%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT171^3 : TPTP v9.3.1. Released v5.3.0.
% 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 08:21:46 AM UTC 2026
% Result : Theorem 2.61s 1.22s
% Output : CNFRefutation 2.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SCT171^3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 % Computer : n016.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Tue Sep 29 13:39:19 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.33 Running higher-order theorem proving
% 0.42/0.59 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.ApMYCEVPkx/E---3.1_353464.p
% 2.61/1.22 % Version: 3.5.1-ho
% 2.61/1.22 % Preprocessing class: HMLMSMSMSSLCHSA.
% 2.61/1.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.61/1.22 % Starting new_ho_10 with 1500s (5) cores
% 2.61/1.22 % Starting sh5l with 300s (1) cores
% 2.61/1.22 % Starting new_bool_1 with 300s (1) cores
% 2.61/1.22 % Starting new_bool_2 with 300s (1) cores
% 2.61/1.22 % new_ho_10 with pid 353487 completed with status 0
% 2.61/1.22 % Result found by new_ho_10
% 2.61/1.22 % Preprocessing class: HMLMSMSMSSLCHSA.
% 2.61/1.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.61/1.22 % Starting new_ho_10 with 1500s (5) cores
% 2.61/1.22 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.61/1.22 % No SInE strategy applied
% 2.61/1.22 % Search class: HGHSM-SMLM33-MHSFFSBN
% 2.61/1.22 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.61/1.22 % Starting SubtermCWHack with 136s (1) cores
% 2.61/1.22 % Starting new_ho_10 with 151s (1) cores
% 2.61/1.22 % Starting pre_casc_5 with 184s (1) cores
% 2.61/1.22 % Starting lpo5_rw_fix with 136s (1) cores
% 2.61/1.22 % Starting ho_unfolding_6 with 136s (1) cores
% 2.61/1.22 % new_ho_10 with pid 353501 completed with status 0
% 2.61/1.22 % Result found by new_ho_10
% 2.61/1.22 % Preprocessing class: HMLMSMSMSSLCHSA.
% 2.61/1.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.61/1.22 % Starting new_ho_10 with 1500s (5) cores
% 2.61/1.22 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.61/1.22 % No SInE strategy applied
% 2.61/1.22 % Search class: HGHSM-SMLM33-MHSFFSBN
% 2.61/1.22 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.61/1.22 % Starting SubtermCWHack with 136s (1) cores
% 2.61/1.22 % Starting new_ho_10 with 151s (1) cores
% 2.61/1.22 % Preprocessing time : 0.083 s
% 2.61/1.22 % Presaturation interreduction done
% 2.61/1.22
% 2.61/1.22 % Proof found!
% 2.61/1.22 % SZS status Theorem
% 2.61/1.22 % SZS output start CNFRefutation
% 2.61/1.22 thf(decl_sort1, type, produc1572197287le_alt: $tType).
% 2.61/1.22 thf(decl_sort2, type, arrow_1196572341e_indi: $tType).
% 2.61/1.22 thf(decl_sort3, type, arrow_1389031998le_alt: $tType).
% 2.61/1.22 thf(decl_sort4, type, nat: $tType).
% 2.61/1.22 thf(decl_27, type, arrow_556571452_above: (produc1572197287le_alt > $o) > arrow_1389031998le_alt > arrow_1389031998le_alt > produc1572197287le_alt > $o).
% 2.61/1.22 thf(decl_30, type, arrow_1821416136_mkbot: (produc1572197287le_alt > $o) > arrow_1389031998le_alt > produc1572197287le_alt > $o).
% 2.61/1.22 thf(decl_31, type, arrow_1970123222_mktop: (produc1572197287le_alt > $o) > arrow_1389031998le_alt > produc1572197287le_alt > $o).
% 2.61/1.22 thf(decl_79, type, if_Pro278423000_alt_o: $o > (produc1572197287le_alt > $o) > (produc1572197287le_alt > $o) > produc1572197287le_alt > $o).
% 2.61/1.22 thf(decl_94, type, ord_less_nat: nat > nat > $o).
% 2.61/1.22 thf(decl_117, type, produc897867031le_alt: arrow_1389031998le_alt > arrow_1389031998le_alt > produc1572197287le_alt).
% 2.61/1.22 thf(decl_168, type, member285112084le_alt: produc1572197287le_alt > (produc1572197287le_alt > $o) > $o).
% 2.61/1.22 thf(decl_169, type, f: (arrow_1196572341e_indi > produc1572197287le_alt > $o) > produc1572197287le_alt > $o).
% 2.61/1.22 thf(decl_172, type, p: arrow_1196572341e_indi > produc1572197287le_alt > $o).
% 2.61/1.22 thf(decl_175, type, c: arrow_1389031998le_alt).
% 2.61/1.22 thf(decl_176, type, d: arrow_1389031998le_alt).
% 2.61/1.22 thf(decl_177, type, e: arrow_1389031998le_alt).
% 2.61/1.22 thf(decl_178, type, h: arrow_1196572341e_indi > nat).
