%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO324^5 : 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 : n004.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 08:42:45 AM UTC 2026
% Result : Theorem 0.27s 0.36s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO324^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 % Computer : n004.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Tue Sep 29 16:45:22 UTC 2026
% 0.09/0.25 % CPUTime :
% 0.09/0.25 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.31 Running higher-order theorem proving
% 0.27/0.33 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.YlPWuVMPaD/E---3.1_1544730.p
% 0.27/0.36 % Version: 3.5.1-ho
% 0.27/0.36 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.27/0.36 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.36 % Starting sh2lt with 1200s (4) cores
% 0.27/0.36 % Starting new_ho_10_unif with 300s (1) cores
% 0.27/0.36 % Starting full_lambda_6 with 300s (1) cores
% 0.27/0.36 % Starting post_as_ho1 with 300s (1) cores
% 0.27/0.36 % Starting ehoh_best3_rw with 300s (1) cores
% 0.27/0.36 % post_as_ho1 with pid 1544746 completed with status 0
% 0.27/0.36 % Result found by post_as_ho1
% 0.27/0.36 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.27/0.36 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.36 % Starting sh2lt with 1200s (4) cores
% 0.27/0.36 % Starting new_ho_10_unif with 300s (1) cores
% 0.27/0.36 % Starting full_lambda_6 with 300s (1) cores
% 0.27/0.36 % Starting post_as_ho1 with 300s (1) cores
% 0.27/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.36 % No SInE strategy applied
% 0.27/0.36 % Search class: HGHNF-FFSF00-SHHFFMBN
% 0.27/0.36 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.36 % Starting SubtermCWHack with 28s (1) cores
% 0.27/0.36 % SubtermCWHack with pid 1544748 completed with status 0
% 0.27/0.36 % Result found by SubtermCWHack
% 0.27/0.36 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.27/0.36 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.36 % Starting sh2lt with 1200s (4) cores
% 0.27/0.36 % Starting new_ho_10_unif with 300s (1) cores
% 0.27/0.36 % Starting full_lambda_6 with 300s (1) cores
% 0.27/0.36 % Starting post_as_ho1 with 300s (1) cores
% 0.27/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.36 % No SInE strategy applied
% 0.27/0.36 % Search class: HGHNF-FFSF00-SHHFFMBN
% 0.27/0.36 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.36 % Starting SubtermCWHack with 28s (1) cores
% 0.27/0.36 % Preprocessing time : 0.002 s
% 0.27/0.36
% 0.27/0.36 % Proof found!
% 0.27/0.36 % SZS status Theorem
% 0.27/0.36 % SZS output start CNFRefutation
% 0.27/0.36 thf(decl_23, type, esk1_0: ($i > $o) > $i).
% 0.27/0.36 thf(decl_24, type, epred1_2: ($i > $o) > ($i > $o) > $i > $o).
% 0.27/0.36 thf(decl_25, type, epred2_0: $i > $o).
% 0.27/0.36 thf(decl_26, type, epred3_0: $i > $o).
% 0.27/0.36 thf(decl_27, type, epred4_1: $i > $i > $o).
% 0.27/0.36 thf(decl_28, type, epred5_2: $i > ($i > $o) > $i > $o).
% 0.27/0.36 thf(cTHM143_EXPANDB, conjecture, ![X1:($i > $o) > $i]:((?[X2:$i > $o, X3:$i > $o]:((![X4:$i > $o]:((~((X4 @ (X1 @ X2)))|(X4 @ (X1 @ X3))))&?[X5:$i]:(~(((X2 @ X5)<=>(X3 @ X5))))))|![X6:$i > $o]:(((X6 @ (X1 @ X6))|?[X3:$i > $o]:(((X3 @ (X1 @ (^[X7:$i]:(?[X8:$i > $o]:(((~((X8 @ (X1 @ X8))))&(![X9:$i > $o]:(((~((X9 @ X7)))|((X9 @ (X1 @ X8))))))))))))&~((X3 @ (X1 @ X6))))))))), file('/export/starexec/sandbox/tmp/tmp.YlPWuVMPaD/E---3.1_1544730.p', cTHM143_EXPANDB)).
