%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV428^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:35:30 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV428^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n010.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 15:47:18 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.CfOPzEDH0z/E---3.1_3027311.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % partial match(1): HSSSSMSSSLSNHHA
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSCHHA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.25 % Starting sh3l with 300s (1) cores
% 0.07/0.25 % Starting lpo6_lambda_fix with 300s (1) cores
% 0.07/0.25 % Starting full_lambda_8 with 300s (1) cores
% 0.07/0.25 % new_ho_10_cnf2 with pid 3027324 completed with status 0
% 0.07/0.25 % Result found by new_ho_10_cnf2
% 0.07/0.25 % partial match(1): HSSSSMSSSLSNHHA
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSCHHA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HHHNF-FFSF11-SHHFMMBC
% 0.07/0.25 % partial match(2): HHHNF-FFSF11-SHSSMMBC
% 0.07/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.25 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.07/0.25 % Starting sh5l with 169s (1) cores
% 0.07/0.25 % Starting new_bool_1 with 169s (1) cores
% 0.07/0.25 % Starting new_bool_2 with 169s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 3027329 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % partial match(1): HSSSSMSSSLSNHHA
% 0.07/0.25 % Preprocessing class: HSSSSMSSSLSCHHA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HHHNF-FFSF11-SHHFMMBC
% 0.07/0.25 % partial match(2): HHHNF-FFSF11-SHSSMMBC
% 0.07/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% 0.07/0.25 thf(decl_23, type, eps: ($i > $o) > $i).
% 0.07/0.25 thf(decl_24, type, epsio: (($i > $o) > $o) > $i > $o).
% 0.07/0.25 thf(decl_25, type, setunion: (($i > $o) > $o) > $i > $o).
% 0.07/0.25 thf(decl_26, type, choosenonempty: (($i > $o) > $o) > $i > $o).
% 0.07/0.25 thf(decl_27, type, c: ($i > $o) > $o).
% 0.07/0.25 thf(decl_28, type, a: $i).
% 0.07/0.25 thf(decl_29, type, epred1_0: $i > $o).
% 0.07/0.25 thf(decl_30, type, epred2_0: ($i > $o) > $o).
% 0.07/0.25 thf(setuniond, axiom, ((setunion)=(^[X5:($i > $o) > $o, X2:$i]:(?[X6:$i > $o]:((((X5 @ X6))&((X6 @ X2))))))), file('/export/starexec/sandbox/tmp/tmp.CfOPzEDH0z/E---3.1_3027311.p', setuniond)).
% 0.07/0.25 thf(ca, axiom, (setunion @ c @ a), file('/export/starexec/sandbox/tmp/tmp.CfOPzEDH0z/E---3.1_3027311.p', ca)).
% 0.07/0.25 thf(conj, conjecture, ((c @ (choosenonempty @ c))&?[X2:$i]:((choosenonempty @ c @ X2))), file('/export/starexec/sandbox/tmp/tmp.CfOPzEDH0z/E---3.1_3027311.p', conj)).
% 0.07/0.25 thf(choosenonemptyd, axiom, ((choosenonempty)=(^[X5:($i > $o) > $o]:(epsio @ (^[X6:$i > $o]:((((X5 @ X6))&((X6 @ (eps @ X6))))))))), file('/export/starexec/sandbox/tmp/tmp.CfOPzEDH0z/E---3.1_3027311.p', choosenonemptyd)).
% 0.07/0.25 thf(choiceax, axiom, ![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(X1 @ (eps @ X1)))), file('/export/starexec/sandbox/tmp/tmp.CfOPzEDH0z/E---3.1_3027311.p', choiceax)).
% 0.07/0.25 thf(choiceaxio, axiom, ![X3:($i > $o) > $o]:((?[X4:$i > $o]:((X3 @ X4))=>(X3 @ (epsio @ X3)))), file('/export/starexec/sandbox/tmp/tmp.CfOPzEDH0z/E---3.1_3027311.p', choiceaxio)).
% 0.07/0.25 thf(c_0_6, plain, ((setunion)=(^[Z0:($i > $o) > $o, Z1:$i]:(?[X6:$i > $o]:((((Z0 @ X6))&((X6 @ Z1))))))), inference(fof_simplification,[status(thm)],[setuniond])).
% 0.07/0.25 thf(c_0_7, plain, ?[X12:$i > $o]:(((c @ X12)&(X12 @ a))), inference(apply_def,[status(thm)],[ca, c_0_6])).
% 0.07/0.25 thf(c_0_8, negated_conjecture, ~(((c @ (choosenonempty @ c))&?[X2:$i]:((choosenonempty @ c @ X2)))), inference(assume_negation,[status(cth)],[conj])).
% 0.07/0.25 thf(c_0_9, plain, ((choosenonempty)=(^[Z0:($i > $o) > $o]:(epsio @ (^[Z1:$i > $o]:((((Z0 @ Z1))&((Z1 @ (eps @ Z1))))))))), inference(fof_simplification,[status(thm)],[choosenonemptyd])).
% 0.07/0.25 thf(c_0_10, plain, ![X13:$i > $o, X14:$i]:((~(X13 @ X14)|(X13 @ (eps @ X13)))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceax])])])])).
% 0.07/0.25 thf(c_0_11, plain, ((c @ epred1_0)&(epred1_0 @ a)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])).
% 0.07/0.25 thf(c_0_12, negated_conjecture, ~(((c @ (epsio @ (^[Z0:$i > $o]:((((c @ Z0))&(Z0 @ (eps @ Z0)))))))&?[X2:$i]:((epsio @ (^[Z0:$i > $o]:((((c @ Z0))&(Z0 @ (eps @ Z0))))) @ X2)))), inference(apply_def,[status(thm)],[c_0_8, c_0_9])).
