%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV246^6 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 08:35:16 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV246^6 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n016.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 15:32:04 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 Running higher-order theorem proving
% 0.23/0.27 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.1UReCDky31/E---3.1_486138.p
% 0.23/0.30 % Version: 3.5.1-ho
% 0.23/0.30 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.23/0.30 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting post_as_ho12 with 300s (1) cores
% 0.23/0.30 % Starting new_bool_9 with 300s (1) cores
% 0.23/0.30 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.30 % Starting post_as_ho4 with 300s (1) cores
% 0.23/0.30 % Starting post_as_ho2 with 300s (1) cores
% 0.23/0.30 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.23/0.30 % Starting full_lambda_10 with 300s (1) cores
% 0.23/0.30 % Starting new_ho_8 with 300s (1) cores
% 0.23/0.30 % post_as_ho1 with pid 486153 completed with status 0
% 0.23/0.30 % Result found by post_as_ho1
% 0.23/0.30 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.23/0.30 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting post_as_ho12 with 300s (1) cores
% 0.23/0.30 % Starting new_bool_9 with 300s (1) cores
% 0.23/0.30 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.30 % No SInE strategy applied
% 0.23/0.30 % Search class: HGHNF-FFSF21-SSSFFMBN
% 0.23/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.30 % SubtermCWHack with pid 486164 completed with status 0
% 0.23/0.30 % Result found by SubtermCWHack
% 0.23/0.30 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.23/0.30 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting post_as_ho12 with 300s (1) cores
% 0.23/0.30 % Starting new_bool_9 with 300s (1) cores
% 0.23/0.30 % Starting post_as_ho1 with 300s (1) cores
% 0.23/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.30 % No SInE strategy applied
% 0.23/0.30 % Search class: HGHNF-FFSF21-SSSFFMBN
% 0.23/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.30 % Preprocessing time : 0.001 s
% 0.23/0.30
% 0.23/0.30 % Proof found!
% 0.23/0.30 % SZS status Theorem
% 0.23/0.30 % SZS output start CNFRefutation
% 0.23/0.30 thf(decl_sort1, type, a: $tType).
% 0.23/0.30 thf(decl_23, type, cK: (a > $o) > a > $o).
% 0.23/0.30 thf(decl_24, type, esk1_2: (a > $o) > (a > $o) > a).
% 0.23/0.30 thf(decl_25, type, esk2_0: a).
% 0.23/0.30 thf(decl_26, type, esk3_1: (a > $o) > a).
% 0.23/0.30 thf(decl_27, type, epred1_0: a > $o).
% 0.23/0.30 thf(decl_28, type, epred2_1: a > a > $o).
% 0.23/0.30 thf(decl_29, type, esk4_2: a > (a > $o) > a).
% 0.23/0.30 thf(cTHM116_1S, conjecture, (![X1:a > $o, X2:a > $o]:((![X3:a]:(((X1 @ X3)=>(X2 @ X3)))=>![X3:a]:(((cK @ X1 @ X3)=>(cK @ X2 @ X3)))))=>![X3:a]:(((cK @ (^[X4:a]:(?[X5:a > $o]:(((![X6:a]:((((X5 @ X6))=>((cK @ X5 @ X6)))))&((X5 @ X4)))))) @ X3)=>?[X5:a > $o]:((![X4:a]:(((X5 @ X4)=>(cK @ X5 @ X4)))&(X5 @ X3)))))), file('/export/starexec/sandbox/tmp/tmp.1UReCDky31/E---3.1_486138.p', cTHM116_1S)).
% 0.23/0.30 thf(c_0_1, negated_conjecture, ~((![X1:a > $o, X2:a > $o]:((![X3:a]:(((X1 @ X3)=>(X2 @ X3)))=>![X3:a]:(((cK @ X1 @ X3)=>(cK @ X2 @ X3)))))=>![X3:a]:(((cK @ (^[X4:a]:(?[X5:a > $o]:(((![X6:a]:((((X5 @ X6))=>((cK @ X5 @ X6)))))&((X5 @ X4)))))) @ X3)=>?[X5:a > $o]:((![X4:a]:(((X5 @ X4)=>(cK @ X5 @ X4)))&(X5 @ X3))))))), inference(assume_negation,[status(cth)],[cTHM116_1S])).
