%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO113^5 : 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 : n013.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 08:42:24 AM UTC 2026
% Result : Theorem 0.26s 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO113^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:33:36 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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.ZLobkoSkjs/E---3.1_2339381.p
% 0.26/0.26 % Version: 3.5.1-ho
% 0.26/0.26 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.26/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.26/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.26 % Starting full_lambda_5 with 300s (1) cores
% 0.26/0.26 % Starting new_ho_10_unif with 300s (1) cores
% 0.26/0.26 % new_bool_1 with pid 2339395 completed with status 0
% 0.26/0.26 % Result found by new_bool_1
% 0.26/0.26 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.26/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.26/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.26 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.26 % Search class: HGUNF-FFSF11-SFFFFFNN
% 0.26/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.26 % SubtermCWHack with pid 2339399 completed with status 0
% 0.26/0.26 % Result found by SubtermCWHack
% 0.26/0.26 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.26/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.26/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.26 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.26 % Search class: HGUNF-FFSF11-SFFFFFNN
% 0.26/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.26 % Preprocessing time : 0.001 s
% 0.26/0.26
% 0.26/0.26 % Proof found!
% 0.26/0.26 % SZS status Theorem
% 0.26/0.26 % SZS output start CNFRefutation
% 0.26/0.26 thf(decl_23, type, cNUMBER: $i > $o).
% 0.26/0.26 thf(decl_24, type, cODD: $i > $o).
% 0.26/0.26 thf(decl_25, type, cEVEN: $i > $o).
% 0.26/0.26 thf(decl_26, type, cS: $i > $i).
% 0.26/0.26 thf(decl_27, type, c0: $i).
% 0.26/0.26 thf(decl_28, type, epred1_0: $o).
% 0.26/0.26 thf(decl_29, type, esk1_0: $i).
% 0.26/0.26 thf(decl_30, type, esk2_0: $i).
% 0.26/0.26 thf(cTHM350, conjecture, (((((((cEVEN @ c0)&![X1:$i]:(((cEVEN @ X1)=>(cEVEN @ (cS @ (cS @ X1))))))&(cODD @ (cS @ c0)))&![X1:$i]:(((cODD @ X1)=>(cODD @ (cS @ (cS @ X1))))))&((((cNUMBER @ c0)&(cNUMBER @ (cS @ c0)))&![X2:$i]:((((cNUMBER @ X2)&(cNUMBER @ (cS @ X2)))=>((cNUMBER @ (cS @ X2))&(cNUMBER @ (cS @ (cS @ X2)))))))=>![X2:$i]:(((cNUMBER @ X2)&(cNUMBER @ (cS @ X2))))))&![X1:$i]:(((cNUMBER @ X1)<=>((cEVEN @ X1)|(cODD @ X1)))))=>![X1:$i]:((cNUMBER @ X1))), file('/export/starexec/sandbox/tmp/tmp.ZLobkoSkjs/E---3.1_2339381.p', cTHM350)).
% 0.26/0.26 thf(c_0_1, plain, ((epred1_0)<=>((((((cEVEN @ c0)&![X1:$i]:(((cEVEN @ X1)=>(cEVEN @ (cS @ (cS @ X1))))))&(cODD @ (cS @ c0)))&![X1:$i]:(((cODD @ X1)=>(cODD @ (cS @ (cS @ X1))))))&((((cNUMBER @ c0)&(cNUMBER @ (cS @ c0)))&![X2:$i]:((((cNUMBER @ X2)&(cNUMBER @ (cS @ X2)))=>((cNUMBER @ (cS @ X2))&(cNUMBER @ (cS @ (cS @ X2)))))))=>![X2:$i]:(((cNUMBER @ X2)&(cNUMBER @ (cS @ X2))))))&![X1:$i]:(((cNUMBER @ X1)<=>((cEVEN @ X1)|(cODD @ X1)))))), introduced(definition)).
% 0.26/0.26 thf(c_0_2, negated_conjecture, ~((((((((cEVEN @ c0)&![X1:$i]:(((cEVEN @ X1)=>(cEVEN @ (cS @ (cS @ X1))))))&(cODD @ (cS @ c0)))&![X1:$i]:(((cODD @ X1)=>(cODD @ (cS @ (cS @ X1))))))&((((cNUMBER @ c0)&(cNUMBER @ (cS @ c0)))&![X2:$i]:((((cNUMBER @ X2)&(cNUMBER @ (cS @ X2)))=>((cNUMBER @ (cS @ X2))&(cNUMBER @ (cS @ (cS @ X2)))))))=>![X2:$i]:(((cNUMBER @ X2)&(cNUMBER @ (cS @ X2))))))&![X1:$i]:(((cNUMBER @ X1)<=>((cEVEN @ X1)|(cODD @ X1)))))=>![X1:$i]:((cNUMBER @ X1)))), inference(assume_negation,[status(cth)],[cTHM350])).
