%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SCT171^1 : 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 : n020.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 08:21:47 AM UTC 2026
% Result : Theorem 0.21s 0.33s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT171^1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:35:02 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.21/0.28 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.qFlznFxx7o/E---3.1_1051831.p
% 0.21/0.32 % Version: 3.5.1-ho
% 0.21/0.32 % Preprocessing class: HSLSSMSSSSLNHSA.
% 0.21/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.32 % Starting pre_casc_6 with 1200s (4) cores
% 0.21/0.32 % Starting sh4 with 600s (2) cores
% 0.21/0.32 % Starting pre_casc_4 with 300s (1) cores
% 0.21/0.32 % Starting full_lambda_7 with 300s (1) cores
% 0.21/0.32 % pre_casc_6 with pid 1051869 completed with status 0
% 0.21/0.32 % Result found by pre_casc_6
% 0.21/0.32 % Preprocessing class: HSLSSMSSSSLNHSA.
% 0.21/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.32 % Starting pre_casc_6 with 1200s (4) cores
% 0.21/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,3,,5,20000,1.0,true))
% 0.21/0.32 % SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.21/0.32 % Search class: HGHSM-FSLM32-MHSFFSBN
% 0.21/0.32 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 0.21/0.32 % Starting SubtermCWHack with 109s (1) cores
% 0.21/0.32 % Starting pre_casc_6 with 121s (1) cores
% 0.21/0.32 % Starting full_lambda_9 with 109s (1) cores
% 0.21/0.32 % Starting ehoh_best with 109s (1) cores
% 0.21/0.32 % full_lambda_9 with pid 1051881 completed with status 0
% 0.21/0.33 % Result found by full_lambda_9
% 0.21/0.33 % Preprocessing class: HSLSSMSSSSLNHSA.
% 0.21/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.33 % Starting pre_casc_6 with 1200s (4) cores
% 0.21/0.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,3,,5,20000,1.0,true))
% 0.21/0.33 % SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.21/0.33 % Search class: HGHSM-FSLM32-MHSFFSBN
% 0.21/0.33 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 0.21/0.33 % Starting SubtermCWHack with 109s (1) cores
% 0.21/0.33 % Starting pre_casc_6 with 121s (1) cores
% 0.21/0.33 % Starting full_lambda_9 with 109s (1) cores
% 0.21/0.33 % Preprocessing time : 0.005 s
% 0.21/0.33 % Presaturation interreduction done
% 0.21/0.33
% 0.21/0.33 % Proof found!
% 0.21/0.33 % SZS status Theorem
% 0.21/0.33 % SZS output start CNFRefutation
% 0.21/0.33 thf(decl_sort1, type, produc1832616231le_alt: $tType).
% 0.21/0.33 thf(decl_sort2, type, arrow_1092341143e_indi: $tType).
% 0.21/0.33 thf(decl_sort3, type, arrow_1346734812le_alt: $tType).
% 0.21/0.33 thf(decl_sort4, type, nat: $tType).
% 0.21/0.33 thf(decl_27, type, arrow_452340254_above: (produc1832616231le_alt > $o) > arrow_1346734812le_alt > arrow_1346734812le_alt > produc1832616231le_alt > $o).
% 0.21/0.33 thf(decl_29, type, arrow_1717184938_mkbot: (produc1832616231le_alt > $o) > arrow_1346734812le_alt > produc1832616231le_alt > $o).
% 0.21/0.33 thf(decl_30, type, arrow_1865892024_mktop: (produc1832616231le_alt > $o) > arrow_1346734812le_alt > produc1832616231le_alt > $o).
% 0.21/0.33 thf(decl_52, type, if_Pro399136856_alt_o: $o > (produc1832616231le_alt > $o) > (produc1832616231le_alt > $o) > produc1832616231le_alt > $o).
% 0.21/0.33 thf(decl_59, type, ord_less_nat: nat > nat > $o).
% 0.21/0.33 thf(decl_67, type, produc990411159le_alt: arrow_1346734812le_alt > arrow_1346734812le_alt > produc1832616231le_alt).
% 0.21/0.33 thf(decl_92, type, member545531028le_alt: produc1832616231le_alt > (produc1832616231le_alt > $o) > $o).
% 0.21/0.33 thf(decl_93, type, f: (arrow_1092341143e_indi > produc1832616231le_alt > $o) > produc1832616231le_alt > $o).
% 0.21/0.33 thf(decl_96, type, p: arrow_1092341143e_indi > produc1832616231le_alt > $o).
% 0.21/0.33 thf(decl_99, type, c: arrow_1346734812le_alt).
% 0.21/0.33 thf(decl_100, type, d: arrow_1346734812le_alt).
% 0.21/0.33 thf(decl_101, type, e: arrow_1346734812le_alt).
