%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP138^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:04:28 AM UTC 2026
% Result : Theorem 0.57s 0.43s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP138^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.18 % Computer : n016.cluster.edu
% 0.13/0.18 % Model : x86_64 x86_64
% 0.13/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.18 % Memory : 8046.5625MB
% 0.13/0.18 % OS : Linux 6.8.0-71-generic
% 0.13/0.18 % CPULimit : 300
% 0.13/0.18 % WCLimit : 300
% 0.13/0.18 % DateTime : Tue Sep 29 20:04:05 UTC 2026
% 0.13/0.18 % CPUTime :
% 0.13/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.22 Running higher-order theorem proving
% 0.13/0.28 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.M2TYhtiS62/E---3.1_837447.p
% 0.57/0.43 % Version: 3.5.1-ho
% 0.57/0.43 % Preprocessing class: HSLSSMSMSSLCHSA.
% 0.57/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.43 % Starting lpo5_fix with 1500s (5) cores
% 0.57/0.43 % Starting lpo8_s with 300s (1) cores
% 0.57/0.43 % Starting sh4 with 300s (1) cores
% 0.57/0.43 % Starting sh2lt with 300s (1) cores
% 0.57/0.43 % lpo5_fix with pid 837476 completed with status 0
% 0.57/0.43 % Result found by lpo5_fix
% 0.57/0.43 % Preprocessing class: HSLSSMSMSSLCHSA.
% 0.57/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.43 % Starting lpo5_fix with 1500s (5) cores
% 0.57/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.57/0.43 % No SInE strategy applied
% 0.57/0.43 % Search class: HGHSM-FSLM32-MHSFFSBN
% 0.57/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.57/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.57/0.43 % Starting lpo5_fix with 151s (1) cores
% 0.57/0.43 % Starting full_lambda_9 with 136s (1) cores
% 0.57/0.43 % Starting ehoh_best with 136s (1) cores
% 0.57/0.43 % Starting post_as_ho6 with 136s (1) cores
% 0.57/0.43 % lpo5_fix with pid 837496 completed with status 0
% 0.57/0.43 % Result found by lpo5_fix
% 0.57/0.43 % Preprocessing class: HSLSSMSMSSLCHSA.
% 0.57/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.43 % Starting lpo5_fix with 1500s (5) cores
% 0.57/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.57/0.43 % No SInE strategy applied
% 0.57/0.43 % Search class: HGHSM-FSLM32-MHSFFSBN
% 0.57/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.57/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.57/0.43 % Starting lpo5_fix with 151s (1) cores
% 0.57/0.43 % Preprocessing time : 0.016 s
% 0.57/0.43
% 0.57/0.43 % Proof found!
% 0.57/0.43 % SZS status Theorem
% 0.57/0.43 % SZS output start CNFRefutation
% 0.57/0.43 thf(decl_sort1, type, set_list_char: $tType).
% 0.57/0.43 thf(decl_sort2, type, set_Pa1764573435lle_tv: $tType).
% 0.57/0.43 thf(decl_sort3, type, list_char: $tType).
% 0.57/0.43 thf(decl_sort4, type, paraco1605129243lle_tv: $tType).
% 0.57/0.43 thf(decl_sort5, type, set_nat: $tType).
% 0.57/0.43 thf(decl_sort6, type, nat: $tType).
% 0.57/0.43 thf(decl_sort7, type, paraco1604210848lle_fm: $tType).
% 0.57/0.43 thf(decl_33, type, ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o).
% 0.57/0.43 thf(decl_43, type, top_to748628679t_char: set_list_char).
% 0.57/0.43 thf(decl_44, type, top_top_set_nat: set_nat).
% 0.57/0.43 thf(decl_45, type, top_to1057771083lle_tv: set_Pa1764573435lle_tv).
% 0.57/0.43 thf(decl_48, type, paraco1933902578domain: set_nat > set_Pa1764573435lle_tv).
% 0.57/0.43 thf(decl_49, type, paraco1325918602e_eval: (list_char > paraco1605129243lle_tv) > paraco1604210848lle_fm > paraco1605129243lle_tv).
% 0.57/0.43 thf(decl_56, type, paraco1344940915le_Det: $o > paraco1605129243lle_tv).
% 0.57/0.43 thf(decl_62, type, collect_nat: (nat > $o) > set_nat).