% 0.23/0.30 thf(c_0_2, negated_conjecture, ~((![X1:a > $o, X2:a > $o]:((![X3:a]:(((X1 @ X3)=>(X2 @ X3)))=>![X3:a]:(((cK @ X1 @ X3)=>(cK @ X2 @ X3)))))=>![X3:a]:(((cK @ (^[Z0:a]:(?[X5:a > $o]:(((![X6:a]:(((X5 @ X6)=>((cK @ X5 @ X6)))))&(X5 @ Z0))))) @ X3)=>?[X5:a > $o]:((![X4:a]:(((X5 @ X4)=>(cK @ X5 @ X4)))&(X5 @ X3))))))), inference(fof_simplification,[status(thm)],[c_0_1])).
% 0.23/0.30 thf(c_0_3, negated_conjecture, ![X14:a > $o, X15:a > $o, X17:a, X19:a > $o]:(((((X14 @ (esk1_2 @ X14 @ X15))|(~(cK @ X14 @ X17)|(cK @ X15 @ X17)))&(~(X15 @ (esk1_2 @ X14 @ X15))|(~(cK @ X14 @ X17)|(cK @ X15 @ X17))))&((cK @ (^[Z0:a]:(?[X5:a > $o]:(((![X6:a]:(((X5 @ X6)=>((cK @ X5 @ X6)))))&(X5 @ Z0))))) @ esk2_0)&(((X19 @ (esk3_1 @ X19))|~(X19 @ esk2_0))&(~(cK @ X19 @ (esk3_1 @ X19))|~(X19 @ 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])])])])])])).
% 0.23/0.30 thf(c_0_4, plain, ![X24:a, X26:a, X27:a > $o]:((((~(epred2_1 @ X24 @ X26)|(cK @ (epred2_1 @ X24) @ X26)|~(epred1_0 @ X24))&((epred2_1 @ X24 @ X24)|~(epred1_0 @ X24)))&(((X27 @ (esk4_2 @ X24 @ X27))|~(X27 @ X24)|(epred1_0 @ X24))&(~(cK @ X27 @ (esk4_2 @ X24 @ X27))|~(X27 @ X24)|(epred1_0 @ X24))))), 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)],[])])])])])])).
% 0.23/0.30 thf(c_0_5, negated_conjecture, ![X1:a > $o, X2:a > $o, X3:a]:(((X1 @ (esk1_2 @ X1 @ X2))|(cK @ X2 @ X3)|~((cK @ X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_3])).
% 0.23/0.30 thf(c_0_6, plain, ![X4:a, X3:a]:(((cK @ (epred2_1 @ X3) @ X4)|~((epred2_1 @ X3 @ X4))|~((epred1_0 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_4])).
% 0.23/0.30 thf(c_0_7, plain, ![X1:a > $o, X3:a]:(((epred1_0 @ X3)|~((cK @ X1 @ (esk4_2 @ X3 @ X1)))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_4])).
% 0.23/0.30 thf(c_0_8, plain, ![X1:a > $o, X3:a]:(((X1 @ (esk4_2 @ X3 @ X1))|(epred1_0 @ X3)|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_4])).
% 0.23/0.30 thf(c_0_9, plain, ![X1:a > $o, X4:a, X3:a]:(((epred2_1 @ X3 @ (esk1_2 @ (epred2_1 @ X3) @ X1))|(cK @ X1 @ X4)|~((epred2_1 @ X3 @ X4))|~((epred1_0 @ X3)))), inference(spm,[status(thm)],[c_0_5, c_0_6])).
% 0.23/0.30 thf(c_0_10, plain, ![X3:a]:(((epred2_1 @ X3 @ X3)|~((epred1_0 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_4])).
% 0.23/0.30 thf(c_0_11, plain, ![X3:a, X4:a]:(((epred1_0 @ X3)|~((epred2_1 @ X4 @ X3))|~((epred1_0 @ X4)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7, c_0_6]), c_0_8])).
% 0.23/0.30 thf(c_0_12, plain, ![X1:a > $o, X3:a]:(((epred2_1 @ X3 @ (esk1_2 @ (epred2_1 @ X3) @ X1))|(cK @ X1 @ X3)|~((epred1_0 @ X3)))), inference(spm,[status(thm)],[c_0_9, c_0_10])).