% 0.21/0.33 thf(decl_102, type, h: arrow_1092341143e_indi > nat).
% 0.21/0.33 thf(decl_103, type, n: nat).
% 0.21/0.33 thf(decl_121, type, epred4_0: arrow_1092341143e_indi > produc1832616231le_alt > $o).
% 0.21/0.33 thf(conj_0, conjecture, (member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p)), file('/export/starexec/sandbox2/tmp/tmp.qFlznFxx7o/E---3.1_1051831.p', conj_0)).
% 0.21/0.33 thf(fact_14_PW, axiom, ((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))<=>(member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[X11:arrow_1092341143e_indi]:(if_Pro399136856_alt_o @ ((ord_less_nat @ (h @ X11) @ n)) @ (arrow_1865892024_mktop @ (p @ X11) @ e) @ (if_Pro399136856_alt_o @ (((h @ X11)=(n))) @ (arrow_452340254_above @ (p @ X11) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ X11) @ e))))))), file('/export/starexec/sandbox2/tmp/tmp.qFlznFxx7o/E---3.1_1051831.p', fact_14_PW)).
% 0.21/0.33 thf(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, axiom, (member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[X11:arrow_1092341143e_indi]:(if_Pro399136856_alt_o @ ((ord_less_nat @ (h @ X11) @ n)) @ (arrow_1865892024_mktop @ (p @ X11) @ e) @ (if_Pro399136856_alt_o @ (((h @ X11)=(n))) @ (arrow_452340254_above @ (p @ X11) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ X11) @ e)))))), file('/export/starexec/sandbox2/tmp/tmp.qFlznFxx7o/E---3.1_1051831.p', fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto)).
% 0.21/0.33 thf(c_0_3, negated_conjecture, ~((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))), inference(assume_negation,[status(cth)],[conj_0])).
% 0.21/0.33 thf(c_0_4, plain, ((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))<=>(member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Z0:arrow_1092341143e_indi]:(if_Pro399136856_alt_o @ ((ord_less_nat @ (h @ Z0) @ n)) @ (arrow_1865892024_mktop @ (p @ Z0) @ e) @ (if_Pro399136856_alt_o @ (((h @ Z0)=(n))) @ (arrow_452340254_above @ (p @ Z0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ Z0) @ e))))))), inference(fof_simplification,[status(thm)],[fact_14_PW])).
% 0.21/0.33 thf(c_0_5, plain, (member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Z0:arrow_1092341143e_indi]:(if_Pro399136856_alt_o @ ((ord_less_nat @ (h @ Z0) @ n)) @ (arrow_1865892024_mktop @ (p @ Z0) @ e) @ (if_Pro399136856_alt_o @ (((h @ Z0)=(n))) @ (arrow_452340254_above @ (p @ Z0) @ c @ e) @ (arrow_1717184938_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])).
% 0.21/0.33 thf(c_0_6, plain, ![X999:arrow_1092341143e_indi]:(((epred4_0 @ X999)=(if_Pro399136856_alt_o @ ((ord_less_nat @ (h @ X999) @ n)) @ (arrow_1865892024_mktop @ (p @ X999) @ e) @ (if_Pro399136856_alt_o @ (((h @ X999)=(n))) @ (arrow_452340254_above @ (p @ X999) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ X999) @ e))))), introduced(definition)).
% 0.21/0.33 thf(c_0_7, negated_conjecture, ~(member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p)), inference(fof_simplification,[status(thm)],[c_0_3])).
% 0.21/0.33 thf(c_0_8, plain, ((~(member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))|(member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Z0:arrow_1092341143e_indi]:(if_Pro399136856_alt_o @ ((ord_less_nat @ (h @ Z0) @ n)) @ (arrow_1865892024_mktop @ (p @ Z0) @ e) @ (if_Pro399136856_alt_o @ (((h @ Z0)=(n))) @ (arrow_452340254_above @ (p @ Z0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ Z0) @ e)))))))&(~(member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ (^[Z0:arrow_1092341143e_indi]:(if_Pro399136856_alt_o @ ((ord_less_nat @ (h @ Z0) @ n)) @ (arrow_1865892024_mktop @ (p @ Z0) @ e) @ (if_Pro399136856_alt_o @ (((h @ Z0)=(n))) @ (arrow_452340254_above @ (p @ Z0) @ c @ e) @ (arrow_1717184938_mkbot @ (p @ Z0) @ e))))))|(member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p)))), inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])).
% 0.21/0.33 thf(c_0_9, plain, (((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ epred4_0)))=(($true))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_5]), c_0_6])).
% 0.21/0.33 thf(c_0_10, negated_conjecture, ~(member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p)), inference(fof_nnf,[status(thm)],[c_0_7])).