% 2.61/1.22 thf(decl_179, type, n: nat).
% 2.61/1.22 thf(decl_730, type, epred306_0: arrow_1196572341e_indi > produc1572197287le_alt > $o).
% 2.61/1.22 thf(conj_0, conjecture, (member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ p)), file('/export/starexec/sandbox2/tmp/tmp.ApMYCEVPkx/E---3.1_353464.p', conj_0)).
% 2.61/1.22 thf(fact_14_PW, axiom, ((member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ p))<=>(member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ (^[X11:arrow_1196572341e_indi]:(if_Pro278423000_alt_o @ ((ord_less_nat @ (h @ X11) @ n)) @ (arrow_1970123222_mktop @ (p @ X11) @ e) @ (if_Pro278423000_alt_o @ (((h @ X11)=(n))) @ (arrow_556571452_above @ (p @ X11) @ c @ e) @ (arrow_1821416136_mkbot @ (p @ X11) @ e))))))), file('/export/starexec/sandbox2/tmp/tmp.ApMYCEVPkx/E---3.1_353464.p', fact_14_PW)).
% 2.61/1.22 thf(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, axiom, (member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ (^[X11:arrow_1196572341e_indi]:(if_Pro278423000_alt_o @ ((ord_less_nat @ (h @ X11) @ n)) @ (arrow_1970123222_mktop @ (p @ X11) @ e) @ (if_Pro278423000_alt_o @ (((h @ X11)=(n))) @ (arrow_556571452_above @ (p @ X11) @ c @ e) @ (arrow_1821416136_mkbot @ (p @ X11) @ e)))))), file('/export/starexec/sandbox2/tmp/tmp.ApMYCEVPkx/E---3.1_353464.p', fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto)).
% 2.61/1.22 thf(c_0_3, negated_conjecture, ~((member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ p))), inference(assume_negation,[status(cth)],[conj_0])).
% 2.61/1.22 thf(c_0_4, plain, ((member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ p))<=>(member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ (^[Z0:arrow_1196572341e_indi]:(if_Pro278423000_alt_o @ ((ord_less_nat @ (h @ Z0) @ n)) @ (arrow_1970123222_mktop @ (p @ Z0) @ e) @ (if_Pro278423000_alt_o @ (((h @ Z0)=(n))) @ (arrow_556571452_above @ (p @ Z0) @ c @ e) @ (arrow_1821416136_mkbot @ (p @ Z0) @ e))))))), inference(fof_simplification,[status(thm)],[fact_14_PW])).
% 2.61/1.22 thf(c_0_5, negated_conjecture, ~(member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ p)), inference(fof_simplification,[status(thm)],[c_0_3])).
% 2.61/1.22 thf(c_0_6, plain, ((~(member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ p))|(member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ (^[Z0:arrow_1196572341e_indi]:(if_Pro278423000_alt_o @ ((ord_less_nat @ (h @ Z0) @ n)) @ (arrow_1970123222_mktop @ (p @ Z0) @ e) @ (if_Pro278423000_alt_o @ (((h @ Z0)=(n))) @ (arrow_556571452_above @ (p @ Z0) @ c @ e) @ (arrow_1821416136_mkbot @ (p @ Z0) @ e)))))))&(~(member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ (^[Z0:arrow_1196572341e_indi]:(if_Pro278423000_alt_o @ ((ord_less_nat @ (h @ Z0) @ n)) @ (arrow_1970123222_mktop @ (p @ Z0) @ e) @ (if_Pro278423000_alt_o @ (((h @ Z0)=(n))) @ (arrow_556571452_above @ (p @ Z0) @ c @ e) @ (arrow_1821416136_mkbot @ (p @ Z0) @ e))))))|(member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ p)))), inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])).
% 2.61/1.22 thf(c_0_7, plain, ![X10444:arrow_1196572341e_indi]:(((epred306_0 @ X10444)=(if_Pro278423000_alt_o @ ((ord_less_nat @ (h @ X10444) @ n)) @ (arrow_1970123222_mktop @ (p @ X10444) @ e) @ (if_Pro278423000_alt_o @ (((h @ X10444)=(n))) @ (arrow_556571452_above @ (p @ X10444) @ c @ e) @ (arrow_1821416136_mkbot @ (p @ X10444) @ e))))), introduced(definition)).
% 2.61/1.22 thf(c_0_8, negated_conjecture, ~(member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ p)), inference(fof_nnf,[status(thm)],[c_0_5])).
% 2.61/1.22 thf(c_0_9, plain, (member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ (^[Z0:arrow_1196572341e_indi]:(if_Pro278423000_alt_o @ ((ord_less_nat @ (h @ Z0) @ n)) @ (arrow_1970123222_mktop @ (p @ Z0) @ e) @ (if_Pro278423000_alt_o @ (((h @ Z0)=(n))) @ (arrow_556571452_above @ (p @ Z0) @ c @ e) @ (arrow_1821416136_mkbot @ (p @ Z0) @ e)))))), inference(fof_simplification,[status(thm)],[fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto])).
