%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SYO325^5 : 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 08:44:12 AM UTC 2026
% Result : Theorem 0.23s 0.32s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO325^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n005.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 16:45:16 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.29 Running higher-order theorem proving
% 0.23/0.30 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.bn0OeiPZUr/E---3.1_1902155.p
% 0.23/0.32 % Version: 3.5.1-ho
% 0.23/0.32 % Preprocessing class: HSSSSMSSSSMNSSA.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting sh3 with 1500s (5) cores
% 0.23/0.32 % Starting lpo8_s with 300s (1) cores
% 0.23/0.32 % Starting sh2lt with 300s (1) cores
% 0.23/0.32 % Starting sh2l with 300s (1) cores
% 0.23/0.32 % sh2lt with pid 1902170 completed with status 0
% 0.23/0.32 % Result found by sh2lt
% 0.23/0.32 % Preprocessing class: HSSSSMSSSSMNSSA.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting sh3 with 1500s (5) cores
% 0.23/0.32 % Starting lpo8_s with 300s (1) cores
% 0.23/0.32 % Starting sh2lt with 300s (1) cores
% 0.23/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.23/0.32 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.23/0.32 % Search class: HGUNF-FFSF22-SSSFFMBN
% 0.23/0.32 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.32 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.32 % SubtermCWHack with pid 1902174 completed with status 0
% 0.23/0.32 % Result found by SubtermCWHack
% 0.23/0.32 % Preprocessing class: HSSSSMSSSSMNSSA.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting sh3 with 1500s (5) cores
% 0.23/0.32 % Starting lpo8_s with 300s (1) cores
% 0.23/0.32 % Starting sh2lt with 300s (1) cores
% 0.23/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.23/0.32 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.23/0.32 % Search class: HGUNF-FFSF22-SSSFFMBN
% 0.23/0.32 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.32 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.32 % Preprocessing time : 0.001 s
% 0.23/0.32
% 0.23/0.32 % Proof found!
% 0.23/0.32 % SZS status Theorem
% 0.23/0.32 % SZS output start CNFRefutation
% 0.23/0.32 thf(decl_sort1, type, a: $tType).
% 0.23/0.32 thf(decl_23, type, cK: (a > $o) > a > $o).
% 0.23/0.32 thf(decl_24, type, esk1_2: (a > $o) > (a > $o) > a).
% 0.23/0.32 thf(decl_25, type, esk2_0: a).
% 0.23/0.32 thf(decl_26, type, epred1_0: a > $o).
% 0.23/0.32 thf(decl_27, type, epred2_1: a > a > $o).
% 0.23/0.32 thf(decl_28, type, esk3_2: a > (a > $o) > a).
% 0.23/0.32 thf(cTHM116_1SS, 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)=>(cK @ (cK @ (^[X4:a]:(?[X5:a > $o]:(((![X6:a]:((((X5 @ X6))=>((cK @ X5 @ X6)))))&((X5 @ X4))))))) @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.bn0OeiPZUr/E---3.1_1902155.p', cTHM116_1SS)).
% 0.23/0.32 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)=>(cK @ (cK @ (^[X4:a]:(?[X5:a > $o]:(((![X6:a]:((((X5 @ X6))=>((cK @ X5 @ X6)))))&((X5 @ X4))))))) @ X3))))), inference(assume_negation,[status(cth)],[cTHM116_1SS])).
% 0.23/0.32 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)=>(cK @ (cK @ (^[Z0:a]:(?[X5:a > $o]:(((![X6:a]:(((X5 @ X6)=>((cK @ X5 @ X6)))))&(X5 @ Z0)))))) @ X3))))), inference(fof_simplification,[status(thm)],[c_0_1])).
% 0.23/0.32 thf(c_0_3, negated_conjecture, ![X12:a > $o, X13:a > $o, X15:a]:(((((X12 @ (esk1_2 @ X12 @ X13))|(~(cK @ X12 @ X15)|(cK @ X13 @ X15)))&(~(X13 @ (esk1_2 @ X12 @ X13))|(~(cK @ X12 @ X15)|(cK @ X13 @ X15))))&((cK @ (^[Z0:a]:(?[X5:a > $o]:(((![X6:a]:(((X5 @ X6)=>((cK @ X5 @ X6)))))&(X5 @ Z0))))) @ esk2_0)&~(cK @ (cK @ (^[Z0:a]:(?[X5:a > $o]:(((![X6:a]:(((X5 @ X6)=>((cK @ X5 @ X6)))))&(X5 @ 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])])])])])])).
