%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV067^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:34:49 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV067^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n005.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 15:06:15 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 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.MPOVLtqN4N/E---3.1_1778521.p
% 0.10/0.25 % Version: 3.5.1-ho
% 0.10/0.25 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.25 % Starting full_lambda_5 with 300s (1) cores
% 0.10/0.25 % Starting new_ho_10_unif with 300s (1) cores
% 0.10/0.25 % new_ho_10 with pid 1778534 completed with status 0
% 0.10/0.25 % Result found by new_ho_10
% 0.10/0.25 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.25 % No SInE strategy applied
% 0.10/0.25 % Search class: HGUSF-FFSS00-SFFFFFNN
% 0.10/0.25 % partial match(1): HGUSF-FFSF00-SFFFFFNN
% 0.10/0.25 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.25 % Starting SubtermCWHack with 151s (1) cores
% 0.10/0.25 % Starting new_ho_10 with 901s (1) cores
% 0.10/0.25 % Starting ehoh_best8_lambda with 151s (1) cores
% 0.10/0.25 % Starting ho_unfolding_6 with 151s (1) cores
% 0.10/0.25 % Starting sh4l with 146s (1) cores
% 0.10/0.25 % new_ho_10 with pid 1778539 completed with status 0
% 0.10/0.25 % Result found by new_ho_10
% 0.10/0.25 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.25 % No SInE strategy applied
% 0.10/0.25 % Search class: HGUSF-FFSS00-SFFFFFNN
% 0.10/0.25 % partial match(1): HGUSF-FFSF00-SFFFFFNN
% 0.10/0.25 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.25 % Starting SubtermCWHack with 151s (1) cores
% 0.10/0.25 % Starting new_ho_10 with 901s (1) cores
% 0.10/0.25 % Preprocessing time : 0.001 s
% 0.10/0.25 % Presaturation interreduction done
% 0.10/0.25
% 0.10/0.25 % Proof found!
% 0.10/0.25 % SZS status Theorem
% 0.10/0.25 % SZS output start CNFRefutation
% 0.10/0.25 thf(decl_sort1, type, a: $tType).
% 0.10/0.25 thf(decl_23, type, cS: a > $o).
% 0.10/0.25 thf(decl_24, type, cT: a > $o).
% 0.10/0.25 thf(decl_25, type, cR: a > a > $o).
% 0.10/0.25 thf(decl_26, type, epred1_0: $o).
% 0.10/0.25 thf(decl_27, type, esk1_0: a).
% 0.10/0.25 thf(decl_28, type, esk2_0: a).
% 0.10/0.25 thf(cTHM553_pme, conjecture, ((((((![X1:a, X2:a, X3:a]:((((cR @ X1 @ X2)&(cR @ X2 @ X3))=>(cR @ X1 @ X3)))&![X1:a]:((cR @ X1 @ X1)))&![X1:a, X2:a]:((((cR @ X1 @ X2)&(cR @ X2 @ X1))=>((X1)=(X2)))))&![X1:a, X2:a]:(((cR @ X1 @ X2)|(cR @ X2 @ X1))))&![X4:a, X5:a]:((((cR @ X4 @ X5)&(cS @ X5))=>(cS @ X4))))&![X4:a, X5:a]:((((cR @ X4 @ X5)&(cT @ X5))=>(cT @ X4))))=>(![X1:a]:(((cS @ X1)=>(cT @ X1)))|![X1:a]:(((cT @ X1)=>(cS @ X1))))), file('/export/starexec/sandbox2/tmp/tmp.MPOVLtqN4N/E---3.1_1778521.p', cTHM553_pme)).
% 0.10/0.25 thf(c_0_1, plain, ((epred1_0)<=>(((((![X1:a, X2:a, X3:a]:((((cR @ X1 @ X2)&(cR @ X2 @ X3))=>(cR @ X1 @ X3)))&![X1:a]:((cR @ X1 @ X1)))&![X1:a, X2:a]:((((cR @ X1 @ X2)&(cR @ X2 @ X1))=>((X1)=(X2)))))&![X1:a, X2:a]:(((cR @ X1 @ X2)|(cR @ X2 @ X1))))&![X4:a, X5:a]:((((cR @ X4 @ X5)&(cS @ X5))=>(cS @ X4))))&![X4:a, X5:a]:((((cR @ X4 @ X5)&(cT @ X5))=>(cT @ X4))))), introduced(definition)).
