%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV245^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:35:16 AM UTC 2026
% Result : Theorem 0.23s 0.27s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV245^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % 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 15:26:21 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.mdVmF0vLUi/E---3.1_2247760.p
% 0.23/0.27 % Version: 3.5.1-ho
% 0.23/0.27 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.23/0.27 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting sh2lt with 1200s (4) cores
% 0.23/0.27 % Starting new_ho_10_unif with 300s (1) cores
% 0.23/0.27 % Starting full_lambda_6 with 300s (1) cores
% 0.23/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.27 % Starting ehoh_best3_rw with 300s (1) cores
% 0.23/0.27 % post_as_ho1 with pid 2247776 completed with status 0
% 0.23/0.27 % Result found by post_as_ho1
% 0.23/0.27 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.23/0.27 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting sh2lt with 1200s (4) cores
% 0.23/0.27 % Starting new_ho_10_unif with 300s (1) cores
% 0.23/0.27 % Starting full_lambda_6 with 300s (1) cores
% 0.23/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.27 % No SInE strategy applied
% 0.23/0.27 % Search class: HGUNF-FFSF22-SHHFFSBN
% 0.23/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.27 % SubtermCWHack with pid 2247784 completed with status 0
% 0.23/0.27 % Result found by SubtermCWHack
% 0.23/0.27 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.23/0.27 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting sh2lt with 1200s (4) cores
% 0.23/0.27 % Starting new_ho_10_unif with 300s (1) cores
% 0.23/0.27 % Starting full_lambda_6 with 300s (1) cores
% 0.23/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.27 % No SInE strategy applied
% 0.23/0.27 % Search class: HGUNF-FFSF22-SHHFFSBN
% 0.23/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.27 % Preprocessing time : 0.001 s
% 0.23/0.27
% 0.23/0.27 % Proof found!
% 0.23/0.27 % SZS status Theorem
% 0.23/0.27 % SZS output start CNFRefutation
% 0.23/0.27 thf(decl_23, type, epred1_0: ($i > $o) > $i > $o).
% 0.23/0.27 thf(decl_24, type, esk1_2: ($i > $o) > ($i > $o) > $i).
% 0.23/0.27 thf(decl_25, type, esk2_0: $i).
% 0.23/0.27 thf(decl_26, type, epred2_0: $i > $o).
% 0.23/0.27 thf(decl_27, type, epred3_0: $i > $o).
% 0.23/0.27 thf(decl_28, type, epred4_1: $i > $i > $o).
% 0.23/0.27 thf(decl_29, type, esk3_2: $i > ($i > $o) > $i).
% 0.23/0.27 thf(cTHM2A_TWO_pme, conjecture, ![X1:($i > $o) > $i > $o]:((![X2:$i > $o, X3:$i > $o]:((![X4:$i]:(((X2 @ X4)=>(X3 @ X4)))=>![X4:$i]:(((X1 @ X2 @ X4)=>(X1 @ X3 @ X4)))))=>![X5:$i]:((?[X6:$i > $o]:((![X4:$i]:(((X6 @ X4)=>(X1 @ X6 @ X4)))&(X6 @ X5)))=>(X1 @ (^[X4:$i]:(?[X6:$i > $o]:(((![X7:$i]:((((X6 @ X7))=>((X1 @ X6 @ X7)))))&((X6 @ X4)))))) @ X5))))), file('/export/starexec/sandbox/tmp/tmp.mdVmF0vLUi/E---3.1_2247760.p', cTHM2A_TWO_pme)).
% 0.23/0.27 thf(c_0_1, negated_conjecture, ~(![X1:($i > $o) > $i > $o]:((![X2:$i > $o, X3:$i > $o]:((![X4:$i]:(((X2 @ X4)=>(X3 @ X4)))=>![X4:$i]:(((X1 @ X2 @ X4)=>(X1 @ X3 @ X4)))))=>![X5:$i]:((?[X6:$i > $o]:((![X4:$i]:(((X6 @ X4)=>(X1 @ X6 @ X4)))&(X6 @ X5)))=>(X1 @ (^[X4:$i]:(?[X6:$i > $o]:(((![X7:$i]:((((X6 @ X7))=>((X1 @ X6 @ X7)))))&((X6 @ X4)))))) @ X5)))))), inference(assume_negation,[status(cth)],[cTHM2A_TWO_pme])).
% 0.23/0.27 thf(c_0_2, negated_conjecture, ~(![X1:($i > $o) > $i > $o]:((![X2:$i > $o, X3:$i > $o]:((![X4:$i]:(((X2 @ X4)=>(X3 @ X4)))=>![X4:$i]:(((X1 @ X2 @ X4)=>(X1 @ X3 @ X4)))))=>![X5:$i]:((?[X6:$i > $o]:((![X4:$i]:(((X6 @ X4)=>(X1 @ X6 @ X4)))&(X6 @ X5)))=>(X1 @ (^[Z0:$i]:(?[X6:$i > $o]:(((![X7:$i]:(((X6 @ X7)=>(X1 @ X6 @ X7))))&(X6 @ Z0))))) @ X5)))))), inference(fof_simplification,[status(thm)],[c_0_1])).
