%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP132^1 : 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 08:04:27 AM UTC 2026
% Result : Theorem 0.24s 0.37s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP132^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n016.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 20:03:34 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.07/0.26 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.UoVgCHxFBE/E---3.1_836169.p
% 0.24/0.37 % Version: 3.5.1-ho
% 0.24/0.37 % Preprocessing class: HSLSSMSSSSLNHSA.
% 0.24/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.37 % Starting pre_casc_6 with 1200s (4) cores
% 0.24/0.37 % Starting sh4 with 600s (2) cores
% 0.24/0.37 % Starting pre_casc_4 with 300s (1) cores
% 0.24/0.37 % Starting full_lambda_7 with 300s (1) cores
% 0.24/0.37 % sh4 with pid 836183 completed with status 0
% 0.24/0.37 % Result found by sh4
% 0.24/0.37 % Preprocessing class: HSLSSMSSSSLNHSA.
% 0.24/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.37 % Starting pre_casc_6 with 1200s (4) cores
% 0.24/0.37 % Starting sh4 with 600s (2) cores
% 0.24/0.37 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.37 % No SInE strategy applied
% 0.24/0.37 % Search class: HGHSM-FSLM32-MHSFFSBC
% 0.24/0.37 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.24/0.37 % Starting SubtermCWHack with 55s (1) cores
% 0.24/0.37 % Starting sh4 with 61s (1) cores
% 0.24/0.37 % sh4 with pid 836193 completed with status 0
% 0.24/0.37 % Result found by sh4
% 0.24/0.37 % Preprocessing class: HSLSSMSSSSLNHSA.
% 0.24/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.37 % Starting pre_casc_6 with 1200s (4) cores
% 0.24/0.37 % Starting sh4 with 600s (2) cores
% 0.24/0.37 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.37 % No SInE strategy applied
% 0.24/0.37 % Search class: HGHSM-FSLM32-MHSFFSBC
% 0.24/0.37 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.24/0.37 % Starting SubtermCWHack with 55s (1) cores
% 0.24/0.37 % Starting sh4 with 61s (1) cores
% 0.24/0.37 % Preprocessing time : 0.009 s
% 0.24/0.37
% 0.24/0.37 % Proof found!
% 0.24/0.37 % SZS status Theorem
% 0.24/0.37 % SZS output start CNFRefutation
% 0.24/0.37 thf(decl_sort1, type, nat: $tType).
% 0.24/0.37 thf(decl_sort2, type, set_nat: $tType).
% 0.24/0.37 thf(decl_24, type, minus_minus_nat: nat > nat > nat).
% 0.24/0.37 thf(decl_25, type, one_one_nat: nat).
% 0.24/0.37 thf(decl_26, type, times_times_nat: nat > nat > nat).
% 0.24/0.37 thf(decl_27, type, zero_zero_nat: nat).
% 0.24/0.37 thf(decl_28, type, groups1842438620at_nat: (nat > nat) > set_nat > nat).
% 0.24/0.37 thf(decl_30, type, number1551313001itions: (nat > nat) > nat > $o).
% 0.24/0.37 thf(decl_32, type, ord_less_eq_nat: nat > nat > $o).
% 0.24/0.37 thf(decl_37, type, set_ord_atMost_nat: nat > set_nat).
% 0.24/0.37 thf(decl_41, type, k: nat).
% 0.24/0.37 thf(decl_42, type, n: nat).
% 0.24/0.37 thf(decl_43, type, p: nat > nat).
% 0.24/0.37 thf(decl_62, type, esk19_2: (nat > nat) > nat > nat).
% 0.24/0.37 thf(decl_138, type, esk92_1: (nat > nat) > nat > nat).
% 0.24/0.37 thf(conj_0, conjecture, ((minus_minus_nat @ (groups1842438620at_nat @ (^[X3:nat]:(times_times_nat @ (p @ X3) @ X3)) @ (set_ord_atMost_nat @ n)) @ k)=(minus_minus_nat @ n @ k)), file('/export/starexec/sandbox2/tmp/tmp.UoVgCHxFBE/E---3.1_836169.p', conj_0)).
% 0.24/0.37 thf(fact_61_partitions__def, axiom, ((number1551313001itions)=(^[X67:nat > nat, X10:nat]:(((![X3:nat]:(((((X67 @ X3)!=(zero_zero_nat)))=>((((ord_less_eq_nat @ one_one_nat @ X3))&((ord_less_eq_nat @ X3 @ X10)))))))&(((groups1842438620at_nat @ (^[X3:nat]:(times_times_nat @ (X67 @ X3) @ X3)) @ (set_ord_atMost_nat @ X10))=(X10))))))), file('/export/starexec/sandbox2/tmp/tmp.UoVgCHxFBE/E---3.1_836169.p', fact_61_partitions__def)).
