%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT171^2 : 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 : n001.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 0.34s 0.41s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT171^2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n001.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:40:04 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.21/0.33 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.QpnnIbnS07/E---3.1_1245515.p
% 0.34/0.41 % Version: 3.5.1-ho
% 0.34/0.41 % Preprocessing class: HSLMSMSMSSLCHSA.
% 0.34/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.41 % Starting new_bool_8 with 1500s (5) cores
% 0.34/0.41 % Starting new_ho_6 with 300s (1) cores
% 0.34/0.41 % Starting full_lambda_4 with 300s (1) cores
% 0.34/0.41 % Starting new_bool_7 with 300s (1) cores
% 0.34/0.41 % new_bool_8 with pid 1245528 completed with status 0
% 0.34/0.41 % Result found by new_bool_8
% 0.34/0.41 % Preprocessing class: HSLMSMSMSSLCHSA.
% 0.34/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.41 % Starting new_bool_8 with 1500s (5) cores
% 0.34/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 0.34/0.41 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.34/0.41 % Search class: HGHSM-FSLM33-MHSFFFBN
% 0.34/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.34/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.34/0.41 % Starting new_bool_8 with 151s (1) cores
% 0.34/0.41 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.34/0.41 % Starting ehoh_best8_lambda with 136s (1) cores
% 0.34/0.41 % Starting ho_unfolding_6 with 136s (1) cores
% 0.34/0.41 % new_bool_8 with pid 1245535 completed with status 0
% 0.34/0.41 % Result found by new_bool_8
% 0.34/0.41 % Preprocessing class: HSLMSMSMSSLCHSA.
% 0.34/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.41 % Starting new_bool_8 with 1500s (5) cores
% 0.34/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 0.34/0.41 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.34/0.41 % Search class: HGHSM-FSLM33-MHSFFFBN
% 0.34/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.34/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.34/0.41 % Starting new_bool_8 with 151s (1) cores
% 0.34/0.41 % Preprocessing time : 0.004 s
% 0.34/0.41 % Presaturation interreduction done
% 0.34/0.41
% 0.34/0.41 % Proof found!
% 0.34/0.41 % SZS status Theorem
% 0.34/0.41 % SZS output start CNFRefutation
% 0.34/0.41 thf(decl_sort1, type, produc1501160679le_alt: $tType).
% 0.34/0.41 thf(decl_sort2, type, arrow_1429601828e_indi: $tType).
% 0.34/0.41 thf(decl_sort3, type, arrow_475358991le_alt: $tType).
% 0.34/0.41 thf(decl_sort4, type, nat: $tType).
% 0.34/0.41 thf(decl_27, type, arrow_789600939_above: (produc1501160679le_alt > $o) > arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt > $o).
% 0.34/0.41 thf(decl_30, type, arrow_2054445623_mkbot: (produc1501160679le_alt > $o) > arrow_475358991le_alt > produc1501160679le_alt > $o).
% 0.34/0.41 thf(decl_31, type, arrow_55669061_mktop: (produc1501160679le_alt > $o) > arrow_475358991le_alt > produc1501160679le_alt > $o).
% 0.34/0.41 thf(decl_93, type, if_Pro1561232536_alt_o: $o > (produc1501160679le_alt > $o) > (produc1501160679le_alt > $o) > produc1501160679le_alt > $o).
% 0.34/0.41 thf(decl_104, type, ord_less_nat: nat > nat > $o).
% 0.34/0.41 thf(decl_125, type, produc1347929815le_alt: arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt).
% 0.34/0.41 thf(decl_172, type, member214075476le_alt: produc1501160679le_alt > (produc1501160679le_alt > $o) > $o).
% 0.34/0.41 thf(decl_173, type, f: (arrow_1429601828e_indi > produc1501160679le_alt > $o) > produc1501160679le_alt > $o).
% 0.34/0.41 thf(decl_176, type, p: arrow_1429601828e_indi > produc1501160679le_alt > $o).
% 0.34/0.41 thf(decl_179, type, c: arrow_475358991le_alt).
% 0.34/0.41 thf(decl_180, type, d: arrow_475358991le_alt).
% 0.34/0.41 thf(decl_181, type, e: arrow_475358991le_alt).
% 0.34/0.41 thf(decl_182, type, h: arrow_1429601828e_indi > nat).
% 0.34/0.41 thf(decl_183, type, n: nat).
% 0.34/0.41 thf(decl_193, type, epred3_0: arrow_1429601828e_indi > produc1501160679le_alt > $o).