% 0.07/0.25 thf(c_0_13, plain, ![X21:$i > $o]:(((((c @ X21)|~(epred2_0 @ X21))&((X21 @ (eps @ X21))|~(epred2_0 @ X21)))&(~(c @ X21)|~(X21 @ (eps @ X21))|(epred2_0 @ X21)))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])).
% 0.07/0.25 thf(c_0_14, plain, ![X1:$i > $o, X2:$i]:(((X1 @ (eps @ X1))|~((X1 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_10])).
% 0.07/0.25 thf(c_0_15, plain, (epred1_0 @ a), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.07/0.25 thf(c_0_16, negated_conjecture, ![X18:$i]:((~(c @ (epsio @ (^[Z0:$i > $o]:((((c @ Z0))&(Z0 @ (eps @ Z0)))))))|~(epsio @ (^[Z0:$i > $o]:((((c @ Z0))&(Z0 @ (eps @ Z0))))) @ X18))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])).
% 0.07/0.25 thf(c_0_17, plain, ![X19:$i > $o]:(((epred2_0 @ X19)<=>((c @ X19)&(X19 @ (eps @ X19))))), introduced(definition)).
% 0.07/0.25 thf(c_0_18, plain, ![X15:($i > $o) > $o, X16:$i > $o]:((~(X15 @ X16)|(X15 @ (epsio @ X15)))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceaxio])])])])).
% 0.07/0.25 thf(c_0_19, plain, ![X1:$i > $o]:(((epred2_0 @ X1)|~((c @ X1))|~((X1 @ (eps @ X1))))), inference(split_conjunct,[status(thm)],[c_0_13])).
% 0.07/0.25 thf(c_0_20, plain, (epred1_0 @ (eps @ epred1_0)), inference(spm,[status(thm)],[c_0_14, c_0_15])).
% 0.07/0.25 thf(c_0_21, plain, (c @ epred1_0), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.07/0.25 thf(c_0_22, negated_conjecture, ![X2:$i]:((~((((c @ (epsio @ epred2_0)))=(($true))))|~((((epsio @ epred2_0 @ X2))=(($true)))))), inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_16]), c_0_17]), c_0_17])).
% 0.07/0.25 thf(c_0_23, plain, ![X3:($i > $o) > $o, X1:$i > $o]:(((X3 @ (epsio @ X3))|~((X3 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_18])).
% 0.07/0.25 thf(c_0_24, plain, (epred2_0 @ epred1_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_20]), c_0_21])])).
% 0.07/0.25 thf(c_0_25, negated_conjecture, ![X2:$i]:((~((c @ (epsio @ epred2_0)))|~((epsio @ epred2_0 @ X2)))), inference(cn,[status(thm)],[c_0_22])).
% 0.07/0.25 thf(c_0_26, plain, ![X1:$i > $o]:(((c @ X1)|~((epred2_0 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_13])).
% 0.07/0.25 thf(c_0_27, plain, (epred2_0 @ (epsio @ epred2_0)), inference(spm,[status(thm)],[c_0_23, c_0_24])).
% 0.07/0.25 thf(c_0_28, plain, ![X2:$i]:(~((epsio @ epred2_0 @ X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26]), c_0_27])])).
% 0.07/0.25 thf(c_0_29, plain, ![X1:$i > $o]:(((X1 @ (eps @ X1))|~((epred2_0 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_13])).
% 0.07/0.25 thf(c_0_30, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_27])]), ['proof']).
% 0.07/0.25 % SZS output end CNFRefutation
% 0.07/0.25 % Parsed axioms : 12
% 0.07/0.25 % Removed by relevancy pruning/SinE : 0
% 0.07/0.25 % Initial clauses : 14
% 0.07/0.25 % Removed in clause preprocessing : 6
% 0.07/0.25 % Initial clauses in saturation : 8
% 0.07/0.25 % Processed clauses : 15
% 0.07/0.25 % ...of these trivial : 1
% 0.07/0.25 % ...subsumed : 1
% 0.07/0.25 % ...remaining for further processing : 13
% 0.07/0.25 % Other redundant clauses eliminated : 0
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 1
% 0.07/0.25 % Backward-rewritten : 0
% 0.07/0.25 % Generated clauses : 12
% 0.07/0.25 % ...of the previous two non-redundant : 7
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 12
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 0
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 7
% 0.07/0.25 % ...of those cached : 3
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 12
% 0.07/0.25 % Positive orientable unit clauses : 6
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 1
% 0.07/0.25 % Non-unit-clauses : 5
% 0.07/0.25 % Current number of unprocessed clauses: 0
% 0.07/0.25 % ...number of literals in the above : 0
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 1
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 7
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 7
% 0.07/0.25 % Non-unit clause-clause subsumptions : 1
% 0.07/0.25 % Unit Clause-clause subsumption calls : 1
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 0
% 0.07/0.25 % BW rewrite match successes : 0
% 0.07/0.25 % Condensation attempts : 0
% 0.07/0.25 % Condensation successes : 0
% 0.07/0.25 % Termbank termtop insertions : 983
% 0.07/0.25 % Search garbage collected termcells : 168
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.004 s
% 0.07/0.25 % System time : 0.002 s
% 0.07/0.25 % Total time : 0.006 s
% 0.07/0.25 % Maximum resident set size: 3640 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.010 s
% 0.07/0.25 % System time : 0.011 s
% 0.07/0.25 % Total time : 0.021 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------