%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO534^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:43:22 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO534^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n026.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 17:16:12 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 Running higher-order theorem proving
% 0.23/0.27 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.E9ba3sFvaz/E---3.1_892849.p
% 0.23/0.29 % Version: 3.5.1-ho
% 0.23/0.29 % Preprocessing class: HSSSSMSSSSMCHSA.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting lpo8_s with 1500s (5) cores
% 0.23/0.29 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.23/0.29 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.23/0.29 % Starting sh1 with 300s (1) cores
% 0.23/0.29 % lpo8_s with pid 892862 completed with status 0
% 0.23/0.29 % Result found by lpo8_s
% 0.23/0.29 % Preprocessing class: HSSSSMSSSSMCHSA.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting lpo8_s with 1500s (5) cores
% 0.23/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,4.0,,6,20000,1.0))
% 0.23/0.29 % SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.23/0.29 % Search class: HHUNF-FFSF11-MHSFFSBC
% 0.23/0.29 % partial match(3): HHUNF-FFSF11-SHHFFSBN
% 0.23/0.29 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.29 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.29 % Starting lpo8_s with 151s (1) cores
% 0.23/0.29 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.23/0.29 % Starting sh5l with 136s (1) cores
% 0.23/0.29 % Starting new_bool_3 with 136s (1) cores
% 0.23/0.29 % lpo8_s with pid 892869 completed with status 0
% 0.23/0.29 % Result found by lpo8_s
% 0.23/0.29 % Preprocessing class: HSSSSMSSSSMCHSA.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting lpo8_s with 1500s (5) cores
% 0.23/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,4.0,,6,20000,1.0))
% 0.23/0.29 % SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.23/0.29 % Search class: HHUNF-FFSF11-MHSFFSBC
% 0.23/0.29 % partial match(3): HHUNF-FFSF11-SHHFFSBN
% 0.23/0.29 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.29 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.29 % Starting lpo8_s with 151s (1) cores
% 0.23/0.29 % Preprocessing time : 0.001 s
% 0.23/0.29 % Presaturation interreduction done
% 0.23/0.29
% 0.23/0.29 % Proof found!
% 0.23/0.29 % SZS status Theorem
% 0.23/0.29 % SZS output start CNFRefutation
% 0.23/0.29 thf(decl_23, type, eps: ($i > $o) > $i).
% 0.23/0.29 thf(decl_24, type, epsa: ($i > $i > $i > $o) > $i).
% 0.23/0.29 thf(decl_25, type, epsb: ($i > $i > $i > $o) > $i).
% 0.23/0.29 thf(decl_26, type, epsc: ($i > $i > $i > $o) > $i).
% 0.23/0.29 thf(decl_27, type, epred1_0: $i > $i > $i > $o).
% 0.23/0.29 thf(decl_28, type, esk1_0: $i).
% 0.23/0.29 thf(decl_29, type, esk2_0: $i).
% 0.23/0.29 thf(decl_30, type, esk3_0: $i).
% 0.23/0.29 thf(decl_31, type, epred2_0: $i > $o).
% 0.23/0.29 thf(decl_32, type, epred3_0: $i > $o).
% 0.23/0.29 thf(decl_33, type, esk4_1: $i > $i).
% 0.23/0.29 thf(decl_34, type, esk5_1: $i > $i).
% 0.23/0.29 thf(decl_35, type, esk6_1: $i > $i).
% 0.23/0.29 thf(epsbd, axiom, ((epsb)=(^[X3:$i > $i > $i > $o]:(eps @ (^[X4:$i]:(?[X5:$i]:((X3 @ (epsa @ X3) @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.E9ba3sFvaz/E---3.1_892849.p', epsbd)).
% 0.23/0.29 thf(epsad, axiom, ((epsa)=(^[X3:$i > $i > $i > $o]:(eps @ (^[X2:$i]:(?[X4:$i, X5:$i]:((X3 @ X2 @ X4 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.E9ba3sFvaz/E---3.1_892849.p', epsad)).
% 0.23/0.29 thf(epscd, axiom, ((epsc)=(^[X3:$i > $i > $i > $o]:(eps @ (^[X5:$i]:((X3 @ (epsa @ X3) @ (epsb @ X3) @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.E9ba3sFvaz/E---3.1_892849.p', epscd)).
% 0.23/0.29 thf(conj, conjecture, ![X3:$i > $i > $i > $o]:((?[X2:$i, X4:$i, X5:$i]:((X3 @ X2 @ X4 @ X5))=>(X3 @ (epsa @ X3) @ (epsb @ X3) @ (epsc @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.E9ba3sFvaz/E---3.1_892849.p', conj)).
