%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SYO500^1 : 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 : n003.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 08:44:42 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO500^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n003.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 17:12:58 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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.A3OFv9v0eQ/E---3.1_2785185.p
% 0.07/0.24 % Version: 3.5.1-ho
% 0.07/0.24 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.24 % Starting sh4l with 300s (1) cores
% 0.07/0.24 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.07/0.24 % new_ho_10 with pid 2785215 completed with status 0
% 0.07/0.24 % Result found by new_ho_10
% 0.07/0.24 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.24 % No SInE strategy applied
% 0.07/0.24 % Search class: HGHNF-FFSS00-SFFFFFNN
% 0.07/0.24 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.24 % Starting SubtermCWHack with 151s (1) cores
% 0.07/0.24 % Starting new_ho_10 with 901s (1) cores
% 0.07/0.24 % Starting sh5l with 151s (1) cores
% 0.07/0.24 % Starting new_bool_1 with 151s (1) cores
% 0.07/0.24 % Starting new_bool_9 with 146s (1) cores
% 0.07/0.24 % SubtermCWHack with pid 2785219 completed with status 0
% 0.07/0.24 % Result found by SubtermCWHack
% 0.07/0.24 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.24 % No SInE strategy applied
% 0.07/0.24 % Search class: HGHNF-FFSS00-SFFFFFNN
% 0.07/0.24 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.24 % Starting SubtermCWHack with 151s (1) cores
% 0.07/0.24 % Preprocessing time : 0.001 s
% 0.07/0.24
% 0.07/0.24 % Proof found!
% 0.07/0.24 % SZS status Theorem
% 0.07/0.24 % SZS output start CNFRefutation
% 0.07/0.24 thf(decl_23, type, f: $o > $o).
% 0.07/0.24 thf(decl_24, type, x: $o).
% 0.07/0.24 thf(decl_25, type, epred1_0: $o).
% 0.07/0.24 thf(decl_26, type, epred2_0: $o).
% 0.07/0.24 thf(con, conjecture, ((f @ ((f @ ((f @ ((x)))))))<=>(f @ ((x)))), file('/export/starexec/sandbox/tmp/tmp.A3OFv9v0eQ/E---3.1_2785185.p', con)).
% 0.07/0.24 thf(c_0_1, negated_conjecture, ~(((f @ ((f @ ((f @ ((x)))))))<=>(f @ ((x))))), inference(assume_negation,[status(cth)],[con])).
% 0.07/0.24 thf(c_0_2, plain, ((epred1_0)<=>((((~(x)|~(f @ $true))&((x)|~(f @ $false)))|~(f @ $true))&(((~(x)|(f @ $true))&((x)|(f @ $false)))|~(f @ $false)))), introduced(definition)).
% 0.07/0.24 thf(c_0_3, plain, ((epred2_0)<=>((((~(x)|~(f @ $true))&((x)|~(f @ $false)))|(f @ $true))&(((~(x)|(f @ $true))&((x)|(f @ $false)))|(f @ $false)))), introduced(definition)).
% 0.07/0.24 thf(c_0_4, negated_conjecture, ~(((((epred1_0)|(f @ $true))&((epred2_0)|(f @ $false)))<=>((~(x)|(f @ $true))&((x)|(f @ $false))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[c_0_1]), c_0_2]), c_0_3])).
% 0.07/0.24 thf(c_0_5, plain, ((((~(x)|~(f @ $true)|(f @ $true)|~(epred2_0))&((x)|~(f @ $false)|(f @ $true)|~(epred2_0)))&((~(x)|(f @ $true)|(f @ $false)|~(epred2_0))&((x)|(f @ $false)|(f @ $false)|~(epred2_0))))&(((((((~(x)|(x)|(~(x)|(x))|(epred2_0))&(~(f @ $false)|(x)|(~(x)|(x))|(epred2_0)))&((~(x)|~(f @ $true)|(~(x)|(x))|(epred2_0))&(~(f @ $false)|~(f @ $true)|(~(x)|(x))|(epred2_0))))&(~(f @ $false)|(~(x)|(x))|(epred2_0)))&((((~(x)|(x)|((f @ $false)|(x))|(epred2_0))&(~(f @ $false)|(x)|((f @ $false)|(x))|(epred2_0)))&((~(x)|~(f @ $true)|((f @ $false)|(x))|(epred2_0))&(~(f @ $false)|~(f @ $true)|((f @ $false)|(x))|(epred2_0))))&(~(f @ $false)|((f @ $false)|(x))|(epred2_0))))&(((((~(x)|(x)|(~(x)|(f @ $true))|(epred2_0))&(~(f @ $false)|(x)|(~(x)|(f @ $true))|(epred2_0)))&((~(x)|~(f @ $true)|(~(x)|(f @ $true))|(epred2_0))&(~(f @ $false)|~(f @ $true)|(~(x)|(f @ $true))|(epred2_0))))&(~(f @ $false)|(~(x)|(f @ $true))|(epred2_0)))&((((~(x)|(x)|((f @ $false)|(f @ $true))|(epred2_0))&(~(f @ $false)|(x)|((f @ $false)|(f @ $true))|(epred2_0)))&((~(x)|~(f @ $true)|((f @ $false)|(f @ $true))|(epred2_0))&(~(f @ $false)|~(f @ $true)|((f @ $false)|(f @ $true))|(epred2_0))))&(~(f @ $false)|((f @ $false)|(f @ $true))|(epred2_0)))))&((((~(x)|(x)|~(f @ $true)|(epred2_0))&(~(f @ $false)|(x)|~(f @ $true)|(epred2_0)))&((~(x)|~(f @ $true)|~(f @ $true)|(epred2_0))&(~(f @ $false)|~(f @ $true)|~(f @ $true)|(epred2_0))))&(~(f @ $false)|~(f @ $true)|(epred2_0))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])).
