%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PHI003^2 : TPTP v9.3.1. Released v6.1.0.
% 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 08:20:07 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI003^2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n026.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:19:57 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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.UzD53lb0oP/E---3.1_567005.p
% 0.09/0.26 % Version: 3.5.1-ho
% 0.09/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.26 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.26 % Starting almost_fo_3_lam with 300s (1) cores
% 0.09/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.26 % post_as_ho1 with pid 567022 completed with status 0
% 0.09/0.26 % Result found by post_as_ho1
% 0.09/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.26 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.26 % Starting almost_fo_3_lam with 300s (1) cores
% 0.09/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HGHNF-FFSF22-SHSSMSBN
% 0.09/0.26 % partial match(1): HGHNF-FFSF22-SHSSMMBN
% 0.09/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.26 % SubtermCWHack with pid 567030 completed with status 0
% 0.09/0.26 % Result found by SubtermCWHack
% 0.09/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.26 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.09/0.26 % Starting almost_fo_3_lam with 300s (1) cores
% 0.09/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HGHNF-FFSF22-SHSSMSBN
% 0.09/0.26 % partial match(1): HGHNF-FFSF22-SHSSMMBN
% 0.09/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.26 % Preprocessing time : 0.001 s
% 0.09/0.26
% 0.09/0.26 % Proof found!
% 0.09/0.26 % SZS status Theorem
% 0.09/0.26 % SZS output start CNFRefutation
% 0.09/0.26 thf(decl_sort1, type, mu: $tType).
% 0.09/0.26 thf(decl_29, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.09/0.26 thf(decl_34, type, mforall_indset: ((mu > $i > $o) > $i > $o) > $i > $o).
% 0.09/0.26 thf(decl_36, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.09/0.26 thf(decl_40, type, mdia_generic: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.09/0.26 thf(decl_41, type, rel: $i > $i > $o).
% 0.09/0.26 thf(decl_43, type, mdia: ($i > $o) > $i > $o).
% 0.09/0.26 thf(decl_44, type, mvalid: ($i > $o) > $o).
% 0.09/0.26 thf(decl_46, type, positive: (mu > $i > $o) > $i > $o).
% 0.09/0.26 thf(decl_47, type, god: mu > $i > $o).
% 0.09/0.26 thf(decl_48, type, esk1_2: $i > (mu > $i > $o) > $i).
% 0.09/0.26 thf(decl_49, type, esk2_2: $i > (mu > $i > $o) > mu).
% 0.09/0.26 thf(decl_50, type, esk3_0: $i).
% 0.09/0.26 thf(decl_51, type, epred1_2: $i > mu > mu > $i > $o).
% 0.09/0.26 thf(decl_52, type, epred2_0: mu > $i > $o).
% 0.09/0.26 thf(decl_53, type, epred3_2: $i > mu > mu > $i > $o).
% 0.09/0.26 thf(mdia_generic, axiom, ((mdia_generic)=(^[X15:$i > $i > $o, X4:$i > $o, X3:$i]:(?[X16:$i]:((((X15 @ X3 @ X16))&((X4 @ X16))))))), file('/export/starexec/sandbox2/tmp/tmp.UzD53lb0oP/E---3.1_567005.p', mdia_generic)).
% 0.09/0.26 thf(defD1, axiom, ((god)=(^[X1:mu]:(mforall_indset @ (^[X17:mu > $i > $o]:(mimplies @ (positive @ X17) @ (X17 @ X1)))))), file('/export/starexec/sandbox2/tmp/tmp.UzD53lb0oP/E---3.1_567005.p', defD1)).
% 0.09/0.26 thf(mimplies, axiom, ((mimplies)=(^[X4:$i > $o, X5:$i > $o, X3:$i]:((((X4 @ X3))=>((X5 @ X3)))))), file('/export/starexec/sandbox2/tmp/tmp.UzD53lb0oP/E---3.1_567005.p', mimplies)).
% 0.09/0.26 thf(mforall_indset, axiom, ((mforall_indset)=(^[X7:(mu > $i > $o) > $i > $o, X3:$i]:(![X8:mu > $i > $o]:((X7 @ X8 @ X3))))), file('/export/starexec/sandbox2/tmp/tmp.UzD53lb0oP/E---3.1_567005.p', mforall_indset)).
% 0.09/0.26 thf(corC, conjecture, (mvalid @ (mdia @ (mexists_ind @ (^[X1:mu]:(god @ X1))))), file('/export/starexec/sandbox2/tmp/tmp.UzD53lb0oP/E---3.1_567005.p', corC)).