% 0.10/0.25 thf(c_0_2, negated_conjecture, ~(((((((![X1:a, X2:a, X3:a]:((((cR @ X1 @ X2)&(cR @ X2 @ X3))=>(cR @ X1 @ X3)))&![X1:a]:((cR @ X1 @ X1)))&![X1:a, X2:a]:((((cR @ X1 @ X2)&(cR @ X2 @ X1))=>((X1)=(X2)))))&![X1:a, X2:a]:(((cR @ X1 @ X2)|(cR @ X2 @ X1))))&![X4:a, X5:a]:((((cR @ X4 @ X5)&(cS @ X5))=>(cS @ X4))))&![X4:a, X5:a]:((((cR @ X4 @ X5)&(cT @ X5))=>(cT @ X4))))=>(![X1:a]:(((cS @ X1)=>(cT @ X1)))|![X1:a]:(((cT @ X1)=>(cS @ X1)))))), inference(assume_negation,[status(cth)],[cTHM553_pme])).
% 0.10/0.25 thf(c_0_3, plain, ((epred1_0)=>(((((![X1:a, X2:a, X3:a]:((((cR @ X1 @ X2)&(cR @ X2 @ X3))=>(cR @ X1 @ X3)))&![X1:a]:((cR @ X1 @ X1)))&![X1:a, X2:a]:((((cR @ X1 @ X2)&(cR @ X2 @ X1))=>((X1)=(X2)))))&![X1:a, X2:a]:(((cR @ X1 @ X2)|(cR @ X2 @ X1))))&![X4:a, X5:a]:((((cR @ X4 @ X5)&(cS @ X5))=>(cS @ X4))))&![X4:a, X5:a]:((((cR @ X4 @ X5)&(cT @ X5))=>(cT @ X4))))), inference(split_equiv,[status(thm)],[c_0_1])).
% 0.10/0.25 thf(c_0_4, negated_conjecture, ~(((epred1_0)=>(![X1:a]:(((cS @ X1)=>(cT @ X1)))|![X1:a]:(((cT @ X1)=>(cS @ X1)))))), inference(apply_def,[status(thm)],[c_0_2, c_0_1])).
% 0.10/0.25 thf(c_0_5, plain, ![X22:a, X23:a, X24:a, X25:a, X26:a, X27:a, X28:a, X29:a, X30:a, X31:a, X32:a, X33:a]:(((((((~(cR @ X22 @ X23)|~(cR @ X23 @ X24)|(cR @ X22 @ X24)|~(epred1_0))&((cR @ X25 @ X25)|~(epred1_0)))&(~(cR @ X26 @ X27)|~(cR @ X27 @ X26)|((X26)=(X27))|~(epred1_0)))&((cR @ X28 @ X29)|(cR @ X29 @ X28)|~(epred1_0)))&(~(cR @ X30 @ X31)|~(cS @ X31)|(cS @ X30)|~(epred1_0)))&(~(cR @ X32 @ X33)|~(cT @ X33)|(cT @ X32)|~(epred1_0)))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])])).
% 0.10/0.25 thf(c_0_6, negated_conjecture, ((epred1_0)&(((cS @ esk1_0)&~(cT @ esk1_0))&((cT @ esk2_0)&~(cS @ esk2_0)))), inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])).
% 0.10/0.25 thf(c_0_7, plain, ![X1:a, X2:a]:(((cT @ X1)|~((cR @ X1 @ X2))|~((cT @ X2))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.10/0.25 thf(c_0_8, negated_conjecture, (epred1_0), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.10/0.25 thf(c_0_9, plain, ![X2:a, X1:a]:(((cR @ X1 @ X2)|(cR @ X2 @ X1)|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.10/0.25 thf(c_0_10, plain, ![X1:a, X2:a]:(((cT @ X1)|~((cR @ X1 @ X2))|~((cT @ X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_7, c_0_8])])).
% 0.10/0.25 thf(c_0_11, plain, ![X2:a, X1:a]:(((cR @ X1 @ X2)|(cR @ X2 @ X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9, c_0_8])])).
% 0.10/0.25 thf(c_0_12, plain, ![X2:a, X1:a]:(((cR @ X1 @ X2)|(cT @ X2)|~((cT @ X1)))), inference(spm,[status(thm)],[c_0_10, c_0_11])).
% 0.10/0.25 thf(c_0_13, negated_conjecture, (cT @ esk2_0), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.10/0.25 thf(c_0_14, plain, ![X1:a, X2:a]:(((cS @ X1)|~((cR @ X1 @ X2))|~((cS @ X2))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.10/0.25 thf(c_0_15, negated_conjecture, ~((cT @ esk1_0)), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.10/0.25 thf(c_0_16, negated_conjecture, ![X1:a]:(((cR @ esk2_0 @ X1)|(cT @ X1))), inference(spm,[status(thm)],[c_0_12, c_0_13])).
% 0.10/0.25 thf(c_0_17, plain, ![X1:a, X2:a]:(((cS @ X1)|~((cR @ X1 @ X2))|~((cS @ X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_8])])).