% 0.07/0.24 thf(c_0_6, negated_conjecture, ((((((~(x)|(x)|(~(epred2_0)|~(epred1_0)))&(~(f @ $false)|(x)|(~(epred2_0)|~(epred1_0))))&((~(x)|~(f @ $true)|(~(epred2_0)|~(epred1_0)))&(~(f @ $false)|~(f @ $true)|(~(epred2_0)|~(epred1_0)))))&(((~(x)|(x)|(~(f @ $false)|~(epred1_0)))&(~(f @ $false)|(x)|(~(f @ $false)|~(epred1_0))))&((~(x)|~(f @ $true)|(~(f @ $false)|~(epred1_0)))&(~(f @ $false)|~(f @ $true)|(~(f @ $false)|~(epred1_0))))))&((((~(x)|(x)|(~(epred2_0)|~(f @ $true)))&(~(f @ $false)|(x)|(~(epred2_0)|~(f @ $true))))&((~(x)|~(f @ $true)|(~(epred2_0)|~(f @ $true)))&(~(f @ $false)|~(f @ $true)|(~(epred2_0)|~(f @ $true)))))&(((~(x)|(x)|(~(f @ $false)|~(f @ $true)))&(~(f @ $false)|(x)|(~(f @ $false)|~(f @ $true))))&((~(x)|~(f @ $true)|(~(f @ $false)|~(f @ $true)))&(~(f @ $false)|~(f @ $true)|(~(f @ $false)|~(f @ $true)))))))&(((~(x)|(f @ $true)|((epred1_0)|(f @ $true)))&((x)|(f @ $false)|((epred1_0)|(f @ $true))))&((~(x)|(f @ $true)|((epred2_0)|(f @ $false)))&((x)|(f @ $false)|((epred2_0)|(f @ $false)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])).
% 0.07/0.24 thf(c_0_7, plain, ((x)|(f @ (~($true)))|(f @ (~($true)))|~((epred2_0))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.07/0.24 thf(c_0_8, negated_conjecture, ((x)|(f @ (~($true)))|(epred2_0)|(f @ (~($true)))), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.07/0.24 thf(c_0_9, negated_conjecture, (~((x))|~((f @ (($true))))|~((epred2_0))|~((f @ (($true))))), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.07/0.24 thf(c_0_10, plain, ((epred2_0)|~((x))|~((f @ (($true))))|~((f @ (($true))))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.07/0.24 thf(c_0_11, negated_conjecture, (~((f @ (~($true))))|~((f @ (($true))))|~((f @ (~($true))))|~((f @ (($true))))), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.07/0.24 thf(c_0_12, plain, ((x)|(f @ (~($true)))|~((epred2_0))), inference(cn,[status(thm)],[c_0_7])).
% 0.07/0.24 thf(c_0_13, negated_conjecture, ((x)|(epred2_0)|(f @ (~($true)))), inference(cn,[status(thm)],[c_0_8])).
% 0.07/0.24 thf(c_0_14, negated_conjecture, (~((x))|~((epred2_0))|~((f @ (($true))))), inference(cn,[status(thm)],[c_0_9])).
% 0.07/0.24 thf(c_0_15, plain, ((epred2_0)|~((x))|~((f @ (($true))))), inference(cn,[status(thm)],[c_0_10])).
% 0.07/0.24 thf(c_0_16, negated_conjecture, (~((f @ (($true))))|~((f @ (~($true))))), inference(cn,[status(thm)],[c_0_11])).
% 0.07/0.24 thf(c_0_17, plain, ((f @ (~($true)))|(x)), inference(csr,[status(thm)],[c_0_12, c_0_13])).