% 0.26/0.26 thf(c_0_3, plain, ((epred1_0)=>((((((cEVEN @ c0)&![X1:$i]:(((cEVEN @ X1)=>(cEVEN @ (cS @ (cS @ X1))))))&(cODD @ (cS @ c0)))&![X1:$i]:(((cODD @ X1)=>(cODD @ (cS @ (cS @ X1))))))&((((cNUMBER @ c0)&(cNUMBER @ (cS @ c0)))&![X2:$i]:((((cNUMBER @ X2)&(cNUMBER @ (cS @ X2)))=>((cNUMBER @ (cS @ X2))&(cNUMBER @ (cS @ (cS @ X2)))))))=>![X2:$i]:(((cNUMBER @ X2)&(cNUMBER @ (cS @ X2))))))&![X1:$i]:(((cNUMBER @ X1)<=>((cEVEN @ X1)|(cODD @ X1)))))), inference(split_equiv,[status(thm)],[c_0_1])).
% 0.26/0.26 thf(c_0_4, negated_conjecture, ~(((epred1_0)=>![X1:$i]:((cNUMBER @ X1)))), inference(apply_def,[status(thm)],[c_0_2, c_0_1])).
% 0.26/0.26 thf(c_0_5, plain, ![X10:$i, X11:$i, X13:$i, X14:$i]:((((((((cEVEN @ c0)|~(epred1_0))&(~(cEVEN @ X10)|(cEVEN @ (cS @ (cS @ X10)))|~(epred1_0)))&((cODD @ (cS @ c0))|~(epred1_0)))&(~(cODD @ X11)|(cODD @ (cS @ (cS @ X11)))|~(epred1_0)))&(((((cNUMBER @ X13)|((cNUMBER @ esk2_0)|(~(cNUMBER @ c0)|~(cNUMBER @ (cS @ c0))))|~(epred1_0))&((cNUMBER @ (cS @ X13))|((cNUMBER @ esk2_0)|(~(cNUMBER @ c0)|~(cNUMBER @ (cS @ c0))))|~(epred1_0)))&(((cNUMBER @ X13)|((cNUMBER @ (cS @ esk2_0))|(~(cNUMBER @ c0)|~(cNUMBER @ (cS @ c0))))|~(epred1_0))&((cNUMBER @ (cS @ X13))|((cNUMBER @ (cS @ esk2_0))|(~(cNUMBER @ c0)|~(cNUMBER @ (cS @ c0))))|~(epred1_0))))&(((cNUMBER @ X13)|(~(cNUMBER @ (cS @ esk2_0))|~(cNUMBER @ (cS @ (cS @ esk2_0)))|(~(cNUMBER @ c0)|~(cNUMBER @ (cS @ c0))))|~(epred1_0))&((cNUMBER @ (cS @ X13))|(~(cNUMBER @ (cS @ esk2_0))|~(cNUMBER @ (cS @ (cS @ esk2_0)))|(~(cNUMBER @ c0)|~(cNUMBER @ (cS @ c0))))|~(epred1_0)))))&((~(cNUMBER @ X14)|((cEVEN @ X14)|(cODD @ X14))|~(epred1_0))&((~(cEVEN @ X14)|(cNUMBER @ X14)|~(epred1_0))&(~(cODD @ X14)|(cNUMBER @ X14)|~(epred1_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_3])])])])])])).
% 0.26/0.26 thf(c_0_6, negated_conjecture, ((epred1_0)&~(cNUMBER @ esk1_0)), inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])).
% 0.26/0.26 thf(c_0_7, plain, ![X1:$i]:(((cNUMBER @ X1)|~((cEVEN @ X1))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.26/0.26 thf(c_0_8, negated_conjecture, (epred1_0), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.26/0.26 thf(c_0_9, plain, ((cEVEN @ c0)|~((epred1_0))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.26/0.26 thf(c_0_10, plain, ![X1:$i]:(((cNUMBER @ X1)|~((cODD @ X1))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.26/0.26 thf(c_0_11, plain, ((cODD @ (cS @ c0))|~((epred1_0))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.26/0.26 thf(c_0_12, plain, ![X1:$i]:(((cNUMBER @ X1)|~((cEVEN @ X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_7, c_0_8])])).