% 0.27/0.36 thf(c_0_1, negated_conjecture, ~(![X1:($i > $o) > $i]:((?[X2:$i > $o, X3:$i > $o]:((![X4:$i > $o]:((~((X4 @ (X1 @ X2)))|(X4 @ (X1 @ X3))))&?[X5:$i]:(~(((X2 @ X5)<=>(X3 @ X5))))))|![X6:$i > $o]:(((X6 @ (X1 @ X6))|?[X3:$i > $o]:(((X3 @ (X1 @ (^[X7:$i]:(?[X8:$i > $o]:(((~((X8 @ (X1 @ X8))))&(![X9:$i > $o]:(((~((X9 @ X7)))|((X9 @ (X1 @ X8))))))))))))&~((X3 @ (X1 @ X6)))))))))), inference(assume_negation,[status(cth)],[cTHM143_EXPANDB])).
% 0.27/0.36 thf(c_0_2, negated_conjecture, ~(![X1:($i > $o) > $i]:((?[X2:$i > $o, X3:$i > $o]:((![X4:$i > $o]:((~((X4 @ (X1 @ X2)))|(X4 @ (X1 @ X3))))&?[X5:$i]:(~(((X2 @ X5)<=>(X3 @ X5))))))|![X6:$i > $o]:(((X6 @ (X1 @ X6))|?[X3:$i > $o]:(((X3 @ (X1 @ (^[Z0:$i]:(?[X8:$i > $o]:(((~(X8 @ (X1 @ X8)))&(![X9:$i > $o]:(((~(X9 @ Z0))|(X9 @ (X1 @ X8)))))))))))&~((X3 @ (X1 @ X6)))))))))), inference(fof_simplification,[status(thm)],[c_0_1])).
% 0.27/0.36 thf(c_0_3, plain, ![X27:$i, X29:$i > $o, X30:$i, X31:$i > $o]:((((~(epred4_1 @ X27 @ (esk1_0 @ (epred4_1 @ X27)))|~(epred3_0 @ X27))&(~(X29 @ X27)|(X29 @ (esk1_0 @ (epred4_1 @ X27)))|~(epred3_0 @ X27)))&(((epred5_2 @ X30 @ X31 @ X30)|(X31 @ (esk1_0 @ X31))|(epred3_0 @ X30))&(~(epred5_2 @ X30 @ X31 @ (esk1_0 @ X31))|(X31 @ (esk1_0 @ X31))|(epred3_0 @ X30))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])])).
% 0.27/0.36 thf(c_0_4, negated_conjecture, ![X18:$i > $o, X19:$i > $o, X21:$i, X23:$i > $o]:(((((~(X18 @ X21)|(X19 @ X21)|(epred1_2 @ X18 @ X19 @ (esk1_0 @ X18)))&(~(X19 @ X21)|(X18 @ X21)|(epred1_2 @ X18 @ X19 @ (esk1_0 @ X18))))&((~(X18 @ X21)|(X19 @ X21)|~(epred1_2 @ X18 @ X19 @ (esk1_0 @ X19)))&(~(X19 @ X21)|(X18 @ X21)|~(epred1_2 @ X18 @ X19 @ (esk1_0 @ X19)))))&(~(epred2_0 @ (esk1_0 @ epred2_0))&(~(X23 @ (esk1_0 @ (^[Z0:$i]:(?[X8:$i > $o]:(((~(X8 @ (esk1_0 @ X8)))&(![X9:$i > $o]:(((~(X9 @ Z0))|(X9 @ (esk1_0 @ X8)))))))))))|(X23 @ (esk1_0 @ epred2_0)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])])])).
% 0.27/0.36 thf(c_0_5, plain, ![X26:$i]:(((epred3_0 @ X26)<=>?[X24:$i > $o]:((~((X24 @ (esk1_0 @ X24)))&![X25:$i > $o]:((~((X25 @ X26))|(X25 @ (esk1_0 @ X24)))))))), introduced(definition)).