% 0.57/0.43 thf(decl_63, type, collec1111687558lle_tv: (paraco1605129243lle_tv > $o) > set_Pa1764573435lle_tv).
% 0.57/0.43 thf(decl_73, type, image_1187894195lle_tv: (list_char > paraco1605129243lle_tv) > set_list_char > set_Pa1764573435lle_tv).
% 0.57/0.43 thf(decl_90, type, p: paraco1604210848lle_fm).
% 0.57/0.43 thf(decl_284, type, esk158_0: list_char > paraco1605129243lle_tv).
% 0.57/0.43 thf(decl_285, type, esk159_0: list_char > paraco1605129243lle_tv).
% 0.57/0.43 thf(decl_286, type, epred37_0: nat > $o).
% 0.57/0.43 thf(decl_287, type, epred38_0: paraco1605129243lle_tv > $o).
% 0.57/0.43 thf(conj_0, conjecture, (![X7:list_char > paraco1605129243lle_tv]:(((paraco1325918602e_eval @ X7 @ p)=(paraco1344940915le_Det @ (($true)))))<~>~(![X7:list_char > paraco1605129243lle_tv]:(((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X7 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[X1:nat]:(($true))))))=>((paraco1325918602e_eval @ X7 @ p)=(paraco1344940915le_Det @ (($true)))))))), file('/export/starexec/sandbox2/tmp/tmp.M2TYhtiS62/E---3.1_837447.p', conj_0)).
% 0.57/0.43 thf(fact_0_universal__domain, axiom, ((paraco1933902578domain @ (collect_nat @ (^[X1:nat]:(($true)))))=(collec1111687558lle_tv @ (^[X2:paraco1605129243lle_tv]:(($true))))), file('/export/starexec/sandbox2/tmp/tmp.M2TYhtiS62/E---3.1_837447.p', fact_0_universal__domain)).
% 0.57/0.43 thf(fact_202_UNIV__def, axiom, ((top_top_set_nat)=(collect_nat @ (^[X532:nat]:(($true))))), file('/export/starexec/sandbox2/tmp/tmp.M2TYhtiS62/E---3.1_837447.p', fact_202_UNIV__def)).
% 0.57/0.43 thf(fact_203_UNIV__def, axiom, ((top_to1057771083lle_tv)=(collec1111687558lle_tv @ (^[X2:paraco1605129243lle_tv]:(($true))))), file('/export/starexec/sandbox2/tmp/tmp.M2TYhtiS62/E---3.1_837447.p', fact_203_UNIV__def)).
% 0.57/0.43 thf(fact_213_top__greatest, axiom, ![X123:set_Pa1764573435lle_tv]:((ord_le241064091lle_tv @ X123 @ top_to1057771083lle_tv)), file('/export/starexec/sandbox2/tmp/tmp.M2TYhtiS62/E---3.1_837447.p', fact_213_top__greatest)).
% 0.57/0.43 thf(c_0_5, negated_conjecture, ~((![X7:list_char > paraco1605129243lle_tv]:(((paraco1325918602e_eval @ X7 @ p)=(paraco1344940915le_Det @ (($true)))))<~>~(![X7:list_char > paraco1605129243lle_tv]:(((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X7 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[X1:nat]:(($true))))))=>((paraco1325918602e_eval @ X7 @ p)=(paraco1344940915le_Det @ (($true))))))))), inference(assume_negation,[status(cth)],[conj_0])).
% 0.57/0.43 thf(c_0_6, negated_conjecture, ~(~((![X7:list_char > paraco1605129243lle_tv]:(((paraco1325918602e_eval @ X7 @ p)=(paraco1344940915le_Det @ $true)))<=>~(![X7:list_char > paraco1605129243lle_tv]:(((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X7 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Z0:nat]:($true)))))=>((paraco1325918602e_eval @ X7 @ p)=(paraco1344940915le_Det @ $true)))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5])])).
% 0.57/0.43 thf(c_0_7, plain, ((paraco1933902578domain @ (collect_nat @ (^[Z0:nat]:($true))))=(collec1111687558lle_tv @ (^[Z0:paraco1605129243lle_tv]:($true)))), inference(fof_simplification,[status(thm)],[fact_0_universal__domain])).
% 0.57/0.43 thf(c_0_8, plain, ![X3133:paraco1605129243lle_tv]:(((epred38_0 @ X3133)<=>($true))), introduced(definition)).