% 0.23/0.29 thf(choiceax, axiom, ![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(X1 @ (eps @ X1)))), file('/export/starexec/sandbox2/tmp/tmp.E9ba3sFvaz/E---3.1_892849.p', choiceax)).
% 0.23/0.29 thf(c_0_5, plain, ((epsb)=(^[Z0:$i > $i > $i > $o]:(eps @ (^[Z1:$i]:(?[X5:$i]:((Z0 @ (eps @ (^[Z2:$i]:(?[X12:$i, X13:$i]:((Z0 @ Z2 @ X12 @ X13))))) @ Z1 @ X5))))))), inference(fof_simplification,[status(thm)],[epsbd])).
% 0.23/0.29 thf(c_0_6, plain, ((epsa)=(^[Z0:$i > $i > $i > $o]:(eps @ (^[Z1:$i]:(?[X4:$i, X5:$i]:((Z0 @ Z1 @ X4 @ X5))))))), inference(fof_simplification,[status(thm)],[epsad])).
% 0.23/0.29 thf(c_0_7, plain, ((epsc)=(^[Z0:$i > $i > $i > $o]:(eps @ (^[Z1:$i]:((Z0 @ (eps @ (^[Z2:$i]:(?[X14:$i, X15:$i]:((Z0 @ Z2 @ X14 @ X15))))) @ (eps @ (^[Z2:$i]:(?[X16:$i]:((Z0 @ (eps @ (^[Z3:$i]:(?[X17:$i, X18:$i]:((Z0 @ Z3 @ X17 @ X18))))) @ Z2 @ X16))))) @ Z1)))))), inference(fof_simplification,[status(thm)],[epscd])).
% 0.23/0.29 thf(c_0_8, plain, ((epsb)=(^[Z0:$i > $i > $i > $o]:(eps @ (^[Z1:$i]:(?[X5:$i]:((Z0 @ (eps @ (^[Z2:$i]:(?[X12:$i, X13:$i]:((Z0 @ Z2 @ X12 @ X13))))) @ Z1 @ X5))))))), inference(apply_def,[status(thm)],[c_0_5, c_0_6])).
% 0.23/0.29 thf(c_0_9, negated_conjecture, ~(![X3:$i > $i > $i > $o]:((?[X2:$i, X4:$i, X5:$i]:((X3 @ X2 @ X4 @ X5))=>(X3 @ (epsa @ X3) @ (epsb @ X3) @ (epsc @ X3))))), inference(assume_negation,[status(cth)],[conj])).
% 0.23/0.29 thf(c_0_10, plain, ((epsc)=(^[Z0:$i > $i > $i > $o]:(eps @ (^[Z1:$i]:((Z0 @ (eps @ (^[Z2:$i]:(?[X14:$i, X15:$i]:((Z0 @ Z2 @ X14 @ X15))))) @ (eps @ (^[Z2:$i]:(?[X16:$i]:((Z0 @ (eps @ (^[Z3:$i]:(?[X17:$i, X18:$i]:((Z0 @ Z3 @ X17 @ X18))))) @ Z2 @ X16))))) @ Z1)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7, c_0_6]), c_0_8])).
% 0.23/0.29 thf(c_0_11, negated_conjecture, ~(![X3:$i > $i > $i > $o]:((?[X2:$i, X4:$i, X5:$i]:((X3 @ X2 @ X4 @ X5))=>(X3 @ (eps @ (^[Z0:$i]:(?[X19:$i, X20:$i]:(X3 @ Z0 @ X19 @ X20)))) @ (eps @ (^[Z0:$i]:(?[X21:$i]:(X3 @ (eps @ (^[Z1:$i]:(?[X22:$i, X23:$i]:(X3 @ Z1 @ X22 @ X23)))) @ Z0 @ X21)))) @ (eps @ (^[Z0:$i]:(X3 @ (eps @ (^[Z1:$i]:(?[X24:$i, X25:$i]:(X3 @ Z1 @ X24 @ X25)))) @ (eps @ (^[Z1:$i]:(?[X26:$i]:(X3 @ (eps @ (^[Z2:$i]:(?[X27:$i, X28:$i]:(X3 @ Z2 @ X27 @ X28)))) @ Z1 @ X26)))) @ Z0))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_9, c_0_10]), c_0_6]), c_0_8])).
% 0.23/0.29 thf(c_0_12, plain, ![X51:$i, X54:$i, X55:$i, X56:$i]:(((~(epred2_0 @ X51)|(epred1_0 @ X51 @ (esk4_1 @ X51) @ (esk5_1 @ X51)))&(~(epred1_0 @ X54 @ X55 @ X56)|(epred2_0 @ X54)))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])).