% 0.09/0.26 thf(mexists_ind, axiom, ((mexists_ind)=(^[X11:mu > $i > $o, X3:$i]:(?[X1:mu]:((X11 @ X1 @ X3))))), file('/export/starexec/sandbox2/tmp/tmp.UzD53lb0oP/E---3.1_567005.p', mexists_ind)).
% 0.09/0.26 thf(mdia, axiom, ((mdia)=(^[Z0:$i > $o, Z1:$i]:(?[X20:$i]:((((rel @ Z1 @ X20))&((Z0 @ X20))))))), file('/export/starexec/sandbox2/tmp/tmp.UzD53lb0oP/E---3.1_567005.p', mdia)).
% 0.09/0.26 thf(mvalid, axiom, ((mvalid)=(^[X4:$i > $o]:(![X3:$i]:((X4 @ X3))))), file('/export/starexec/sandbox2/tmp/tmp.UzD53lb0oP/E---3.1_567005.p', mvalid)).
% 0.09/0.26 thf(thmT1, lemma, (mvalid @ (mforall_indset @ (^[X18:mu > $i > $o]:(mimplies @ (positive @ X18) @ (mdia @ (mexists_ind @ (^[X1:mu]:(X18 @ X1)))))))), file('/export/starexec/sandbox2/tmp/tmp.UzD53lb0oP/E---3.1_567005.p', thmT1)).
% 0.09/0.26 thf(axA3, axiom, (mvalid @ (positive @ god)), file('/export/starexec/sandbox2/tmp/tmp.UzD53lb0oP/E---3.1_567005.p', axA3)).
% 0.09/0.26 thf(c_0_10, plain, ((mdia_generic)=(^[Z0:$i > $i > $o, Z1:$i > $o, Z2:$i]:(?[X16:$i]:((((Z0 @ Z2 @ X16))&((Z1 @ X16))))))), inference(fof_simplification,[status(thm)],[mdia_generic])).
% 0.09/0.26 thf(c_0_11, plain, ((god)=(^[Z0:mu, Z1:$i]:(![X21:mu > $i > $o]:(((((positive @ X21 @ Z1))=>((X21 @ Z0 @ Z1)))))))), inference(fof_simplification,[status(thm)],[defD1])).
% 0.09/0.26 thf(c_0_12, plain, ((mimplies)=(^[Z0:$i > $o, Z1:$i > $o, Z2:$i]:((((Z0 @ Z2))=>((Z1 @ Z2)))))), inference(fof_simplification,[status(thm)],[mimplies])).
% 0.09/0.26 thf(c_0_13, plain, ((mforall_indset)=(^[Z0:(mu > $i > $o) > $i > $o, Z1:$i]:(![X8:mu > $i > $o]:((Z0 @ X8 @ Z1))))), inference(fof_simplification,[status(thm)],[mforall_indset])).
% 0.09/0.26 thf(c_0_14, negated_conjecture, ~((mvalid @ (mdia @ (mexists_ind @ (^[X1:mu]:(god @ X1)))))), inference(assume_negation,[status(cth)],[corC])).
% 0.09/0.26 thf(c_0_15, plain, ((mexists_ind)=(^[Z0:mu > $i > $o, Z1:$i]:(?[X1:mu]:((Z0 @ X1 @ Z1))))), inference(fof_simplification,[status(thm)],[mexists_ind])).
% 0.09/0.26 thf(c_0_16, axiom, ((mdia)=(^[Z0:$i > $o, Z1:$i]:(?[X20:$i]:((((rel @ Z1 @ X20))&((Z0 @ X20))))))), inference(apply_def,[status(thm)],[mdia, c_0_10])).
% 0.09/0.26 thf(c_0_17, plain, ((mvalid)=(^[Z0:$i > $o]:(![X3:$i]:((Z0 @ X3))))), inference(fof_simplification,[status(thm)],[mvalid])).
% 0.09/0.26 thf(c_0_18, plain, ((god)=(^[Z0:mu, Z1:$i]:(![X21:mu > $i > $o]:(((((positive @ X21 @ Z1))=>((X21 @ Z0 @ Z1)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11, c_0_12]), c_0_13])).
% 0.09/0.26 thf(c_0_19, negated_conjecture, ~(![X31:$i]:(?[X30:$i]:(((rel @ X31 @ X30)&?[X29:mu]:(![X28:mu > $i > $o]:(((positive @ X28 @ X30)=>(X28 @ X29 @ X30)))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_14]), c_0_15]), c_0_16]), c_0_17]), c_0_18])).