% 0.57/0.43 thf(c_0_9, plain, ![X3132:nat]:(((epred37_0 @ X3132)<=>($true))), introduced(definition)).
% 0.57/0.43 thf(c_0_10, plain, ((top_top_set_nat)=(collect_nat @ (^[Z0:nat]:($true)))), inference(fof_simplification,[status(thm)],[fact_202_UNIV__def])).
% 0.57/0.43 thf(c_0_11, negated_conjecture, ![X3130:list_char > paraco1605129243lle_tv, X3131:list_char > paraco1605129243lle_tv]:(((((ord_le241064091lle_tv @ (image_1187894195lle_tv @ esk159_0 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Z0:nat]:($true)))))|((paraco1325918602e_eval @ esk158_0 @ p)!=(paraco1344940915le_Det @ $true)))&(((paraco1325918602e_eval @ esk159_0 @ p)!=(paraco1344940915le_Det @ $true))|((paraco1325918602e_eval @ esk158_0 @ p)!=(paraco1344940915le_Det @ $true))))&(~(ord_le241064091lle_tv @ (image_1187894195lle_tv @ X3130 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ (^[Z0:nat]:($true)))))|((paraco1325918602e_eval @ X3130 @ p)=(paraco1344940915le_Det @ $true))|((paraco1325918602e_eval @ X3131 @ p)=(paraco1344940915le_Det @ $true))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])])).
% 0.57/0.43 thf(c_0_12, plain, ((paraco1933902578domain @ (collect_nat @ epred37_0))=(collec1111687558lle_tv @ epred38_0)), inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7]), c_0_8]), c_0_9])).
% 0.57/0.43 thf(c_0_13, plain, ((top_top_set_nat)=(collect_nat @ epred37_0)), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_10]), c_0_9])).
% 0.57/0.43 thf(c_0_14, plain, ((top_to1057771083lle_tv)=(collec1111687558lle_tv @ (^[Z0:paraco1605129243lle_tv]:($true)))), inference(fof_simplification,[status(thm)],[fact_203_UNIV__def])).
% 0.57/0.43 thf(c_0_15, plain, ![X2589:set_Pa1764573435lle_tv]:((ord_le241064091lle_tv @ X2589 @ top_to1057771083lle_tv)), inference(variable_rename,[status(thm)],[fact_213_top__greatest])).
% 0.57/0.43 thf(c_0_16, negated_conjecture, ![X50:list_char > paraco1605129243lle_tv, X7:list_char > paraco1605129243lle_tv]:((((paraco1325918602e_eval @ X7 @ p)=(paraco1344940915le_Det @ (($true))))|((paraco1325918602e_eval @ X50 @ p)=(paraco1344940915le_Det @ (($true))))|~((((ord_le241064091lle_tv @ (image_1187894195lle_tv @ X7 @ top_to748628679t_char) @ (paraco1933902578domain @ (collect_nat @ epred37_0))))=(($true)))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_11]), c_0_9])).
% 0.57/0.43 thf(c_0_17, plain, ((paraco1933902578domain @ top_top_set_nat)=(collec1111687558lle_tv @ epred38_0)), inference(rw,[status(thm)],[c_0_12, c_0_13])).
% 0.57/0.43 thf(c_0_18, plain, ((top_to1057771083lle_tv)=(collec1111687558lle_tv @ epred38_0)), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_14]), c_0_8])).
% 0.57/0.43 thf(c_0_19, plain, ![X21:set_Pa1764573435lle_tv]:((ord_le241064091lle_tv @ X21 @ top_to1057771083lle_tv)), inference(split_conjunct,[status(thm)],[c_0_15])).
% 0.57/0.43 thf(c_0_20, negated_conjecture, (((paraco1325918602e_eval @ esk159_0 @ p)!=(paraco1344940915le_Det @ (($true))))|((paraco1325918602e_eval @ esk158_0 @ p)!=(paraco1344940915le_Det @ (($true))))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 0.57/0.43 thf(c_0_21, negated_conjecture, ![X7:list_char > paraco1605129243lle_tv]:(((paraco1325918602e_eval @ X7 @ p)=(paraco1344940915le_Det @ (($true))))), inference(condense,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[c_0_16]), c_0_13]), c_0_17]), c_0_18]), c_0_19])])])).