% 0.27/0.36 thf(c_0_6, plain, ![X5:$i, X2:$i > $o]:(((X2 @ (esk1_0 @ X2))|(epred3_0 @ X5)|~((epred5_2 @ X5 @ X2 @ (esk1_0 @ X2))))), inference(split_conjunct,[status(thm)],[c_0_3])).
% 0.27/0.36 thf(c_0_7, plain, ![X2:$i > $o, X5:$i]:(((epred5_2 @ X5 @ X2 @ X5)|(X2 @ (esk1_0 @ X2))|(epred3_0 @ X5))), inference(split_conjunct,[status(thm)],[c_0_3])).
% 0.27/0.36 thf(c_0_8, negated_conjecture, ![X2:$i > $o]:(((X2 @ (esk1_0 @ epred2_0))|~((((X2 @ (esk1_0 @ epred3_0)))=(($true)))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_4]), c_0_5])).
% 0.27/0.36 thf(c_0_9, negated_conjecture, ~((epred2_0 @ (esk1_0 @ epred2_0))), inference(split_conjunct,[status(thm)],[c_0_4])).
% 0.27/0.36 thf(c_0_10, plain, ![X2:$i > $o]:(((epred3_0 @ (esk1_0 @ X2))|(X2 @ (esk1_0 @ X2)))), inference(spm,[status(thm)],[c_0_6, c_0_7])).
% 0.27/0.36 thf(c_0_11, negated_conjecture, ![X2:$i > $o, X5:$i, X3:$i > $o]:(((X3 @ X5)|~((X2 @ X5))|~((epred1_2 @ X2 @ X3 @ (esk1_0 @ X3))))), inference(split_conjunct,[status(thm)],[c_0_4])).
% 0.27/0.36 thf(c_0_12, negated_conjecture, ![X2:$i > $o]:(((X2 @ (esk1_0 @ epred2_0))|~((X2 @ (esk1_0 @ epred3_0))))), inference(cn,[status(thm)],[c_0_8])).
% 0.27/0.36 thf(c_0_13, negated_conjecture, ![X2:$i > $o, X3:$i > $o, X5:$i]:(((X3 @ X5)|(epred1_2 @ X2 @ X3 @ (esk1_0 @ X2))|~((X2 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_4])).
% 0.27/0.36 thf(c_0_14, negated_conjecture, (epred3_0 @ (esk1_0 @ epred2_0)), inference(spm,[status(thm)],[c_0_9, c_0_10])).
% 0.27/0.36 thf(c_0_15, negated_conjecture, ![X2:$i > $o, X5:$i]:(((epred2_0 @ X5)|~((epred1_2 @ X2 @ epred2_0 @ (esk1_0 @ epred3_0)))|~((X2 @ X5)))), inference(spm,[status(thm)],[c_0_11, c_0_12])).
% 0.27/0.36 thf(c_0_16, negated_conjecture, ![X2:$i > $o]:(((epred1_2 @ epred3_0 @ X2 @ (esk1_0 @ epred3_0))|(X2 @ (esk1_0 @ epred2_0)))), inference(spm,[status(thm)],[c_0_13, c_0_14])).
% 0.27/0.36 thf(c_0_17, negated_conjecture, ~((epred2_0 @ (esk1_0 @ epred3_0))), inference(spm,[status(thm)],[c_0_9, c_0_12])).
% 0.27/0.36 thf(c_0_18, negated_conjecture, ![X5:$i]:(((epred2_0 @ X5)|~((epred3_0 @ X5)))), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16]), c_0_9])).
% 0.27/0.36 thf(c_0_19, plain, (epred3_0 @ (esk1_0 @ epred3_0)), inference(ef,[status(thm)],[c_0_10])).
% 0.27/0.36 thf(c_0_20, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17, c_0_18]), c_0_19])]), ['proof']).