% 0.23/0.30 thf(c_0_13, negated_conjecture, ![X1:a > $o, X2:a > $o, X3:a]:(((cK @ X1 @ X3)|~((X1 @ (esk1_2 @ X2 @ X1)))|~((cK @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_3])).
% 0.23/0.30 thf(c_0_14, plain, ![X1:a > $o, X3:a]:(((epred1_0 @ (esk1_2 @ (epred2_1 @ X3) @ X1))|(cK @ X1 @ X3)|~((epred1_0 @ X3)))), inference(spm,[status(thm)],[c_0_11, c_0_12])).
% 0.23/0.30 thf(c_0_15, plain, ![X23:a]:(((epred1_0 @ X23)<=>?[X21:a > $o]:((![X22:a]:(((X21 @ X22)=>(cK @ X21 @ X22)))&(X21 @ X23))))), introduced(definition)).
% 0.23/0.30 thf(c_0_16, negated_conjecture, ![X4:a, X3:a]:(((cK @ epred1_0 @ X3)|(cK @ epred1_0 @ X4)|~((cK @ (epred2_1 @ X3) @ X4))|~((epred1_0 @ X3)))), inference(spm,[status(thm)],[c_0_13, c_0_14])).
% 0.23/0.30 thf(c_0_17, negated_conjecture, ![X1:a > $o]:(((X1 @ (esk3_1 @ X1))|~((X1 @ esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_3])).
% 0.23/0.30 thf(c_0_18, negated_conjecture, (((cK @ epred1_0 @ esk2_0))=(($true))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_3]), c_0_15])).
% 0.23/0.30 thf(c_0_19, plain, ![X3:a, X4:a]:(((cK @ epred1_0 @ X3)|(cK @ epred1_0 @ X4)|~((epred2_1 @ X4 @ X3))|~((epred1_0 @ X4)))), inference(spm,[status(thm)],[c_0_16, c_0_6])).
% 0.23/0.30 thf(c_0_20, negated_conjecture, ![X1:a > $o, X2:a > $o]:(((cK @ X1 @ (esk3_1 @ (cK @ X2)))|(X2 @ (esk1_2 @ X2 @ X1))|~((cK @ X2 @ esk2_0)))), inference(spm,[status(thm)],[c_0_5, c_0_17])).
% 0.23/0.30 thf(c_0_21, negated_conjecture, (cK @ epred1_0 @ esk2_0), inference(cn,[status(thm)],[c_0_18])).
% 0.23/0.30 thf(c_0_22, plain, ![X3:a]:(((cK @ epred1_0 @ X3)|~((epred1_0 @ X3)))), inference(spm,[status(thm)],[c_0_19, c_0_10])).
% 0.23/0.30 thf(c_0_23, negated_conjecture, ![X1:a > $o]:((~((cK @ X1 @ (esk3_1 @ X1)))|~((X1 @ esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_3])).
% 0.23/0.30 thf(c_0_24, negated_conjecture, ![X1:a > $o]:(((cK @ X1 @ (esk3_1 @ (cK @ epred1_0)))|(epred1_0 @ (esk1_2 @ epred1_0 @ X1)))), inference(spm,[status(thm)],[c_0_20, c_0_21])).
% 0.23/0.30 thf(c_0_25, negated_conjecture, ![X1:a > $o, X3:a]:(((cK @ (cK @ epred1_0) @ X3)|~((epred1_0 @ (esk1_2 @ X1 @ (cK @ epred1_0))))|~((cK @ X1 @ X3)))), inference(spm,[status(thm)],[c_0_13, c_0_22])).
% 0.23/0.30 thf(c_0_26, negated_conjecture, (epred1_0 @ (esk1_2 @ epred1_0 @ (cK @ epred1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24]), c_0_21])])).
% 0.23/0.30 thf(c_0_27, negated_conjecture, ![X3:a]:(((cK @ (cK @ epred1_0) @ X3)|~((cK @ epred1_0 @ X3)))), inference(spm,[status(thm)],[c_0_25, c_0_26])).
% 0.23/0.30 thf(c_0_28, negated_conjecture, ~((cK @ epred1_0 @ (esk3_1 @ (cK @ epred1_0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_27]), c_0_21])])).