% 0.07/0.24 thf(c_0_18, negated_conjecture, (~((f @ (($true))))|~((x))), inference(csr,[status(thm)],[c_0_14, c_0_15])).
% 0.07/0.24 thf(c_0_19, negated_conjecture, ((f @ (($true)))|(epred2_0)|(f @ (~($true)))|~((x))), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.07/0.24 thf(c_0_20, plain, ~((f @ (($true)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16, c_0_17]), c_0_18])).
% 0.07/0.24 thf(c_0_21, negated_conjecture, ((x)|~((f @ (~($true))))|~((f @ (~($true))))|~((epred1_0))), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.07/0.24 thf(c_0_22, negated_conjecture, ((f @ (($true)))|(epred1_0)|(f @ (($true)))|~((x))), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.07/0.24 thf(c_0_23, plain, ((((~(x)|~(f @ $true)|~(f @ $true)|~(epred1_0))&((x)|~(f @ $false)|~(f @ $true)|~(epred1_0)))&((~(x)|(f @ $true)|~(f @ $false)|~(epred1_0))&((x)|(f @ $false)|~(f @ $false)|~(epred1_0))))&(((((((~(x)|(x)|(~(x)|(x))|(epred1_0))&(~(f @ $false)|(x)|(~(x)|(x))|(epred1_0)))&((~(x)|~(f @ $true)|(~(x)|(x))|(epred1_0))&(~(f @ $false)|~(f @ $true)|(~(x)|(x))|(epred1_0))))&((f @ $false)|(~(x)|(x))|(epred1_0)))&((((~(x)|(x)|((f @ $false)|(x))|(epred1_0))&(~(f @ $false)|(x)|((f @ $false)|(x))|(epred1_0)))&((~(x)|~(f @ $true)|((f @ $false)|(x))|(epred1_0))&(~(f @ $false)|~(f @ $true)|((f @ $false)|(x))|(epred1_0))))&((f @ $false)|((f @ $false)|(x))|(epred1_0))))&(((((~(x)|(x)|(~(x)|(f @ $true))|(epred1_0))&(~(f @ $false)|(x)|(~(x)|(f @ $true))|(epred1_0)))&((~(x)|~(f @ $true)|(~(x)|(f @ $true))|(epred1_0))&(~(f @ $false)|~(f @ $true)|(~(x)|(f @ $true))|(epred1_0))))&((f @ $false)|(~(x)|(f @ $true))|(epred1_0)))&((((~(x)|(x)|((f @ $false)|(f @ $true))|(epred1_0))&(~(f @ $false)|(x)|((f @ $false)|(f @ $true))|(epred1_0)))&((~(x)|~(f @ $true)|((f @ $false)|(f @ $true))|(epred1_0))&(~(f @ $false)|~(f @ $true)|((f @ $false)|(f @ $true))|(epred1_0))))&((f @ $false)|((f @ $false)|(f @ $true))|(epred1_0)))))&((((~(x)|(x)|(f @ $true)|(epred1_0))&(~(f @ $false)|(x)|(f @ $true)|(epred1_0)))&((~(x)|~(f @ $true)|(f @ $true)|(epred1_0))&(~(f @ $false)|~(f @ $true)|(f @ $true)|(epred1_0))))&((f @ $false)|(f @ $true)|(epred1_0))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])).
% 0.07/0.24 thf(c_0_24, plain, ((f @ (($true)))|(f @ (~($true)))|~((x))|~((epred2_0))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.07/0.24 thf(c_0_25, negated_conjecture, ((f @ (~($true)))|(epred2_0)), inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_19, c_0_20]), c_0_17])).
% 0.07/0.24 thf(c_0_26, negated_conjecture, ((x)|~((epred1_0))|~((f @ (~($true))))), inference(cn,[status(thm)],[c_0_21])).
% 0.07/0.24 thf(c_0_27, negated_conjecture, ((epred1_0)|(f @ (($true)))|~((x))), inference(cn,[status(thm)],[c_0_22])).
% 0.07/0.24 thf(c_0_28, plain, ((x)|(f @ (($true)))|(epred1_0)|~((f @ (~($true))))), inference(split_conjunct,[status(thm)],[c_0_23])).
% 0.07/0.24 thf(c_0_29, plain, (f @ (~($true))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_24, c_0_20]), c_0_25]), c_0_17])).
% 0.07/0.24 thf(c_0_30, negated_conjecture, ((x)|~((epred1_0))), inference(csr,[status(thm)],[c_0_26, c_0_17])).
% 0.07/0.24 thf(c_0_31, negated_conjecture, ((epred1_0)|~((x))), inference(spm,[status(thm)],[c_0_18, c_0_27])).