% 2.61/1.22 thf(c_0_10, plain, ((member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ p))|~((((member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ epred306_0)))=(($true))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_6]), c_0_7])).
% 2.61/1.22 thf(c_0_11, negated_conjecture, ~((member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ p))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 2.61/1.22 thf(c_0_12, plain, (((member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ epred306_0)))=(($true))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_9]), c_0_7])).
% 2.61/1.22 thf(c_0_13, plain, ~((member285112084le_alt @ (produc897867031le_alt @ c @ d) @ (f @ epred306_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[c_0_10]), c_0_11])).
% 2.61/1.22 thf(c_0_14, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[c_0_12]), c_0_13]), ['proof']).
% 2.61/1.22 % SZS output end CNFRefutation
% 2.61/1.22 % Parsed axioms : 1366
% 2.61/1.22 % Removed by relevancy pruning/SinE : 0
% 2.61/1.22 % Initial clauses : 5512
% 2.61/1.22 % Removed in clause preprocessing : 2562
% 2.61/1.22 % Initial clauses in saturation : 2950
% 2.61/1.22 % Processed clauses : 149
% 2.61/1.22 % ...of these trivial : 23
% 2.61/1.22 % ...subsumed : 26
% 2.61/1.22 % ...remaining for further processing : 99
% 2.61/1.22 % Other redundant clauses eliminated : 8
% 2.61/1.22 % Clauses deleted for lack of memory : 0
% 2.61/1.22 % Backward-subsumed : 1
% 2.61/1.22 % Backward-rewritten : 9
% 2.61/1.22 % Generated clauses : 8
% 2.61/1.22 % ...of the previous two non-redundant : 15
% 2.61/1.22 % ...aggressively subsumed : 0
% 2.61/1.22 % Contextual simplify-reflections : 0
% 2.61/1.22 % Paramodulations : 0
% 2.61/1.22 % Factorizations : 0
% 2.61/1.22 % NegExts : 0
% 2.61/1.22 % Equation resolutions : 8
% 2.61/1.22 % Disequality decompositions : 0
% 2.61/1.22 % Total rewrite steps : 49
% 2.61/1.22 % ...of those cached : 32
% 2.61/1.22 % Propositional unsat checks : 0
% 2.61/1.22 % Propositional check models : 0
% 2.61/1.22 % Propositional check unsatisfiable : 0
% 2.61/1.22 % Propositional clauses : 0
% 2.61/1.22 % Propositional clauses after purity: 0
% 2.61/1.22 % Propositional unsat core size : 0
% 2.61/1.22 % Propositional preprocessing time : 0.000
% 2.61/1.22 % Propositional encoding time : 0.000
% 2.61/1.22 % Propositional solver time : 0.000
% 2.61/1.22 % Success case prop preproc time : 0.000
% 2.61/1.22 % Success case prop encoding time : 0.000
% 2.61/1.22 % Success case prop solver time : 0.000
% 2.61/1.22 % Current number of processed clauses : 81
% 2.61/1.22 % Positive orientable unit clauses : 52
% 2.61/1.22 % Positive unorientable unit clauses: 1
% 2.61/1.22 % Negative unit clauses : 28
% 2.61/1.22 % Non-unit-clauses : 0
% 2.61/1.22 % Current number of unprocessed clauses: 2816
% 2.61/1.22 % ...number of literals in the above : 12109
% 2.61/1.22 % Current number of archived formulas : 0
% 2.61/1.22 % Current number of archived clauses : 10
% 2.61/1.22 % Clause-clause subsumption calls (NU) : 1
% 2.61/1.22 % Rec. Clause-clause subsumption calls : 1
% 2.61/1.22 % Non-unit clause-clause subsumptions : 1
% 2.61/1.22 % Unit Clause-clause subsumption calls : 102
% 2.61/1.22 % Rewrite failures with RHS unbound : 0
% 2.61/1.22 % BW rewrite match attempts : 20
% 2.61/1.22 % BW rewrite match successes : 7
% 2.61/1.22 % Condensation attempts : 149
% 2.61/1.22 % Condensation successes : 0
% 2.61/1.22 % Termbank termtop insertions : 343237
% 2.61/1.22 % Search garbage collected termcells : 73865
% 2.61/1.22
% 2.61/1.22 % -------------------------------------------------
% 2.61/1.22 % User time : 0.414 s
% 2.61/1.22 % System time : 0.044 s
% 2.61/1.22 % Total time : 0.458 s
% 2.61/1.22 % Maximum resident set size: 22124 pages
% 2.61/1.22
% 2.61/1.22 % -------------------------------------------------
% 2.61/1.22 % User time : 0.818 s
% 2.61/1.22 % System time : 0.190 s
% 2.61/1.22 % Total time : 1.008 s
% 2.61/1.22 % Maximum resident set size: 8448 pages
% 2.61/1.22 % E exiting
%------------------------------------------------------------------------------