% 0.23/0.32 thf(c_0_4, plain, ![X23:a, X25:a, X26:a > $o]:((((~(epred2_1 @ X23 @ X25)|(cK @ (epred2_1 @ X23) @ X25)|~(epred1_0 @ X23))&((epred2_1 @ X23 @ X23)|~(epred1_0 @ X23)))&(((X26 @ (esk3_2 @ X23 @ X26))|~(X26 @ X23)|(epred1_0 @ X23))&(~(cK @ X26 @ (esk3_2 @ X23 @ X26))|~(X26 @ X23)|(epred1_0 @ X23))))), 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)],[])])])])])])).
% 0.23/0.32 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])).
% 0.23/0.32 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])).
% 0.23/0.32 thf(c_0_7, plain, ![X1:a > $o, X3:a]:(((epred1_0 @ X3)|~((cK @ X1 @ (esk3_2 @ X3 @ X1)))|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_4])).
% 0.23/0.32 thf(c_0_8, plain, ![X1:a > $o, X3:a]:(((X1 @ (esk3_2 @ X3 @ X1))|(epred1_0 @ X3)|~((X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_4])).
% 0.23/0.32 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])).
% 0.23/0.32 thf(c_0_10, plain, ![X3:a]:(((epred2_1 @ X3 @ X3)|~((epred1_0 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_4])).
% 0.23/0.32 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])).
% 0.23/0.32 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])).
% 0.23/0.32 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])).
% 0.23/0.32 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])).
% 0.23/0.32 thf(c_0_15, 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])).
% 0.23/0.32 thf(c_0_16, plain, ![X19:a]:(((epred1_0 @ X19)<=>?[X17:a > $o]:((![X18:a]:(((X17 @ X18)=>(cK @ X17 @ X18)))&(X17 @ X19))))), introduced(definition)).
% 0.23/0.32 thf(c_0_17, plain, ![X3:a, X4:a]:(((cK @ epred1_0 @ X3)|(cK @ epred1_0 @ X4)|~((epred2_1 @ X4 @ X3))|~((epred1_0 @ X4)))), inference(spm,[status(thm)],[c_0_15, c_0_6])).
% 0.23/0.32 thf(c_0_18, negated_conjecture, (((cK @ epred1_0 @ esk2_0))=(($true))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_3]), c_0_16])).
% 0.23/0.32 thf(c_0_19, plain, ![X3:a]:(((cK @ epred1_0 @ X3)|~((epred1_0 @ X3)))), inference(spm,[status(thm)],[c_0_17, c_0_10])).
% 0.23/0.32 thf(c_0_20, negated_conjecture, (cK @ epred1_0 @ esk2_0), inference(cn,[status(thm)],[c_0_18])).
% 0.23/0.32 thf(c_0_21, negated_conjecture, ~((((cK @ (cK @ epred1_0) @ esk2_0))=(($true)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_3]), c_0_16])).
% 0.23/0.32 thf(c_0_22, 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_19])).
% 0.23/0.32 thf(c_0_23, negated_conjecture, ![X1:a > $o]:(((epred1_0 @ (esk1_2 @ epred1_0 @ X1))|(cK @ X1 @ esk2_0))), inference(spm,[status(thm)],[c_0_5, c_0_20])).
% 0.23/0.32 thf(c_0_24, negated_conjecture, ~((cK @ (cK @ epred1_0) @ esk2_0)), inference(cn,[status(thm)],[c_0_21])).
% 0.23/0.32 thf(c_0_25, negated_conjecture, ![X3:a]:(((cK @ (cK @ epred1_0) @ X3)|~((cK @ epred1_0 @ X3)))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23]), c_0_24])).
% 0.23/0.32 thf(c_0_26, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_25]), c_0_20])]), ['proof']).