% 0.26/0.26 thf(c_0_13, plain, (cEVEN @ c0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9, c_0_8])])).
% 0.26/0.26 thf(c_0_14, plain, ![X1:$i]:(((cNUMBER @ X1)|~((cODD @ X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10, c_0_8])])).
% 0.26/0.26 thf(c_0_15, plain, (cODD @ (cS @ c0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11, c_0_8])])).
% 0.26/0.26 thf(c_0_16, plain, ![X1:$i]:(((cNUMBER @ X1)|(cNUMBER @ (cS @ esk2_0))|~((cNUMBER @ c0))|~((cNUMBER @ (cS @ c0)))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.26/0.26 thf(c_0_17, plain, (cNUMBER @ c0), inference(spm,[status(thm)],[c_0_12, c_0_13])).
% 0.26/0.26 thf(c_0_18, plain, (cNUMBER @ (cS @ c0)), inference(spm,[status(thm)],[c_0_14, c_0_15])).
% 0.26/0.26 thf(c_0_19, plain, ![X1:$i]:(((cODD @ (cS @ (cS @ X1)))|~((cODD @ X1))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.26/0.26 thf(c_0_20, plain, ![X1:$i]:(((cEVEN @ (cS @ (cS @ X1)))|~((cEVEN @ X1))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.26/0.26 thf(c_0_21, plain, ![X1:$i]:(((cNUMBER @ (cS @ esk2_0))|(cNUMBER @ X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_8]), c_0_17]), c_0_18])])).
% 0.26/0.26 thf(c_0_22, plain, ![X1:$i]:(((cODD @ (cS @ (cS @ X1)))|~((cODD @ X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_8])])).
% 0.26/0.26 thf(c_0_23, plain, ![X1:$i]:(((cEVEN @ X1)|(cODD @ X1)|~((cNUMBER @ X1))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.26/0.26 thf(c_0_24, plain, ![X1:$i]:(((cEVEN @ (cS @ (cS @ X1)))|~((cEVEN @ X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_8])])).
% 0.26/0.26 thf(c_0_25, plain, ![X1:$i]:(((cNUMBER @ X1)|(cNUMBER @ esk2_0)|~((cNUMBER @ c0))|~((cNUMBER @ (cS @ c0)))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.26/0.26 thf(c_0_26, plain, ![X1:$i]:(((cNUMBER @ X1)|~((cNUMBER @ (cS @ esk2_0)))|~((cNUMBER @ (cS @ (cS @ esk2_0))))|~((cNUMBER @ c0))|~((cNUMBER @ (cS @ c0)))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.26/0.26 thf(c_0_27, plain, (cNUMBER @ (cS @ esk2_0)), inference(ef,[status(thm)],[c_0_21])).
% 0.26/0.26 thf(c_0_28, plain, ![X1:$i]:(((cNUMBER @ (cS @ (cS @ X1)))|~((cODD @ X1)))), inference(spm,[status(thm)],[c_0_14, c_0_22])).
% 0.26/0.26 thf(c_0_29, plain, ![X1:$i]:(((cEVEN @ X1)|(cODD @ X1)|~((cNUMBER @ X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_8])])).
% 0.26/0.26 thf(c_0_30, plain, ![X1:$i]:(((cNUMBER @ (cS @ (cS @ X1)))|~((cEVEN @ X1)))), inference(spm,[status(thm)],[c_0_12, c_0_24])).
% 0.26/0.26 thf(c_0_31, plain, ![X1:$i]:(((cNUMBER @ esk2_0)|(cNUMBER @ X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25, c_0_8]), c_0_17]), c_0_18])])).
% 0.26/0.26 thf(c_0_32, plain, ![X1:$i]:(((cNUMBER @ X1)|~((cNUMBER @ (cS @ (cS @ esk2_0)))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_8]), c_0_17]), c_0_18]), c_0_27])])).
% 0.26/0.26 thf(c_0_33, plain, ![X1:$i]:(((cNUMBER @ (cS @ (cS @ X1)))|~((cNUMBER @ X1)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_30])).
% 0.26/0.26 thf(c_0_34, plain, (cNUMBER @ esk2_0), inference(ef,[status(thm)],[c_0_31])).