% 0.23/0.29 thf(c_0_13, negated_conjecture, ((epred1_0 @ esk1_0 @ esk2_0 @ esk3_0)&~(epred1_0 @ (eps @ (^[Z0:$i]:(?[X19:$i, X20:$i]:(epred1_0 @ Z0 @ X19 @ X20)))) @ (eps @ (^[Z0:$i]:(?[X21:$i]:(epred1_0 @ (eps @ (^[Z1:$i]:(?[X22:$i, X23:$i]:(epred1_0 @ Z1 @ X22 @ X23)))) @ Z0 @ X21)))) @ (eps @ (epred1_0 @ (eps @ (^[Z0:$i]:(?[X24:$i, X25:$i]:(epred1_0 @ Z0 @ X24 @ X25)))) @ (eps @ (^[Z0:$i]:(?[X26:$i]:(epred1_0 @ (eps @ (^[Z1:$i]:(?[X27:$i, X28:$i]:(epred1_0 @ Z1 @ X27 @ X28)))) @ Z0 @ X26)))))))), inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])).
% 0.23/0.29 thf(c_0_14, plain, ![X47:$i]:(((epred3_0 @ X47)<=>?[X37:$i]:((epred1_0 @ (eps @ epred2_0) @ X47 @ X37)))), introduced(definition)).
% 0.23/0.29 thf(c_0_15, plain, ![X45:$i]:(((epred2_0 @ X45)<=>?[X35:$i, X36:$i]:((epred1_0 @ X45 @ X35 @ X36)))), introduced(definition)).
% 0.23/0.29 thf(c_0_16, plain, ![X33:$i > $o, X34:$i]:((~(X33 @ X34)|(X33 @ (eps @ X33)))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceax])])])])).
% 0.23/0.29 thf(c_0_17, plain, ![X2:$i, X4:$i, X5:$i]:(((epred2_0 @ X2)|~((epred1_0 @ X2 @ X4 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.23/0.29 thf(c_0_18, negated_conjecture, (epred1_0 @ esk1_0 @ esk2_0 @ esk3_0), inference(split_conjunct,[status(thm)],[c_0_13])).
% 0.23/0.29 thf(c_0_19, negated_conjecture, ~((((epred1_0 @ (eps @ epred2_0) @ (eps @ epred3_0) @ (eps @ (epred1_0 @ (eps @ epred2_0) @ (eps @ epred3_0)))))=(($true)))), inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_13]), c_0_14]), c_0_15]), c_0_15]), c_0_14]), c_0_15]), c_0_15])).
% 0.23/0.29 thf(c_0_20, plain, ![X57:$i, X59:$i, X60:$i]:(((~(epred3_0 @ X57)|(epred1_0 @ (eps @ epred2_0) @ X57 @ (esk6_1 @ X57)))&(~(epred1_0 @ (eps @ epred2_0) @ X59 @ X60)|(epred3_0 @ X59)))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])).
% 0.23/0.29 thf(c_0_21, plain, ![X1:$i > $o, X2:$i]:(((X1 @ (eps @ X1))|~((X1 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_16])).
% 0.23/0.29 thf(c_0_22, plain, (epred2_0 @ esk1_0), inference(spm,[status(thm)],[c_0_17, c_0_18])).
% 0.23/0.29 thf(c_0_23, negated_conjecture, ~((epred1_0 @ (eps @ epred2_0) @ (eps @ epred3_0) @ (eps @ (epred1_0 @ (eps @ epred2_0) @ (eps @ epred3_0))))), inference(cn,[status(thm)],[c_0_19])).
% 0.23/0.29 thf(c_0_24, plain, ![X2:$i, X4:$i]:(((epred3_0 @ X2)|~((epred1_0 @ (eps @ epred2_0) @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_20])).
% 0.23/0.29 thf(c_0_25, plain, ![X2:$i]:(((epred1_0 @ X2 @ (esk4_1 @ X2) @ (esk5_1 @ X2))|~((epred2_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.23/0.29 thf(c_0_26, plain, (epred2_0 @ (eps @ epred2_0)), inference(spm,[status(thm)],[c_0_21, c_0_22])).
% 0.23/0.29 thf(c_0_27, negated_conjecture, ![X2:$i]:(~((epred1_0 @ (eps @ epred2_0) @ (eps @ epred3_0) @ X2))), inference(sr,[status(thm)],[inference(choice_inst,[status(thm)],[c_0_23, c_0_21]), c_0_23])).
% 0.23/0.29 thf(c_0_28, plain, ![X2:$i]:(((epred1_0 @ (eps @ epred2_0) @ X2 @ (esk6_1 @ X2))|~((epred3_0 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_20])).