% 0.24/0.37 thf(fact_0_partitions, axiom, (number1551313001itions @ p @ n), file('/export/starexec/sandbox2/tmp/tmp.UoVgCHxFBE/E---3.1_836169.p', fact_0_partitions)).
% 0.24/0.37 thf(c_0_3, negated_conjecture, ~(((minus_minus_nat @ (groups1842438620at_nat @ (^[X3:nat]:(times_times_nat @ (p @ X3) @ X3)) @ (set_ord_atMost_nat @ n)) @ k)=(minus_minus_nat @ n @ k))), inference(assume_negation,[status(cth)],[conj_0])).
% 0.24/0.37 thf(c_0_4, negated_conjecture, ((minus_minus_nat @ (groups1842438620at_nat @ (^[Z0:nat]:(times_times_nat @ (p @ Z0) @ Z0)) @ (set_ord_atMost_nat @ n)) @ k)!=(minus_minus_nat @ n @ k)), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_3])])).
% 0.24/0.37 thf(c_0_5, plain, ![X799:nat > nat, X800:nat]:(((number1551313001itions @ X799 @ X800)<=>(![X3:nat]:((((X799 @ X3)!=(zero_zero_nat))=>((ord_less_eq_nat @ one_one_nat @ X3)&(ord_less_eq_nat @ X3 @ X800))))&((groups1842438620at_nat @ (^[Z0:nat]:(times_times_nat @ (X799 @ Z0) @ Z0)) @ (set_ord_atMost_nat @ X800))=(X800))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_61_partitions__def])])])).
% 0.24/0.37 thf(c_0_6, negated_conjecture, ((minus_minus_nat @ (groups1842438620at_nat @ (^[Z0:nat]:(times_times_nat @ (p @ Z0) @ Z0)) @ (set_ord_atMost_nat @ n)) @ k)!=(minus_minus_nat @ n @ k)), inference(fof_nnf,[status(thm)],[c_0_4])).
% 0.24/0.37 thf(c_0_7, plain, ![X1491:nat, X4:nat > nat]:(((esk92_1 @ X4 @ X1491)=(times_times_nat @ (X4 @ X1491) @ X1491))), introduced(definition)).
% 0.24/0.37 thf(c_0_8, plain, ![X985:nat > nat, X986:nat, X987:nat, X988:nat > nat, X989:nat]:((((((ord_less_eq_nat @ one_one_nat @ X987)|((X985 @ X987)=(zero_zero_nat))|~(number1551313001itions @ X985 @ X986))&((ord_less_eq_nat @ X987 @ X986)|((X985 @ X987)=(zero_zero_nat))|~(number1551313001itions @ X985 @ X986)))&(((groups1842438620at_nat @ (^[Z0:nat]:(times_times_nat @ (X985 @ Z0) @ Z0)) @ (set_ord_atMost_nat @ X986))=(X986))|~(number1551313001itions @ X985 @ X986)))&((((X988 @ (esk19_2 @ X988 @ X989))!=(zero_zero_nat))|((groups1842438620at_nat @ (^[Z0:nat]:(times_times_nat @ (X988 @ Z0) @ Z0)) @ (set_ord_atMost_nat @ X989))!=(X989))|(number1551313001itions @ X988 @ X989))&(~(ord_less_eq_nat @ one_one_nat @ (esk19_2 @ X988 @ X989))|~(ord_less_eq_nat @ (esk19_2 @ X988 @ X989) @ X989)|((groups1842438620at_nat @ (^[Z0:nat]:(times_times_nat @ (X988 @ Z0) @ Z0)) @ (set_ord_atMost_nat @ X989))!=(X989))|(number1551313001itions @ X988 @ X989))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])])])).
% 0.24/0.37 thf(c_0_9, negated_conjecture, ((minus_minus_nat @ (groups1842438620at_nat @ (esk92_1 @ p) @ (set_ord_atMost_nat @ n)) @ k)!=(minus_minus_nat @ n @ k)), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_6]), c_0_7])).
% 0.24/0.37 thf(c_0_10, plain, ![X4:nat > nat, X1:nat]:((((groups1842438620at_nat @ (esk92_1 @ X4) @ (set_ord_atMost_nat @ X1))=(X1))|~((number1551313001itions @ X4 @ X1)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_8]), c_0_7])).