% 0.23/0.27 thf(c_0_3, negated_conjecture, ![X17:$i > $o, X18:$i > $o, X20:$i, X23:$i]:(((((X17 @ (esk1_2 @ X17 @ X18))|(~(epred1_0 @ X17 @ X20)|(epred1_0 @ X18 @ X20)))&(~(X18 @ (esk1_2 @ X17 @ X18))|(~(epred1_0 @ X17 @ X20)|(epred1_0 @ X18 @ X20))))&(((~(epred2_0 @ X23)|(epred1_0 @ epred2_0 @ X23))&(epred2_0 @ esk2_0))&~(epred1_0 @ (^[Z0:$i]:(?[X6:$i > $o]:(((![X7:$i]:(((X6 @ X7)=>(epred1_0 @ X6 @ X7))))&(X6 @ Z0))))) @ esk2_0)))), 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_2])])])])])])).
% 0.23/0.27 thf(c_0_4, plain, ![X27:$i, X29:$i, X30:$i > $o]:((((~(epred4_1 @ X27 @ X29)|(epred1_0 @ (epred4_1 @ X27) @ X29)|~(epred3_0 @ X27))&((epred4_1 @ X27 @ X27)|~(epred3_0 @ X27)))&(((X30 @ (esk3_2 @ X27 @ X30))|~(X30 @ X27)|(epred3_0 @ X27))&(~(epred1_0 @ X30 @ (esk3_2 @ X27 @ X30))|~(X30 @ X27)|(epred3_0 @ X27))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])).
% 0.23/0.27 thf(c_0_5, negated_conjecture, ![X2:$i > $o, X3:$i > $o, X4:$i]:(((X2 @ (esk1_2 @ X2 @ X3))|(epred1_0 @ X3 @ X4)|~((epred1_0 @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_3])).
% 0.23/0.27 thf(c_0_6, negated_conjecture, ![X4:$i]:(((epred1_0 @ epred2_0 @ X4)|~((epred2_0 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_3])).
% 0.23/0.27 thf(c_0_7, plain, ![X2:$i > $o, X4:$i]:(((epred3_0 @ X4)|~((epred1_0 @ X2 @ (esk3_2 @ X4 @ X2)))|~((X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_4])).
% 0.23/0.27 thf(c_0_8, plain, ![X2:$i > $o, X4:$i]:(((X2 @ (esk3_2 @ X4 @ X2))|(epred3_0 @ X4)|~((X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_4])).
% 0.23/0.27 thf(c_0_9, negated_conjecture, ![X2:$i > $o, X4:$i]:(((epred2_0 @ (esk1_2 @ epred2_0 @ X2))|(epred1_0 @ X2 @ X4)|~((epred2_0 @ X4)))), inference(spm,[status(thm)],[c_0_5, c_0_6])).
% 0.23/0.27 thf(c_0_10, negated_conjecture, (epred2_0 @ esk2_0), inference(split_conjunct,[status(thm)],[c_0_3])).
% 0.23/0.27 thf(c_0_11, plain, ![X26:$i]:(((epred3_0 @ X26)<=>?[X24:$i > $o]:((![X25:$i]:(((X24 @ X25)=>(epred1_0 @ X24 @ X25)))&(X24 @ X26))))), introduced(definition)).
% 0.23/0.27 thf(c_0_12, negated_conjecture, ![X4:$i]:(((epred3_0 @ X4)|~((epred2_0 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7, c_0_6]), c_0_8])).
% 0.23/0.27 thf(c_0_13, negated_conjecture, ![X2:$i > $o]:(((epred2_0 @ (esk1_2 @ epred2_0 @ X2))|(epred1_0 @ X2 @ esk2_0))), inference(spm,[status(thm)],[c_0_9, c_0_10])).
% 0.23/0.27 thf(c_0_14, negated_conjecture, ~((((epred1_0 @ epred3_0 @ esk2_0))=(($true)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_3]), c_0_11])).
% 0.23/0.27 thf(c_0_15, negated_conjecture, ![X2:$i > $o, X3:$i > $o, X4:$i]:(((epred1_0 @ X2 @ X4)|~((X2 @ (esk1_2 @ X3 @ X2)))|~((epred1_0 @ X3 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_3])).
% 0.23/0.27 thf(c_0_16, negated_conjecture, ![X2:$i > $o]:(((epred3_0 @ (esk1_2 @ epred2_0 @ X2))|(epred1_0 @ X2 @ esk2_0))), inference(spm,[status(thm)],[c_0_12, c_0_13])).