% 0.34/0.41 thf(conj_0, conjecture, (member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p)), file('/export/starexec/sandbox2/tmp/tmp.QpnnIbnS07/E---3.1_1245515.p', conj_0)).
% 0.34/0.41 thf(fact_14_PW, axiom, ((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p))<=>(member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ (^[X11:arrow_1429601828e_indi]:(if_Pro1561232536_alt_o @ ((ord_less_nat @ (h @ X11) @ n)) @ (arrow_55669061_mktop @ (p @ X11) @ e) @ (if_Pro1561232536_alt_o @ (((h @ X11)=(n))) @ (arrow_789600939_above @ (p @ X11) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ X11) @ e))))))), file('/export/starexec/sandbox2/tmp/tmp.QpnnIbnS07/E---3.1_1245515.p', fact_14_PW)).
% 0.34/0.41 thf(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, axiom, (member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ (^[X11:arrow_1429601828e_indi]:(if_Pro1561232536_alt_o @ ((ord_less_nat @ (h @ X11) @ n)) @ (arrow_55669061_mktop @ (p @ X11) @ e) @ (if_Pro1561232536_alt_o @ (((h @ X11)=(n))) @ (arrow_789600939_above @ (p @ X11) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ X11) @ e)))))), file('/export/starexec/sandbox2/tmp/tmp.QpnnIbnS07/E---3.1_1245515.p', fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto)).
% 0.34/0.41 thf(c_0_3, negated_conjecture, ~((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p))), inference(assume_negation,[status(cth)],[conj_0])).
% 0.34/0.41 thf(c_0_4, plain, ((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p))<=>(member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ (^[Z0:arrow_1429601828e_indi]:(if_Pro1561232536_alt_o @ ((ord_less_nat @ (h @ Z0) @ n)) @ (arrow_55669061_mktop @ (p @ Z0) @ e) @ (if_Pro1561232536_alt_o @ (((h @ Z0)=(n))) @ (arrow_789600939_above @ (p @ Z0) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ Z0) @ e))))))), inference(fof_simplification,[status(thm)],[fact_14_PW])).
% 0.34/0.41 thf(c_0_5, negated_conjecture, ~(member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p)), inference(fof_simplification,[status(thm)],[c_0_3])).
% 0.34/0.41 thf(c_0_6, plain, ((~(member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p))|(member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ (^[Z0:arrow_1429601828e_indi]:(if_Pro1561232536_alt_o @ ((ord_less_nat @ (h @ Z0) @ n)) @ (arrow_55669061_mktop @ (p @ Z0) @ e) @ (if_Pro1561232536_alt_o @ (((h @ Z0)=(n))) @ (arrow_789600939_above @ (p @ Z0) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ Z0) @ e)))))))&(~(member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ (^[Z0:arrow_1429601828e_indi]:(if_Pro1561232536_alt_o @ ((ord_less_nat @ (h @ Z0) @ n)) @ (arrow_55669061_mktop @ (p @ Z0) @ e) @ (if_Pro1561232536_alt_o @ (((h @ Z0)=(n))) @ (arrow_789600939_above @ (p @ Z0) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ Z0) @ e))))))|(member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p)))), inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])).
% 0.34/0.41 thf(c_0_7, plain, ![X1647:arrow_1429601828e_indi]:(((epred3_0 @ X1647)=(if_Pro1561232536_alt_o @ ((ord_less_nat @ (h @ X1647) @ n)) @ (arrow_55669061_mktop @ (p @ X1647) @ e) @ (if_Pro1561232536_alt_o @ (((h @ X1647)=(n))) @ (arrow_789600939_above @ (p @ X1647) @ c @ e) @ (arrow_2054445623_mkbot @ (p @ X1647) @ e))))), introduced(definition)).
% 0.34/0.41 thf(c_0_8, negated_conjecture, ~(member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p)), inference(fof_nnf,[status(thm)],[c_0_5])).
% 0.34/0.41 thf(c_0_9, plain, (member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ (^[Z0:arrow_1429601828e_indi]:(if_Pro1561232536_alt_o @ ((ord_less_nat @ (h @ Z0) @ n)) @ (arrow_55669061_mktop @ (p @ Z0) @ e) @ (if_Pro1561232536_alt_o @ (((h @ Z0)=(n))) @ (arrow_789600939_above @ (p @ Z0) @ c @ e) @ (arrow_2054445623_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])).
% 0.34/0.41 thf(c_0_10, plain, ((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p))|~((((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ epred3_0)))=(($true))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_6]), c_0_7])).
% 0.34/0.41 thf(c_0_11, negated_conjecture, ~((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ p))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 0.34/0.41 thf(c_0_12, plain, (((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ epred3_0)))=(($true))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_9]), c_0_7])).