% 0.23/0.32 % SZS output end CNFRefutation
% 0.23/0.32 % Parsed axioms : 3
% 0.23/0.32 % Removed by relevancy pruning/SinE : 2
% 0.23/0.32 % Initial clauses : 8
% 0.23/0.32 % Removed in clause preprocessing : 0
% 0.23/0.32 % Initial clauses in saturation : 8
% 0.23/0.32 % Processed clauses : 24
% 0.23/0.33 % ...of these trivial : 0
% 0.23/0.33 % ...subsumed : 1
% 0.23/0.33 % ...remaining for further processing : 23
% 0.23/0.33 % Other redundant clauses eliminated : 0
% 0.23/0.33 % Clauses deleted for lack of memory : 0
% 0.23/0.33 % Backward-subsumed : 2
% 0.23/0.33 % Backward-rewritten : 0
% 0.23/0.33 % Generated clauses : 43
% 0.23/0.33 % ...of the previous two non-redundant : 36
% 0.23/0.33 % ...aggressively subsumed : 0
% 0.23/0.33 % Contextual simplify-reflections : 1
% 0.23/0.33 % Paramodulations : 43
% 0.23/0.33 % Factorizations : 0
% 0.23/0.33 % NegExts : 0
% 0.23/0.33 % Equation resolutions : 0
% 0.23/0.33 % Disequality decompositions : 0
% 0.23/0.33 % Total rewrite steps : 3
% 0.23/0.33 % ...of those cached : 2
% 0.23/0.33 % Propositional unsat checks : 0
% 0.23/0.33 % Propositional check models : 0
% 0.23/0.33 % Propositional check unsatisfiable : 0
% 0.23/0.33 % Propositional clauses : 0
% 0.23/0.33 % Propositional clauses after purity: 0
% 0.23/0.33 % Propositional unsat core size : 0
% 0.23/0.33 % Propositional preprocessing time : 0.000
% 0.23/0.33 % Propositional encoding time : 0.000
% 0.23/0.33 % Propositional solver time : 0.000
% 0.23/0.33 % Success case prop preproc time : 0.000
% 0.23/0.33 % Success case prop encoding time : 0.000
% 0.23/0.33 % Success case prop solver time : 0.000
% 0.23/0.33 % Current number of processed clauses : 21
% 0.23/0.33 % Positive orientable unit clauses : 1
% 0.23/0.33 % Positive unorientable unit clauses: 0
% 0.23/0.33 % Negative unit clauses : 1
% 0.23/0.33 % Non-unit-clauses : 19
% 0.23/0.33 % Current number of unprocessed clauses: 16
% 0.23/0.33 % ...number of literals in the above : 68
% 0.23/0.33 % Current number of archived formulas : 0
% 0.23/0.33 % Current number of archived clauses : 2
% 0.23/0.33 % Clause-clause subsumption calls (NU) : 70
% 0.23/0.33 % Rec. Clause-clause subsumption calls : 52
% 0.23/0.33 % Non-unit clause-clause subsumptions : 4
% 0.23/0.33 % Unit Clause-clause subsumption calls : 0
% 0.23/0.33 % Rewrite failures with RHS unbound : 0
% 0.23/0.33 % BW rewrite match attempts : 0
% 0.23/0.33 % BW rewrite match successes : 0
% 0.23/0.33 % Condensation attempts : 0
% 0.23/0.33 % Condensation successes : 0
% 0.23/0.33 % Termbank termtop insertions : 1844
% 0.23/0.33 % Search garbage collected termcells : 329
% 0.23/0.33
% 0.23/0.33 % -------------------------------------------------
% 0.23/0.33 % User time : 0.006 s
% 0.23/0.33 % System time : 0.003 s
% 0.23/0.33 % Total time : 0.009 s
% 0.23/0.33 % Maximum resident set size: 3632 pages
% 0.23/0.33
% 0.23/0.33 % -------------------------------------------------
% 0.23/0.33 % User time : 0.010 s
% 0.23/0.33 % System time : 0.005 s
% 0.23/0.33 % Total time : 0.015 s
% 0.23/0.33 % Maximum resident set size: 4864 pages
% 0.23/0.33 % E exiting
%------------------------------------------------------------------------------