% 0.27/0.36 % SZS output end CNFRefutation
% 0.27/0.36 % Parsed axioms : 1
% 0.27/0.36 % Removed by relevancy pruning/SinE : 0
% 0.27/0.36 % Initial clauses : 10
% 0.27/0.36 % Removed in clause preprocessing : 0
% 0.27/0.36 % Initial clauses in saturation : 10
% 0.27/0.36 % Processed clauses : 31
% 0.27/0.36 % ...of these trivial : 1
% 0.27/0.36 % ...subsumed : 2
% 0.27/0.36 % ...remaining for further processing : 28
% 0.27/0.36 % Other redundant clauses eliminated : 0
% 0.27/0.36 % Clauses deleted for lack of memory : 0
% 0.27/0.36 % Backward-subsumed : 0
% 0.27/0.36 % Backward-rewritten : 1
% 0.27/0.36 % Generated clauses : 66
% 0.27/0.36 % ...of the previous two non-redundant : 53
% 0.27/0.36 % ...aggressively subsumed : 0
% 0.27/0.36 % Contextual simplify-reflections : 0
% 0.27/0.36 % Paramodulations : 64
% 0.27/0.36 % Factorizations : 2
% 0.27/0.36 % NegExts : 0
% 0.27/0.36 % Equation resolutions : 0
% 0.27/0.36 % Disequality decompositions : 0
% 0.27/0.36 % Total rewrite steps : 14
% 0.27/0.36 % ...of those cached : 12
% 0.27/0.36 % Propositional unsat checks : 0
% 0.27/0.36 % Propositional check models : 0
% 0.27/0.36 % Propositional check unsatisfiable : 0
% 0.27/0.36 % Propositional clauses : 0
% 0.27/0.36 % Propositional clauses after purity: 0
% 0.27/0.36 % Propositional unsat core size : 0
% 0.27/0.36 % Propositional preprocessing time : 0.000
% 0.27/0.36 % Propositional encoding time : 0.000
% 0.27/0.36 % Propositional solver time : 0.000
% 0.27/0.36 % Success case prop preproc time : 0.000
% 0.27/0.36 % Success case prop encoding time : 0.000
% 0.27/0.36 % Success case prop solver time : 0.000
% 0.27/0.36 % Current number of processed clauses : 27
% 0.27/0.36 % Positive orientable unit clauses : 2
% 0.27/0.36 % Positive unorientable unit clauses: 0
% 0.27/0.36 % Negative unit clauses : 3
% 0.27/0.36 % Non-unit-clauses : 22
% 0.27/0.36 % Current number of unprocessed clauses: 30
% 0.27/0.36 % ...number of literals in the above : 100
% 0.27/0.36 % Current number of archived formulas : 0
% 0.27/0.36 % Current number of archived clauses : 1
% 0.27/0.36 % Clause-clause subsumption calls (NU) : 39
% 0.27/0.36 % Rec. Clause-clause subsumption calls : 38
% 0.27/0.36 % Non-unit clause-clause subsumptions : 2
% 0.27/0.36 % Unit Clause-clause subsumption calls : 0
% 0.27/0.36 % Rewrite failures with RHS unbound : 0
% 0.27/0.36 % BW rewrite match attempts : 1
% 0.27/0.36 % BW rewrite match successes : 1
% 0.27/0.36 % Condensation attempts : 0
% 0.27/0.36 % Condensation successes : 0
% 0.27/0.36 % Termbank termtop insertions : 2069
% 0.27/0.36 % Search garbage collected termcells : 394
% 0.27/0.36
% 0.27/0.36 % -------------------------------------------------
% 0.27/0.36 % User time : 0.007 s
% 0.27/0.36 % System time : 0.003 s
% 0.27/0.36 % Total time : 0.010 s
% 0.27/0.36 % Maximum resident set size: 3636 pages
% 0.27/0.36
% 0.27/0.36 % -------------------------------------------------
% 0.27/0.36 % User time : 0.009 s
% 0.27/0.36 % System time : 0.010 s
% 0.27/0.36 % Total time : 0.019 s
% 0.27/0.36 % Maximum resident set size: 4864 pages
% 0.27/0.36 % E exiting
%------------------------------------------------------------------------------