% 0.24/0.37 thf(c_0_11, plain, (number1551313001itions @ p @ n), inference(split_conjunct,[status(thm)],[fact_0_partitions])).
% 0.24/0.37 thf(c_0_12, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9, c_0_10]), c_0_11])]), ['proof']).
% 0.24/0.37 % SZS output end CNFRefutation
% 0.24/0.37 % Parsed axioms : 269
% 0.24/0.37 % Removed by relevancy pruning/SinE : 0
% 0.24/0.37 % Initial clauses : 524
% 0.24/0.37 % Removed in clause preprocessing : 51
% 0.24/0.37 % Initial clauses in saturation : 473
% 0.24/0.37 % Processed clauses : 122
% 0.24/0.37 % ...of these trivial : 17
% 0.24/0.37 % ...subsumed : 16
% 0.24/0.37 % ...remaining for further processing : 89
% 0.24/0.37 % Other redundant clauses eliminated : 47
% 0.24/0.37 % Clauses deleted for lack of memory : 0
% 0.24/0.37 % Backward-subsumed : 2
% 0.24/0.37 % Backward-rewritten : 3
% 0.24/0.37 % Generated clauses : 121
% 0.24/0.37 % ...of the previous two non-redundant : 62
% 0.24/0.37 % ...aggressively subsumed : 0
% 0.24/0.37 % Contextual simplify-reflections : 0
% 0.24/0.37 % Paramodulations : 53
% 0.24/0.37 % Factorizations : 0
% 0.24/0.37 % NegExts : 0
% 0.24/0.37 % Equation resolutions : 48
% 0.24/0.37 % Disequality decompositions : 0
% 0.24/0.37 % Total rewrite steps : 67
% 0.24/0.37 % ...of those cached : 50
% 0.24/0.37 % Propositional unsat checks : 0
% 0.24/0.37 % Propositional check models : 0
% 0.24/0.37 % Propositional check unsatisfiable : 0
% 0.24/0.37 % Propositional clauses : 0
% 0.24/0.37 % Propositional clauses after purity: 0
% 0.24/0.37 % Propositional unsat core size : 0
% 0.24/0.37 % Propositional preprocessing time : 0.000
% 0.24/0.37 % Propositional encoding time : 0.000
% 0.24/0.37 % Propositional solver time : 0.000
% 0.24/0.37 % Success case prop preproc time : 0.000
% 0.24/0.37 % Success case prop encoding time : 0.000
% 0.24/0.37 % Success case prop solver time : 0.000
% 0.24/0.37 % Current number of processed clauses : 48
% 0.24/0.37 % Positive orientable unit clauses : 25
% 0.24/0.37 % Positive unorientable unit clauses: 0
% 0.24/0.37 % Negative unit clauses : 5
% 0.24/0.37 % Non-unit-clauses : 18
% 0.24/0.37 % Current number of unprocessed clauses: 413
% 0.24/0.37 % ...number of literals in the above : 1319
% 0.24/0.37 % Current number of archived formulas : 0
% 0.24/0.37 % Current number of archived clauses : 5
% 0.24/0.37 % Clause-clause subsumption calls (NU) : 194
% 0.24/0.37 % Rec. Clause-clause subsumption calls : 158
% 0.24/0.37 % Non-unit clause-clause subsumptions : 15
% 0.24/0.37 % Unit Clause-clause subsumption calls : 24
% 0.24/0.37 % Rewrite failures with RHS unbound : 0
% 0.24/0.37 % BW rewrite match attempts : 11
% 0.24/0.37 % BW rewrite match successes : 3
% 0.24/0.37 % Condensation attempts : 122
% 0.24/0.37 % Condensation successes : 0
% 0.24/0.37 % Termbank termtop insertions : 36005
% 0.24/0.37 % Search garbage collected termcells : 9340
% 0.24/0.37
% 0.24/0.37 % -------------------------------------------------
% 0.24/0.37 % User time : 0.042 s
% 0.24/0.37 % System time : 0.008 s
% 0.24/0.37 % Total time : 0.050 s
% 0.24/0.37 % Maximum resident set size: 5856 pages
% 0.24/0.37
% 0.24/0.37 % -------------------------------------------------
% 0.24/0.37 % User time : 0.075 s
% 0.24/0.37 % System time : 0.019 s
% 0.24/0.37 % Total time : 0.094 s
% 0.24/0.37 % Maximum resident set size: 5376 pages
% 0.24/0.37 % E exiting
%------------------------------------------------------------------------------