0.07/0.26 % Propositional check models : 0
% 0.07/0.26 % Propositional check unsatisfiable : 0
% 0.07/0.26 % Propositional clauses : 0
% 0.07/0.26 % Propositional clauses after purity: 0
% 0.07/0.26 % Propositional unsat core size : 0
% 0.07/0.26 % Propositional preprocessing time : 0.000
% 0.07/0.26 % Propositional encoding time : 0.000
% 0.07/0.26 % Propositional solver time : 0.000
% 0.07/0.26 % Success case prop preproc time : 0.000
% 0.07/0.26 % Success case prop encoding time : 0.000
% 0.07/0.26 % Success case prop solver time : 0.000
% 0.07/0.26 % Current number of processed clauses : 8
% 0.07/0.26 % Positive orientable unit clauses : 4
% 0.07/0.26 % Positive unorientable unit clauses: 0
% 0.07/0.26 % Negative unit clauses : 3
% 0.07/0.26 % Non-unit-clauses : 1
% 0.07/0.26 % Current number of unprocessed clauses: 50
% 0.07/0.26 % ...number of literals in the above : 183
% 0.07/0.26 % Current number of archived formulas : 0
% 0.07/0.26 % Current number of archived clauses : 0
% 0.07/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.26 % Non-unit clause-clause subsumptions : 0
% 0.07/0.26 % Unit Clause-clause subsumption calls : 1
% 0.07/0.26 % Rewrite failures with RHS unbound : 0
% 0.07/0.26 % BW rewrite match attempts : 0
% 0.07/0.26 % BW rewrite match successes : 0
% 0.07/0.26 % Condensation attempts : 0
% 0.07/0.26 % Condensation successes : 0
% 0.07/0.26 % Termbank termtop insertions : 6223
% 0.07/0.26 % Search garbage collected termcells : 2317
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.008 s
% 0.07/0.26 % System time : 0.003 s
% 0.07/0.26 % Total time : 0.011 s
% 0.07/0.26 % Maximum resident set size: 4208 pages
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.011 s
% 0.07/0.26 % System time : 0.007 s
% 0.07/0.26 % Total time : 0.018 s
% 0.07/0.26 % Maximum resident set size: 4864 pages
% 0.07/0.26 % E exiting
%------------------------------------------------------------------------------