% 0.09/0.26 thf(c_0_20, plain, ![X44:$i, X45:mu, X46:mu > $i > $o, X47:$i, X48:mu]:(((~(epred2_0 @ X45 @ X44)|(~(positive @ X46 @ X44)|(X46 @ X45 @ X44)))&(((positive @ (epred3_2 @ X47 @ X48) @ X47)|(epred2_0 @ X48 @ X47))&(~(epred3_2 @ X47 @ X48 @ X48 @ X47)|(epred2_0 @ X48 @ X47))))), 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)],[])])])])])])])).
% 0.09/0.26 thf(c_0_21, negated_conjecture, ![X38:$i, X39:mu]:((((positive @ (epred1_2 @ X38 @ X39) @ X38)|~(rel @ esk3_0 @ X38))&(~(epred1_2 @ X38 @ X39 @ X39 @ X38)|~(rel @ esk3_0 @ X38)))), 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_19])])])])])])).
% 0.09/0.26 thf(c_0_22, plain, ![X1:mu, X6:mu > $i > $o, X3:$i]:(((X6 @ X1 @ X3)|~((epred2_0 @ X1 @ X3))|~((positive @ X6 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_20])).
% 0.09/0.26 thf(c_0_23, negated_conjecture, ![X1:mu, X3:$i]:(((positive @ (epred1_2 @ X3 @ X1) @ X3)|~((rel @ esk3_0 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_21])).
% 0.09/0.26 thf(c_0_24, lemma, ![X27:$i, X26:mu > $i > $o]:(((positive @ X26 @ X27)=>?[X25:$i]:(((rel @ X27 @ X25)&?[X24:mu]:((X26 @ X24 @ X25)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[thmT1]), c_0_12]), c_0_13]), c_0_15]), c_0_16]), c_0_17])).
% 0.09/0.26 thf(c_0_25, plain, ![X23:$i]:((positive @ (^[Z0:mu, Z1:$i]:(![X22:mu > $i > $o]:((((positive @ X22 @ Z1))=>(X22 @ Z0 @ Z1))))) @ X23)), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axA3, c_0_17]), c_0_18])).
% 0.09/0.26 thf(c_0_26, negated_conjecture, ![X1:mu, X3:$i]:((~((epred1_2 @ X3 @ X1 @ X1 @ X3))|~((rel @ esk3_0 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_21])).
% 0.09/0.26 thf(c_0_27, negated_conjecture, ![X1:mu, X2:mu, X3:$i]:(((epred1_2 @ X3 @ X1 @ X2 @ X3)|~((rel @ esk3_0 @ X3))|~((epred2_0 @ X2 @ X3)))), inference(spm,[status(thm)],[c_0_22, c_0_23])).
% 0.09/0.26 thf(c_0_28, lemma, ![X33:$i, X34:mu > $i > $o]:((((rel @ X33 @ (esk1_2 @ X33 @ X34))|~(positive @ X34 @ X33))&((X34 @ (esk2_2 @ X33 @ X34) @ (esk1_2 @ X33 @ X34))|~(positive @ X34 @ X33)))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])])])).
% 0.09/0.26 thf(c_0_29, plain, ![X32:$i]:((positive @ (^[Z0:mu, Z1:$i]:(![X22:mu > $i > $o]:((((positive @ X22 @ Z1))=>(X22 @ Z0 @ Z1))))) @ X32)), inference(variable_rename,[status(thm)],[c_0_25])).
% 0.09/0.26 thf(c_0_30, plain, ![X43:$i, X42:mu]:(((epred2_0 @ X42 @ X43)<=>![X41:mu > $i > $o]:(((positive @ X41 @ X43)=>(X41 @ X42 @ X43))))), introduced(definition)).
% 0.09/0.26 thf(c_0_31, negated_conjecture, ![X1:mu, X3:$i]:((~((rel @ esk3_0 @ X3))|~((epred2_0 @ X1 @ X3)))), inference(spm,[status(thm)],[c_0_26, c_0_27])).
% 0.09/0.26 thf(c_0_32, lemma, ![X6:mu > $i > $o, X3:$i]:(((rel @ X3 @ (esk1_2 @ X3 @ X6))|~((positive @ X6 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_28])).
% 0.09/0.26 thf(c_0_33, plain, ![X3:$i]:((((positive @ epred2_0 @ X3))=(($true)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_29]), c_0_30])).
% 0.09/0.26 thf(c_0_34, lemma, ![X1:mu, X6:mu > $i > $o]:((~((epred2_0 @ X1 @ (esk1_2 @ esk3_0 @ X6)))|~((positive @ X6 @ esk3_0)))), inference(spm,[status(thm)],[c_0_31, c_0_32])).