% 0.23/0.30 thf(c_0_29, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_17]), c_0_21])]), ['proof']).
% 0.23/0.30 % SZS output end CNFRefutation
% 0.23/0.30 % Parsed axioms : 3
% 0.23/0.30 % Removed by relevancy pruning/SinE : 0
% 0.23/0.30 % Initial clauses : 11
% 0.23/0.30 % Removed in clause preprocessing : 2
% 0.23/0.30 % Initial clauses in saturation : 9
% 0.23/0.30 % Processed clauses : 43
% 0.23/0.30 % ...of these trivial : 0
% 0.23/0.30 % ...subsumed : 5
% 0.23/0.30 % ...remaining for further processing : 38
% 0.23/0.30 % Other redundant clauses eliminated : 0
% 0.23/0.30 % Clauses deleted for lack of memory : 0
% 0.23/0.30 % Backward-subsumed : 3
% 0.23/0.30 % Backward-rewritten : 2
% 0.23/0.30 % Generated clauses : 111
% 0.23/0.30 % ...of the previous two non-redundant : 91
% 0.23/0.30 % ...aggressively subsumed : 0
% 0.23/0.30 % Contextual simplify-reflections : 2
% 0.23/0.30 % Paramodulations : 111
% 0.23/0.30 % Factorizations : 0
% 0.23/0.30 % NegExts : 0
% 0.23/0.30 % Equation resolutions : 0
% 0.23/0.30 % Disequality decompositions : 0
% 0.23/0.30 % Total rewrite steps : 18
% 0.23/0.30 % ...of those cached : 15
% 0.23/0.30 % Propositional unsat checks : 0
% 0.23/0.30 % Propositional check models : 0
% 0.23/0.30 % Propositional check unsatisfiable : 0
% 0.23/0.30 % Propositional clauses : 0
% 0.23/0.30 % Propositional clauses after purity: 0
% 0.23/0.30 % Propositional unsat core size : 0
% 0.23/0.30 % Propositional preprocessing time : 0.000
% 0.23/0.30 % Propositional encoding time : 0.000
% 0.23/0.30 % Propositional solver time : 0.000
% 0.23/0.30 % Success case prop preproc time : 0.000
% 0.23/0.30 % Success case prop encoding time : 0.000
% 0.23/0.30 % Success case prop solver time : 0.000
% 0.23/0.30 % Current number of processed clauses : 33
% 0.23/0.30 % Positive orientable unit clauses : 3
% 0.23/0.30 % Positive unorientable unit clauses: 0
% 0.23/0.30 % Negative unit clauses : 2
% 0.23/0.30 % Non-unit-clauses : 28
% 0.23/0.30 % Current number of unprocessed clauses: 53
% 0.23/0.30 % ...number of literals in the above : 210
% 0.23/0.30 % Current number of archived formulas : 0
% 0.23/0.30 % Current number of archived clauses : 5
% 0.23/0.30 % Clause-clause subsumption calls (NU) : 115
% 0.23/0.30 % Rec. Clause-clause subsumption calls : 97
% 0.23/0.30 % Non-unit clause-clause subsumptions : 6
% 0.23/0.30 % Unit Clause-clause subsumption calls : 9
% 0.23/0.30 % Rewrite failures with RHS unbound : 0
% 0.23/0.30 % BW rewrite match attempts : 1
% 0.23/0.30 % BW rewrite match successes : 1
% 0.23/0.30 % Condensation attempts : 0
% 0.23/0.30 % Condensation successes : 0
% 0.23/0.30 % Termbank termtop insertions : 3074
% 0.23/0.30 % Search garbage collected termcells : 352
% 0.23/0.30
% 0.23/0.30 % -------------------------------------------------
% 0.23/0.30 % User time : 0.008 s
% 0.23/0.30 % System time : 0.003 s
% 0.23/0.30 % Total time : 0.010 s
% 0.23/0.30 % Maximum resident set size: 3632 pages
% 0.23/0.30
% 0.23/0.30 % -------------------------------------------------
% 0.23/0.30 % User time : 0.011 s
% 0.23/0.30 % System time : 0.007 s
% 0.23/0.30 % Total time : 0.017 s
% 0.23/0.30 % Maximum resident set size: 4608 pages
% 0.23/0.30 % E exiting
%------------------------------------------------------------------------------