% 0.21/0.33 thf(c_0_11, plain, ((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))|~((((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ epred4_0)))=(($true))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_8]), c_0_6])).
% 0.21/0.33 thf(c_0_12, plain, (member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ epred4_0)), inference(cn,[status(thm)],[c_0_9])).
% 0.21/0.33 thf(c_0_13, negated_conjecture, ~((member545531028le_alt @ (produc990411159le_alt @ c @ d) @ (f @ p))), inference(split_conjunct,[status(thm)],[c_0_10])).
% 0.21/0.33 thf(c_0_14, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[c_0_11]), c_0_12])]), c_0_13]), ['proof']).
% 0.21/0.33 % SZS output end CNFRefutation
% 0.21/0.33 % Parsed axioms : 287
% 0.21/0.33 % Removed by relevancy pruning/SinE : 157
% 0.21/0.33 % Initial clauses : 267
% 0.21/0.33 % Removed in clause preprocessing : 39
% 0.21/0.33 % Initial clauses in saturation : 228
% 0.21/0.33 % Processed clauses : 55
% 0.21/0.33 % ...of these trivial : 10
% 0.21/0.33 % ...subsumed : 4
% 0.21/0.33 % ...remaining for further processing : 40
% 0.21/0.33 % Other redundant clauses eliminated : 3
% 0.21/0.33 % Clauses deleted for lack of memory : 0
% 0.21/0.33 % Backward-subsumed : 0
% 0.21/0.33 % Backward-rewritten : 0
% 0.21/0.33 % Generated clauses : 3
% 0.21/0.33 % ...of the previous two non-redundant : 3
% 0.21/0.33 % ...aggressively subsumed : 0
% 0.21/0.33 % Contextual simplify-reflections : 0
% 0.21/0.33 % Paramodulations : 0
% 0.21/0.33 % Factorizations : 0
% 0.21/0.33 % NegExts : 0
% 0.21/0.33 % Equation resolutions : 3
% 0.21/0.33 % Disequality decompositions : 0
% 0.21/0.33 % Total rewrite steps : 17
% 0.21/0.33 % ...of those cached : 6
% 0.21/0.33 % Propositional unsat checks : 0
% 0.21/0.33 % Propositional check models : 0
% 0.21/0.33 % Propositional check unsatisfiable : 0
% 0.21/0.33 % Propositional clauses : 0
% 0.21/0.33 % Propositional clauses after purity: 0
% 0.21/0.33 % Propositional unsat core size : 0
% 0.21/0.33 % Propositional preprocessing time : 0.000
% 0.21/0.33 % Propositional encoding time : 0.000
% 0.21/0.33 % Propositional solver time : 0.000
% 0.21/0.33 % Success case prop preproc time : 0.000
% 0.21/0.33 % Success case prop encoding time : 0.000
% 0.21/0.33 % Success case prop solver time : 0.000
% 0.21/0.33 % Current number of processed clauses : 37
% 0.21/0.33 % Positive orientable unit clauses : 24
% 0.21/0.33 % Positive unorientable unit clauses: 1
% 0.21/0.33 % Negative unit clauses : 8
% 0.21/0.33 % Non-unit-clauses : 4
% 0.21/0.33 % Current number of unprocessed clauses: 176
% 0.21/0.33 % ...number of literals in the above : 650
% 0.21/0.33 % Current number of archived formulas : 0
% 0.21/0.33 % Current number of archived clauses : 0
% 0.21/0.33 % Clause-clause subsumption calls (NU) : 7
% 0.21/0.33 % Rec. Clause-clause subsumption calls : 6
% 0.21/0.33 % Non-unit clause-clause subsumptions : 4
% 0.21/0.33 % Unit Clause-clause subsumption calls : 7
% 0.21/0.33 % Rewrite failures with RHS unbound : 0
% 0.21/0.33 % BW rewrite match attempts : 2
% 0.21/0.33 % BW rewrite match successes : 0
% 0.21/0.33 % Condensation attempts : 0
% 0.21/0.33 % Condensation successes : 0
% 0.21/0.33 % Termbank termtop insertions : 23392
% 0.21/0.33 % Search garbage collected termcells : 5885
% 0.21/0.33
% 0.21/0.33 % -------------------------------------------------
% 0.21/0.33 % User time : 0.021 s
% 0.21/0.33 % System time : 0.007 s
% 0.21/0.33 % Total time : 0.028 s
% 0.21/0.33 % Maximum resident set size: 4976 pages
% 0.21/0.33
% 0.21/0.33 % -------------------------------------------------
% 0.21/0.33 % User time : 0.045 s
% 0.21/0.33 % System time : 0.018 s
% 0.21/0.33 % Total time : 0.063 s
% 0.21/0.33 % Maximum resident set size: 5376 pages
% 0.21/0.33 % E exiting
%------------------------------------------------------------------------------