% 0.10/0.25 thf(c_0_18, negated_conjecture, (cR @ esk2_0 @ esk1_0), inference(spm,[status(thm)],[c_0_15, c_0_16])).
% 0.10/0.25 thf(c_0_19, negated_conjecture, (cS @ esk1_0), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.10/0.25 thf(c_0_20, negated_conjecture, ~((cS @ esk2_0)), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.10/0.25 thf(c_0_21, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17, c_0_18]), c_0_19])]), c_0_20]), ['proof']).
% 0.10/0.25 % SZS output end CNFRefutation
% 0.10/0.25 % Parsed axioms : 5
% 0.10/0.25 % Removed by relevancy pruning/SinE : 0
% 0.10/0.25 % Initial clauses : 15
% 0.10/0.25 % Removed in clause preprocessing : 4
% 0.10/0.25 % Initial clauses in saturation : 11
% 0.10/0.25 % Processed clauses : 24
% 0.10/0.25 % ...of these trivial : 0
% 0.10/0.25 % ...subsumed : 0
% 0.10/0.25 % ...remaining for further processing : 24
% 0.10/0.25 % Other redundant clauses eliminated : 0
% 0.10/0.25 % Clauses deleted for lack of memory : 0
% 0.10/0.25 % Backward-subsumed : 0
% 0.10/0.25 % Backward-rewritten : 0
% 0.10/0.25 % Generated clauses : 16
% 0.10/0.25 % ...of the previous two non-redundant : 7
% 0.10/0.25 % ...aggressively subsumed : 0
% 0.10/0.25 % Contextual simplify-reflections : 0
% 0.10/0.25 % Paramodulations : 14
% 0.10/0.25 % Factorizations : 2
% 0.10/0.25 % NegExts : 0
% 0.10/0.25 % Equation resolutions : 0
% 0.10/0.25 % Disequality decompositions : 0
% 0.10/0.25 % Total rewrite steps : 10
% 0.10/0.25 % ...of those cached : 5
% 0.10/0.25 % Propositional unsat checks : 0
% 0.10/0.25 % Propositional check models : 0
% 0.10/0.25 % Propositional check unsatisfiable : 0
% 0.10/0.25 % Propositional clauses : 0
% 0.10/0.25 % Propositional clauses after purity: 0
% 0.10/0.25 % Propositional unsat core size : 0
% 0.10/0.25 % Propositional preprocessing time : 0.000
% 0.10/0.25 % Propositional encoding time : 0.000
% 0.10/0.25 % Propositional solver time : 0.000
% 0.10/0.25 % Success case prop preproc time : 0.000
% 0.10/0.25 % Success case prop encoding time : 0.000
% 0.10/0.25 % Success case prop solver time : 0.000
% 0.10/0.25 % Current number of processed clauses : 13
% 0.10/0.25 % Positive orientable unit clauses : 5
% 0.10/0.25 % Positive unorientable unit clauses: 0
% 0.10/0.25 % Negative unit clauses : 2
% 0.10/0.25 % Non-unit-clauses : 6
% 0.10/0.25 % Current number of unprocessed clauses: 5
% 0.10/0.25 % ...number of literals in the above : 15
% 0.10/0.25 % Current number of archived formulas : 0
% 0.10/0.25 % Current number of archived clauses : 11
% 0.10/0.25 % Clause-clause subsumption calls (NU) : 7
% 0.10/0.25 % Rec. Clause-clause subsumption calls : 7
% 0.10/0.25 % Non-unit clause-clause subsumptions : 0
% 0.10/0.25 % Unit Clause-clause subsumption calls : 2
% 0.10/0.25 % Rewrite failures with RHS unbound : 0
% 0.10/0.25 % BW rewrite match attempts : 0
% 0.10/0.25 % BW rewrite match successes : 0
% 0.10/0.25 % Condensation attempts : 24
% 0.10/0.25 % Condensation successes : 0
% 0.10/0.25 % Termbank termtop insertions : 1113
% 0.10/0.25 % Search garbage collected termcells : 266
% 0.10/0.25
% 0.10/0.25 % -------------------------------------------------
% 0.10/0.25 % User time : 0.002 s
% 0.10/0.25 % System time : 0.003 s
% 0.10/0.25 % Total time : 0.005 s
% 0.10/0.25 % Maximum resident set size: 3636 pages
% 0.10/0.25
% 0.10/0.25 % -------------------------------------------------
% 0.10/0.25 % User time : 0.004 s
% 0.10/0.25 % System time : 0.014 s
% 0.10/0.25 % Total time : 0.018 s
% 0.10/0.25 % Maximum resident set size: 4608 pages
% 0.10/0.25 % E exiting
%------------------------------------------------------------------------------