% 0.23/0.27 thf(c_0_17, negated_conjecture, ~((epred1_0 @ epred3_0 @ esk2_0)), inference(cn,[status(thm)],[c_0_14])).
% 0.23/0.27 thf(c_0_18, negated_conjecture, ![X4:$i]:(((epred1_0 @ epred3_0 @ X4)|~((epred1_0 @ epred2_0 @ X4)))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16]), c_0_17])).
% 0.23/0.27 thf(c_0_19, negated_conjecture, ![X4:$i]:(((epred1_0 @ epred3_0 @ X4)|~((epred2_0 @ X4)))), inference(spm,[status(thm)],[c_0_18, c_0_6])).
% 0.23/0.27 thf(c_0_20, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17, c_0_19]), c_0_10])]), ['proof']).
% 0.23/0.27 % SZS output end CNFRefutation
% 0.23/0.27 % Parsed axioms : 1
% 0.23/0.27 % Removed by relevancy pruning/SinE : 0
% 0.23/0.27 % Initial clauses : 9
% 0.23/0.27 % Removed in clause preprocessing : 0
% 0.23/0.27 % Initial clauses in saturation : 9
% 0.23/0.27 % Processed clauses : 17
% 0.23/0.27 % ...of these trivial : 0
% 0.23/0.27 % ...subsumed : 1
% 0.23/0.27 % ...remaining for further processing : 16
% 0.23/0.27 % Other redundant clauses eliminated : 0
% 0.23/0.27 % Clauses deleted for lack of memory : 0
% 0.23/0.27 % Backward-subsumed : 0
% 0.23/0.27 % Backward-rewritten : 0
% 0.23/0.27 % Generated clauses : 21
% 0.23/0.27 % ...of the previous two non-redundant : 18
% 0.23/0.27 % ...aggressively subsumed : 0
% 0.23/0.27 % Contextual simplify-reflections : 1
% 0.23/0.27 % Paramodulations : 21
% 0.23/0.27 % Factorizations : 0
% 0.23/0.27 % NegExts : 0
% 0.23/0.27 % Equation resolutions : 0
% 0.23/0.27 % Disequality decompositions : 0
% 0.23/0.27 % Total rewrite steps : 1
% 0.23/0.27 % ...of those cached : 0
% 0.23/0.27 % Propositional unsat checks : 0
% 0.23/0.27 % Propositional check models : 0
% 0.23/0.27 % Propositional check unsatisfiable : 0
% 0.23/0.27 % Propositional clauses : 0
% 0.23/0.27 % Propositional clauses after purity: 0
% 0.23/0.27 % Propositional unsat core size : 0
% 0.23/0.27 % Propositional preprocessing time : 0.000
% 0.23/0.27 % Propositional encoding time : 0.000
% 0.23/0.27 % Propositional solver time : 0.000
% 0.23/0.27 % Success case prop preproc time : 0.000
% 0.23/0.27 % Success case prop encoding time : 0.000
% 0.23/0.27 % Success case prop solver time : 0.000
% 0.23/0.27 % Current number of processed clauses : 16
% 0.23/0.27 % Positive orientable unit clauses : 2
% 0.23/0.27 % Positive unorientable unit clauses: 0
% 0.23/0.27 % Negative unit clauses : 1
% 0.23/0.27 % Non-unit-clauses : 13
% 0.23/0.27 % Current number of unprocessed clauses: 8
% 0.23/0.27 % ...number of literals in the above : 29
% 0.23/0.27 % Current number of archived formulas : 0
% 0.23/0.27 % Current number of archived clauses : 0
% 0.23/0.27 % Clause-clause subsumption calls (NU) : 11
% 0.23/0.27 % Rec. Clause-clause subsumption calls : 11
% 0.23/0.27 % Non-unit clause-clause subsumptions : 2
% 0.23/0.27 % Unit Clause-clause subsumption calls : 0
% 0.23/0.27 % Rewrite failures with RHS unbound : 0
% 0.23/0.27 % BW rewrite match attempts : 0
% 0.23/0.27 % BW rewrite match successes : 0
% 0.23/0.27 % Condensation attempts : 0
% 0.23/0.27 % Condensation successes : 0
% 0.23/0.27 % Termbank termtop insertions : 1301
% 0.23/0.27 % Search garbage collected termcells : 393
% 0.23/0.27
% 0.23/0.27 % -------------------------------------------------
% 0.23/0.27 % User time : 0.003 s
% 0.23/0.27 % System time : 0.004 s
% 0.23/0.27 % Total time : 0.007 s
% 0.23/0.27 % Maximum resident set size: 3636 pages
% 0.23/0.27
% 0.23/0.27 % -------------------------------------------------
% 0.23/0.27 % User time : 0.004 s
% 0.23/0.27 % System time : 0.008 s
% 0.23/0.27 % Total time : 0.013 s
% 0.23/0.27 % Maximum resident set size: 4864 pages
% 0.23/0.27 % E exiting
%------------------------------------------------------------------------------