% 0.09/0.26 thf(c_0_35, lemma, ![X6:mu > $i > $o, X3:$i]:(((X6 @ (esk2_2 @ X3 @ X6) @ (esk1_2 @ X3 @ X6))|~((positive @ X6 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_28])).
% 0.09/0.26 thf(c_0_36, plain, ![X3:$i]:((positive @ epred2_0 @ X3)), inference(cn,[status(thm)],[c_0_33])).
% 0.09/0.26 thf(c_0_37, lemma, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_35]), c_0_36])]), ['proof']).
% 0.09/0.26 % SZS output end CNFRefutation
% 0.09/0.26 % Parsed axioms : 52
% 0.09/0.26 % Removed by relevancy pruning/SinE : 0
% 0.09/0.26 % Initial clauses : 34
% 0.09/0.26 % Removed in clause preprocessing : 26
% 0.09/0.26 % Initial clauses in saturation : 8
% 0.09/0.26 % Processed clauses : 12
% 0.09/0.26 % ...of these trivial : 0
% 0.09/0.26 % ...subsumed : 0
% 0.09/0.26 % ...remaining for further processing : 12
% 0.09/0.26 % Other redundant clauses eliminated : 0
% 0.09/0.26 % Clauses deleted for lack of memory : 0
% 0.09/0.26 % Backward-subsumed : 1
% 0.09/0.26 % Backward-rewritten : 0
% 0.09/0.26 % Generated clauses : 7
% 0.09/0.26 % ...of the previous two non-redundant : 4
% 0.09/0.26 % ...aggressively subsumed : 0
% 0.09/0.26 % Contextual simplify-reflections : 0
% 0.09/0.26 % Paramodulations : 7
% 0.09/0.26 % Factorizations : 0
% 0.09/0.26 % NegExts : 0
% 0.09/0.26 % Equation resolutions : 0
% 0.09/0.26 % Disequality decompositions : 0
% 0.09/0.26 % Total rewrite steps : 1
% 0.09/0.26 % ...of those cached : 0
% 0.09/0.26 % Propositional unsat checks : 0
% 0.09/0.26 % Propositional check models : 0
% 0.09/0.26 % Propositional check unsatisfiable : 0
% 0.09/0.26 % Propositional clauses : 0
% 0.09/0.26 % Propositional clauses after purity: 0
% 0.09/0.26 % Propositional unsat core size : 0
% 0.09/0.26 % Propositional preprocessing time : 0.000
% 0.09/0.26 % Propositional encoding time : 0.000
% 0.09/0.26 % Propositional solver time : 0.000
% 0.09/0.26 % Success case prop preproc time : 0.000
% 0.09/0.26 % Success case prop encoding time : 0.000
% 0.09/0.26 % Success case prop solver time : 0.000
% 0.09/0.26 % Current number of processed clauses : 11
% 0.09/0.26 % Positive orientable unit clauses : 1
% 0.09/0.26 % Positive unorientable unit clauses: 0
% 0.09/0.26 % Negative unit clauses : 0
% 0.09/0.26 % Non-unit-clauses : 10
% 0.09/0.26 % Current number of unprocessed clauses: 0
% 0.09/0.26 % ...number of literals in the above : 0
% 0.09/0.26 % Current number of archived formulas : 0
% 0.09/0.26 % Current number of archived clauses : 1
% 0.09/0.26 % Clause-clause subsumption calls (NU) : 3
% 0.09/0.26 % Rec. Clause-clause subsumption calls : 2
% 0.09/0.26 % Non-unit clause-clause subsumptions : 1
% 0.09/0.26 % Unit Clause-clause subsumption calls : 0
% 0.09/0.26 % Rewrite failures with RHS unbound : 0
% 0.09/0.26 % BW rewrite match attempts : 0
% 0.09/0.26 % BW rewrite match successes : 0
% 0.09/0.26 % Condensation attempts : 0
% 0.09/0.26 % Condensation successes : 0
% 0.09/0.26 % Termbank termtop insertions : 2048
% 0.09/0.26 % Search garbage collected termcells : 476
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.005 s
% 0.09/0.26 % System time : 0.003 s
% 0.09/0.26 % Total time : 0.008 s
% 0.09/0.26 % Maximum resident set size: 3684 pages
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.006 s
% 0.09/0.26 % System time : 0.007 s
% 0.09/0.26 % Total time : 0.013 s
% 0.09/0.26 % Maximum resident set size: 4864 pages
% 0.09/0.26 % E exiting
%------------------------------------------------------------------------------