% 0.34/0.41 thf(c_0_13, plain, ~((member214075476le_alt @ (produc1347929815le_alt @ c @ d) @ (f @ epred3_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[c_0_10]), c_0_11])).
% 0.34/0.41 thf(c_0_14, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[c_0_12]), c_0_13]), ['proof']).
% 0.34/0.41 % SZS output end CNFRefutation
% 0.34/0.41 % Parsed axioms : 870
% 0.34/0.41 % Removed by relevancy pruning/SinE : 795
% 0.34/0.41 % Initial clauses : 231
% 0.34/0.41 % Removed in clause preprocessing : 49
% 0.34/0.41 % Initial clauses in saturation : 182
% 0.34/0.41 % Processed clauses : 24
% 0.34/0.41 % ...of these trivial : 0
% 0.34/0.41 % ...subsumed : 6
% 0.34/0.41 % ...remaining for further processing : 17
% 0.34/0.41 % Other redundant clauses eliminated : 4
% 0.34/0.41 % Clauses deleted for lack of memory : 0
% 0.34/0.41 % Backward-subsumed : 0
% 0.34/0.41 % Backward-rewritten : 0
% 0.34/0.41 % Generated clauses : 4
% 0.34/0.41 % ...of the previous two non-redundant : 4
% 0.34/0.41 % ...aggressively subsumed : 0
% 0.34/0.41 % Contextual simplify-reflections : 0
% 0.34/0.41 % Paramodulations : 0
% 0.34/0.41 % Factorizations : 0
% 0.34/0.41 % NegExts : 0
% 0.34/0.41 % Equation resolutions : 4
% 0.34/0.41 % Disequality decompositions : 0
% 0.34/0.41 % Total rewrite steps : 0
% 0.34/0.41 % ...of those cached : 0
% 0.34/0.41 % Propositional unsat checks : 0
% 0.34/0.41 % Propositional check models : 0
% 0.34/0.41 % Propositional check unsatisfiable : 0
% 0.34/0.41 % Propositional clauses : 0
% 0.34/0.41 % Propositional clauses after purity: 0
% 0.34/0.41 % Propositional unsat core size : 0
% 0.34/0.41 % Propositional preprocessing time : 0.000
% 0.34/0.41 % Propositional encoding time : 0.000
% 0.34/0.41 % Propositional solver time : 0.000
% 0.34/0.41 % Success case prop preproc time : 0.000
% 0.34/0.41 % Success case prop encoding time : 0.000
% 0.34/0.41 % Success case prop solver time : 0.000
% 0.34/0.41 % Current number of processed clauses : 13
% 0.34/0.41 % Positive orientable unit clauses : 6
% 0.34/0.41 % Positive unorientable unit clauses: 0
% 0.34/0.41 % Negative unit clauses : 7
% 0.34/0.41 % Non-unit-clauses : 0
% 0.34/0.41 % Current number of unprocessed clauses: 162
% 0.34/0.41 % ...number of literals in the above : 651
% 0.34/0.41 % Current number of archived formulas : 0
% 0.34/0.41 % Current number of archived clauses : 2
% 0.34/0.41 % Clause-clause subsumption calls (NU) : 0
% 0.34/0.41 % Rec. Clause-clause subsumption calls : 0
% 0.34/0.41 % Non-unit clause-clause subsumptions : 0
% 0.34/0.41 % Unit Clause-clause subsumption calls : 7
% 0.34/0.41 % Rewrite failures with RHS unbound : 0
% 0.34/0.41 % BW rewrite match attempts : 0
% 0.34/0.41 % BW rewrite match successes : 0
% 0.34/0.41 % Condensation attempts : 0
% 0.34/0.41 % Condensation successes : 0
% 0.34/0.41 % Termbank termtop insertions : 28040
% 0.34/0.41 % Search garbage collected termcells : 9489
% 0.34/0.41
% 0.34/0.41 % -------------------------------------------------
% 0.34/0.41 % User time : 0.022 s
% 0.34/0.41 % System time : 0.005 s
% 0.34/0.41 % Total time : 0.028 s
% 0.34/0.41 % Maximum resident set size: 5976 pages
% 0.34/0.41
% 0.34/0.41 % -------------------------------------------------
% 0.34/0.41 % User time : 0.055 s
% 0.34/0.41 % System time : 0.024 s
% 0.34/0.41 % Total time : 0.079 s
% 0.34/0.41 % Maximum resident set size: 6656 pages
% 0.34/0.41 % E exiting
%------------------------------------------------------------------------------