% 0.07/0.24 thf(c_0_32, plain, (x), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_29])]), c_0_20]), c_0_30])).
% 0.07/0.24 thf(c_0_33, plain, ((f @ (($true)))|~((x))|~((f @ (~($true))))|~((epred1_0))), inference(split_conjunct,[status(thm)],[c_0_23])).
% 0.07/0.24 thf(c_0_34, negated_conjecture, (epred1_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31, c_0_32])])).
% 0.07/0.24 thf(c_0_35, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_32]), c_0_34]), c_0_29])]), c_0_20]), ['proof']).
% 0.07/0.24 % SZS output end CNFRefutation
% 0.07/0.24 % Parsed axioms : 3
% 0.07/0.24 % Removed by relevancy pruning/SinE : 0
% 0.07/0.24 % Initial clauses : 80
% 0.07/0.24 % Removed in clause preprocessing : 48
% 0.07/0.24 % Initial clauses in saturation : 32
% 0.07/0.24 % Processed clauses : 32
% 0.07/0.24 % ...of these trivial : 1
% 0.07/0.24 % ...subsumed : 11
% 0.07/0.24 % ...remaining for further processing : 19
% 0.07/0.24 % Other redundant clauses eliminated : 0
% 0.07/0.24 % Clauses deleted for lack of memory : 0
% 0.07/0.24 % Backward-subsumed : 11
% 0.07/0.24 % Backward-rewritten : 2
% 0.07/0.24 % Generated clauses : 7
% 0.07/0.24 % ...of the previous two non-redundant : 5
% 0.07/0.24 % ...aggressively subsumed : 0
% 0.07/0.24 % Contextual simplify-reflections : 9
% 0.07/0.24 % Paramodulations : 6
% 0.07/0.24 % Factorizations : 0
% 0.07/0.24 % NegExts : 0
% 0.07/0.24 % Equation resolutions : 0
% 0.07/0.24 % Disequality decompositions : 0
% 0.07/0.24 % Total rewrite steps : 10
% 0.07/0.24 % ...of those cached : 7
% 0.07/0.24 % Propositional unsat checks : 0
% 0.07/0.24 % Propositional check models : 0
% 0.07/0.24 % Propositional check unsatisfiable : 0
% 0.07/0.24 % Propositional clauses : 0
% 0.07/0.24 % Propositional clauses after purity: 0
% 0.07/0.24 % Propositional unsat core size : 0
% 0.07/0.24 % Propositional preprocessing time : 0.000
% 0.07/0.24 % Propositional encoding time : 0.000
% 0.07/0.24 % Propositional solver time : 0.000
% 0.07/0.24 % Success case prop preproc time : 0.000
% 0.07/0.24 % Success case prop encoding time : 0.000
% 0.07/0.24 % Success case prop solver time : 0.000
% 0.07/0.24 % Current number of processed clauses : 5
% 0.07/0.24 % Positive orientable unit clauses : 4
% 0.07/0.24 % Positive unorientable unit clauses: 0
% 0.07/0.24 % Negative unit clauses : 1
% 0.07/0.24 % Non-unit-clauses : 0
% 0.07/0.24 % Current number of unprocessed clauses: 5
% 0.07/0.24 % ...number of literals in the above : 20
% 0.07/0.24 % Current number of archived formulas : 0
% 0.07/0.24 % Current number of archived clauses : 14
% 0.07/0.24 % Clause-clause subsumption calls (NU) : 18
% 0.07/0.24 % Rec. Clause-clause subsumption calls : 18
% 0.07/0.24 % Non-unit clause-clause subsumptions : 18
% 0.07/0.24 % Unit Clause-clause subsumption calls : 6
% 0.07/0.24 % Rewrite failures with RHS unbound : 0
% 0.07/0.24 % BW rewrite match attempts : 2
% 0.07/0.24 % BW rewrite match successes : 2
% 0.07/0.24 % Condensation attempts : 0
% 0.07/0.24 % Condensation successes : 0
% 0.07/0.24 % Termbank termtop insertions : 2799
% 0.07/0.24 % Search garbage collected termcells : 475
% 0.07/0.24
% 0.07/0.24 % -------------------------------------------------
% 0.07/0.24 % User time : 0.004 s
% 0.07/0.24 % System time : 0.004 s
% 0.07/0.24 % Total time : 0.008 s
% 0.07/0.24 % Maximum resident set size: 3596 pages
% 0.07/0.24
% 0.07/0.24 % -------------------------------------------------
% 0.07/0.24 % User time : 0.010 s
% 0.07/0.24 % System time : 0.012 s
% 0.07/0.24 % Total time : 0.022 s
% 0.07/0.24 % Maximum resident set size: 4864 pages
% 0.07/0.24 % E exiting
%------------------------------------------------------------------------------