% 0.23/0.29 thf(c_0_29, plain, (epred3_0 @ (esk4_1 @ (eps @ epred2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_25]), c_0_26])])).
% 0.23/0.29 thf(c_0_30, plain, ~((epred3_0 @ (eps @ epred3_0))), inference(spm,[status(thm)],[c_0_27, c_0_28])).
% 0.23/0.29 thf(c_0_31, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_29]), c_0_30]), ['proof']).
% 0.23/0.29 % SZS output end CNFRefutation
% 0.23/0.29 % Parsed axioms : 9
% 0.23/0.29 % Removed by relevancy pruning/SinE : 4
% 0.23/0.29 % Initial clauses : 7
% 0.23/0.29 % Removed in clause preprocessing : 0
% 0.23/0.29 % Initial clauses in saturation : 7
% 0.23/0.29 % Processed clauses : 24
% 0.23/0.29 % ...of these trivial : 2
% 0.23/0.29 % ...subsumed : 1
% 0.23/0.29 % ...remaining for further processing : 21
% 0.23/0.29 % Other redundant clauses eliminated : 0
% 0.23/0.29 % Clauses deleted for lack of memory : 0
% 0.23/0.29 % Backward-subsumed : 1
% 0.23/0.29 % Backward-rewritten : 0
% 0.23/0.29 % Generated clauses : 25
% 0.23/0.29 % ...of the previous two non-redundant : 17
% 0.23/0.29 % ...aggressively subsumed : 0
% 0.23/0.29 % Contextual simplify-reflections : 0
% 0.23/0.29 % Paramodulations : 14
% 0.23/0.29 % Factorizations : 0
% 0.23/0.29 % NegExts : 0
% 0.23/0.29 % Equation resolutions : 0
% 0.23/0.29 % Disequality decompositions : 0
% 0.23/0.29 % Total rewrite steps : 8
% 0.23/0.29 % ...of those cached : 5
% 0.23/0.29 % Propositional unsat checks : 0
% 0.23/0.29 % Propositional check models : 0
% 0.23/0.29 % Propositional check unsatisfiable : 0
% 0.23/0.29 % Propositional clauses : 0
% 0.23/0.29 % Propositional clauses after purity: 0
% 0.23/0.29 % Propositional unsat core size : 0
% 0.23/0.29 % Propositional preprocessing time : 0.000
% 0.23/0.29 % Propositional encoding time : 0.000
% 0.23/0.29 % Propositional solver time : 0.000
% 0.23/0.29 % Success case prop preproc time : 0.000
% 0.23/0.29 % Success case prop encoding time : 0.000
% 0.23/0.29 % Success case prop solver time : 0.000
% 0.23/0.29 % Current number of processed clauses : 13
% 0.23/0.29 % Positive orientable unit clauses : 5
% 0.23/0.29 % Positive unorientable unit clauses: 0
% 0.23/0.29 % Negative unit clauses : 2
% 0.23/0.29 % Non-unit-clauses : 6
% 0.23/0.29 % Current number of unprocessed clauses: 7
% 0.23/0.29 % ...number of literals in the above : 13
% 0.23/0.29 % Current number of archived formulas : 0
% 0.23/0.29 % Current number of archived clauses : 8
% 0.23/0.29 % Clause-clause subsumption calls (NU) : 3
% 0.23/0.29 % Rec. Clause-clause subsumption calls : 3
% 0.23/0.29 % Non-unit clause-clause subsumptions : 1
% 0.23/0.29 % Unit Clause-clause subsumption calls : 1
% 0.23/0.29 % Rewrite failures with RHS unbound : 0
% 0.23/0.29 % BW rewrite match attempts : 1
% 0.23/0.29 % BW rewrite match successes : 0
% 0.23/0.29 % Condensation attempts : 24
% 0.23/0.29 % Condensation successes : 0
% 0.23/0.29 % Termbank termtop insertions : 1538
% 0.23/0.29 % Search garbage collected termcells : 482
% 0.23/0.29
% 0.23/0.29 % -------------------------------------------------
% 0.23/0.29 % User time : 0.005 s
% 0.23/0.29 % System time : 0.003 s
% 0.23/0.29 % Total time : 0.008 s
% 0.23/0.29 % Maximum resident set size: 3636 pages
% 0.23/0.29
% 0.23/0.29 % -------------------------------------------------
% 0.23/0.29 % User time : 0.011 s
% 0.23/0.29 % System time : 0.014 s
% 0.23/0.29 % Total time : 0.025 s
% 0.23/0.29 % Maximum resident set size: 4864 pages
% 0.23/0.29 % E exiting
%------------------------------------------------------------------------------