% 0.57/0.43 thf(c_0_22, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21]), c_0_21])]), ['proof']).
% 0.57/0.43 % SZS output end CNFRefutation
% 0.57/0.43 % Parsed axioms : 435
% 0.57/0.43 % Removed by relevancy pruning/SinE : 0
% 0.57/0.43 % Initial clauses : 955
% 0.57/0.43 % Removed in clause preprocessing : 135
% 0.57/0.43 % Initial clauses in saturation : 820
% 0.57/0.43 % Processed clauses : 111
% 0.57/0.43 % ...of these trivial : 15
% 0.57/0.43 % ...subsumed : 4
% 0.57/0.43 % ...remaining for further processing : 92
% 0.57/0.43 % Other redundant clauses eliminated : 22
% 0.57/0.43 % Clauses deleted for lack of memory : 0
% 0.57/0.43 % Backward-subsumed : 0
% 0.57/0.43 % Backward-rewritten : 7
% 0.57/0.43 % Generated clauses : 44
% 0.57/0.43 % ...of the previous two non-redundant : 19
% 0.57/0.43 % ...aggressively subsumed : 0
% 0.57/0.43 % Contextual simplify-reflections : 0
% 0.57/0.43 % Paramodulations : 5
% 0.57/0.43 % Factorizations : 0
% 0.57/0.43 % NegExts : 0
% 0.57/0.43 % Equation resolutions : 24
% 0.57/0.43 % Disequality decompositions : 0
% 0.57/0.43 % Total rewrite steps : 55
% 0.57/0.43 % ...of those cached : 32
% 0.57/0.43 % Propositional unsat checks : 0
% 0.57/0.43 % Propositional check models : 0
% 0.57/0.43 % Propositional check unsatisfiable : 0
% 0.57/0.43 % Propositional clauses : 0
% 0.57/0.43 % Propositional clauses after purity: 0
% 0.57/0.43 % Propositional unsat core size : 0
% 0.57/0.43 % Propositional preprocessing time : 0.000
% 0.57/0.43 % Propositional encoding time : 0.000
% 0.57/0.43 % Propositional solver time : 0.000
% 0.57/0.43 % Success case prop preproc time : 0.000
% 0.57/0.43 % Success case prop encoding time : 0.000
% 0.57/0.43 % Success case prop solver time : 0.000
% 0.57/0.43 % Current number of processed clauses : 63
% 0.57/0.43 % Positive orientable unit clauses : 32
% 0.57/0.43 % Positive unorientable unit clauses: 0
% 0.57/0.43 % Negative unit clauses : 17
% 0.57/0.43 % Non-unit-clauses : 14
% 0.57/0.43 % Current number of unprocessed clauses: 728
% 0.57/0.43 % ...number of literals in the above : 2150
% 0.57/0.43 % Current number of archived formulas : 0
% 0.57/0.43 % Current number of archived clauses : 7
% 0.57/0.43 % Clause-clause subsumption calls (NU) : 15
% 0.57/0.43 % Rec. Clause-clause subsumption calls : 12
% 0.57/0.43 % Non-unit clause-clause subsumptions : 3
% 0.57/0.43 % Unit Clause-clause subsumption calls : 49
% 0.57/0.43 % Rewrite failures with RHS unbound : 0
% 0.57/0.43 % BW rewrite match attempts : 12
% 0.57/0.43 % BW rewrite match successes : 8
% 0.57/0.43 % Condensation attempts : 111
% 0.57/0.43 % Condensation successes : 1
% 0.57/0.43 % Termbank termtop insertions : 80932
% 0.57/0.43 % Search garbage collected termcells : 22113
% 0.57/0.43
% 0.57/0.43 % -------------------------------------------------
% 0.57/0.43 % User time : 0.079 s
% 0.57/0.43 % System time : 0.016 s
% 0.57/0.43 % Total time : 0.095 s
% 0.57/0.43 % Maximum resident set size: 8840 pages
% 0.57/0.43
% 0.57/0.43 % -------------------------------------------------
% 0.57/0.43 % User time : 0.168 s
% 0.57/0.43 % System time : 0.063 s
% 0.57/0.43 % Total time : 0.231 s
% 0.57/0.43 % Maximum resident set size: 5888 pages
% 0.57/0.43 % E exiting
%------------------------------------------------------------------------------