% 0.26/0.26 thf(c_0_35, negated_conjecture, ~((cNUMBER @ esk1_0)), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.26/0.26 thf(c_0_36, plain, ![X1:$i]:((cNUMBER @ X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_33]), c_0_34])])).
% 0.26/0.26 thf(c_0_37, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36])]), ['proof']).
% 0.26/0.26 % SZS output end CNFRefutation
% 0.26/0.26 % Parsed axioms : 6
% 0.26/0.26 % Removed by relevancy pruning/SinE : 5
% 0.26/0.26 % Initial clauses : 15
% 0.26/0.26 % Removed in clause preprocessing : 0
% 0.26/0.26 % Initial clauses in saturation : 15
% 0.26/0.26 % Processed clauses : 26
% 0.26/0.26 % ...of these trivial : 2
% 0.26/0.26 % ...subsumed : 0
% 0.26/0.26 % ...remaining for further processing : 24
% 0.26/0.26 % Other redundant clauses eliminated : 0
% 0.26/0.26 % Clauses deleted for lack of memory : 0
% 0.26/0.26 % Backward-subsumed : 2
% 0.26/0.26 % Backward-rewritten : 16
% 0.26/0.26 % Generated clauses : 16
% 0.26/0.26 % ...of the previous two non-redundant : 16
% 0.26/0.26 % ...aggressively subsumed : 0
% 0.26/0.26 % Contextual simplify-reflections : 1
% 0.26/0.26 % Paramodulations : 12
% 0.26/0.26 % Factorizations : 4
% 0.26/0.26 % NegExts : 0
% 0.26/0.26 % Equation resolutions : 0
% 0.26/0.26 % Disequality decompositions : 0
% 0.26/0.26 % Total rewrite steps : 43
% 0.26/0.26 % ...of those cached : 27
% 0.26/0.26 % Propositional unsat checks : 0
% 0.26/0.26 % Propositional check models : 0
% 0.26/0.26 % Propositional check unsatisfiable : 0
% 0.26/0.26 % Propositional clauses : 0
% 0.26/0.26 % Propositional clauses after purity: 0
% 0.26/0.26 % Propositional unsat core size : 0
% 0.26/0.26 % Propositional preprocessing time : 0.000
% 0.26/0.26 % Propositional encoding time : 0.000
% 0.26/0.26 % Propositional solver time : 0.000
% 0.26/0.26 % Success case prop preproc time : 0.000
% 0.26/0.26 % Success case prop encoding time : 0.000
% 0.26/0.26 % Success case prop solver time : 0.000
% 0.26/0.26 % Current number of processed clauses : 6
% 0.26/0.26 % Positive orientable unit clauses : 4
% 0.26/0.26 % Positive unorientable unit clauses: 0
% 0.26/0.26 % Negative unit clauses : 0
% 0.26/0.26 % Non-unit-clauses : 2
% 0.26/0.26 % Current number of unprocessed clauses: 1
% 0.26/0.26 % ...number of literals in the above : 6
% 0.26/0.26 % Current number of archived formulas : 0
% 0.26/0.26 % Current number of archived clauses : 18
% 0.26/0.26 % Clause-clause subsumption calls (NU) : 8
% 0.26/0.26 % Rec. Clause-clause subsumption calls : 8
% 0.26/0.26 % Non-unit clause-clause subsumptions : 1
% 0.26/0.26 % Unit Clause-clause subsumption calls : 2
% 0.26/0.26 % Rewrite failures with RHS unbound : 0
% 0.26/0.26 % BW rewrite match attempts : 16
% 0.26/0.26 % BW rewrite match successes : 13
% 0.26/0.26 % Condensation attempts : 0
% 0.26/0.26 % Condensation successes : 0
% 0.26/0.26 % Termbank termtop insertions : 1403
% 0.26/0.26 % Search garbage collected termcells : 263
% 0.26/0.26
% 0.26/0.26 % -------------------------------------------------
% 0.26/0.26 % User time : 0.006 s
% 0.26/0.26 % System time : 0.001 s
% 0.26/0.26 % Total time : 0.007 s
% 0.26/0.26 % Maximum resident set size: 3580 pages
% 0.26/0.26
% 0.26/0.26 % -------------------------------------------------
% 0.26/0.26 % User time : 0.007 s
% 0.26/0.26 % System time : 0.006 s
% 0.26/0.26 % Total time : 0.013 s
% 0.26/0.26 % Maximum resident set size: 4864 pages
% 0.26/0.26 % E exiting
%------------------------------------------------------------------------------