%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN025^3 : TPTP v9.3.1. Released v6.4.0.
% 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 08:19:40 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN025^3 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n013.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:05:51 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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.1PzTL0DaP3/E---3.1_2071846.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.08/0.26 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting post_as_ho12 with 300s (1) cores
% 0.08/0.26 % Starting new_bool_9 with 300s (1) cores
% 0.08/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.26 % Starting post_as_ho4 with 300s (1) cores
% 0.08/0.26 % Starting post_as_ho2 with 300s (1) cores
% 0.08/0.26 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.08/0.26 % Starting full_lambda_10 with 300s (1) cores
% 0.08/0.26 % Starting new_ho_8 with 300s (1) cores
% 0.08/0.26 % new_bool_9 with pid 2071860 completed with status 0
% 0.08/0.26 % Result found by new_bool_9
% 0.08/0.26 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.08/0.26 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting post_as_ho12 with 300s (1) cores
% 0.08/0.26 % Starting new_bool_9 with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 0.08/0.26 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.08/0.26 % Search class: HGHSF-FFSF31-MSSFFSNN
% 0.08/0.26 % partial match(2): HGHPS-FFSF31-MSSFFSNN
% 0.08/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.26 % SubtermCWHack with pid 2071867 completed with status 0
% 0.08/0.26 % Result found by SubtermCWHack
% 0.08/0.26 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.08/0.26 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting post_as_ho12 with 300s (1) cores
% 0.08/0.26 % Starting new_bool_9 with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 0.08/0.26 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.08/0.26 % Search class: HGHSF-FFSF31-MSSFFSNN
% 0.08/0.26 % partial match(2): HGHPS-FFSF31-MSSFFSNN
% 0.08/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.26 % Preprocessing time : 0.001 s
% 0.08/0.26
% 0.08/0.26 % Proof found!
% 0.08/0.26 % SZS status Theorem
% 0.08/0.26 % SZS output start CNFRefutation
% 0.08/0.26 thf(decl_23, type, zero: $i).
% 0.08/0.26 thf(decl_24, type, s: $i > $i).
% 0.08/0.26 thf(decl_25, type, ite: $o > $i > $i > $i).
% 0.08/0.26 thf(decl_26, type, h: $i > $i).
% 0.08/0.26 thf(decl_27, type, epred1_0: $o).
% 0.08/0.26 thf(n10, conjecture, (((((![X1:$o, X2:$i, X3:$i]:(((X1)=>((ite @ ((X1)) @ X2 @ X3)=(X2))))&![X1:$o, X2:$i, X3:$i]:((~((X1))=>((ite @ ((X1)) @ X2 @ X3)=(X3)))))&![X4:$i]:(((s @ X4)!=(zero))))&![X4:$i]:(((s @ X4)!=(X4))))&![X4:$i]:(((h @ X4)=(ite @ (((X4)=(zero))) @ (s @ zero) @ (ite @ (((X4)=(s @ zero))) @ zero @ (s @ zero))))))=>?[X5:$i > $i]:(((((X5 @ zero)=(s @ zero))&((X5 @ (s @ zero))=(zero)))&((X5 @ (s @ (s @ zero)))=(s @ zero))))), file('/export/starexec/sandbox/tmp/tmp.1PzTL0DaP3/E---3.1_2071846.p', n10)).
% 0.08/0.26 thf(c_0_1, plain, ((epred1_0)<=>((((![X1:$o, X2:$i, X3:$i]:(((X1)=>((ite @ ((X1)) @ X2 @ X3)=(X2))))&![X1:$o, X2:$i, X3:$i]:((~(X1)=>((ite @ ((X1)) @ X2 @ X3)=(X3)))))&![X4:$i]:(((s @ X4)!=(zero))))&![X4:$i]:(((s @ X4)!=(X4))))&![X4:$i]:(((((X4)!=(zero))|((((X4)!=(s @ zero))|((h @ X4)=(ite @ $true @ (s @ zero) @ (ite @ $true @ zero @ (s @ zero)))))&(((X4)=(s @ zero))|((h @ X4)=(ite @ $true @ (s @ zero) @ (ite @ $false @ zero @ (s @ zero)))))))&(((X4)=(zero))|((((X4)!=(s @ zero))|((h @ X4)=(ite @ $false @ (s @ zero) @ (ite @ $true @ zero @ (s @ zero)))))&(((X4)=(s @ zero))|((h @ X4)=(ite @ $false @ (s @ zero) @ (ite @ $false @ zero @ (s @ zero))))))))))), introduced(definition)).
% 0.08/0.26 thf(c_0_2, negated_conjecture, ~((((((![X1:$o, X2:$i, X3:$i]:(((X1)=>((ite @ ((X1)) @ X2 @ X3)=(X2))))&![X1:$o, X2:$i, X3:$i]:((~((X1))=>((ite @ ((X1)) @ X2 @ X3)=(X3)))))&![X4:$i]:(((s @ X4)!=(zero))))&![X4:$i]:(((s @ X4)!=(X4))))&![X4:$i]:(((h @ X4)=(ite @ (((X4)=(zero))) @ (s @ zero) @ (ite @ (((X4)=(s @ zero))) @ zero @ (s @ zero))))))=>?[X5:$i > $i]:(((((X5 @ zero)=(s @ zero))&((X5 @ (s @ zero))=(zero)))&((X5 @ (s @ (s @ zero)))=(s @ zero)))))), inference(assume_negation,[status(cth)],[n10])).
% 0.08/0.26 thf(c_0_3, plain, ((epred1_0)=>((((![X1:$o, X2:$i, X3:$i]:(((X1)=>((ite @ ((X1)) @ X2 @ X3)=(X2))))&![X1:$o, X2:$i, X3:$i]:((~(X1)=>((ite @ ((X1)) @ X2 @ X3)=(X3)))))&![X4:$i]:(((s @ X4)!=(zero))))&![X4:$i]:(((s @ X4)!=(X4))))&![X4:$i]:(((((X4)!=(zero))|((((X4)!=(s @ zero))|((h @ X4)=(ite @ $true @ (s @ zero) @ (ite @ $true @ zero @ (s @ zero)))))&(((X4)=(s @ zero))|((h @ X4)=(ite @ $true @ (s @ zero) @ (ite @ $false @ zero @ (s @ zero)))))))&(((X4)=(zero))|((((X4)!=(s @ zero))|((h @ X4)=(ite @ $false @ (s @ zero) @ (ite @ $true @ zero @ (s @ zero)))))&(((X4)=(s @ zero))|((h @ X4)=(ite @ $false @ (s @ zero) @ (ite @ $false @ zero @ (s @ zero))))))))))), inference(split_equiv,[status(thm)],[c_0_1])).
% 0.08/0.26 thf(c_0_4, negated_conjecture, ~(((epred1_0)=>?[X5:$i > $i]:(((((X5 @ zero)=(s @ zero))&((X5 @ (s @ zero))=(zero)))&((X5 @ (s @ (s @ zero)))=(s @ zero)))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[c_0_2])]), c_0_1])).
% 0.08/0.26 thf(c_0_5, plain, ![X17:$o, X18:$i, X19:$i, X20:$o, X21:$i, X22:$i, X23:$i, X24:$i, X25:$i]:((((((~(X17)|((ite @ ((X17)) @ X18 @ X19)=(X18))|~(epred1_0))&((X20)|((ite @ ((X20)) @ X21 @ X22)=(X22))|~(epred1_0)))&(((s @ X23)!=(zero))|~(epred1_0)))&(((s @ X24)!=(X24))|~(epred1_0)))&(((((X25)!=(s @ zero))|((h @ X25)=(ite @ $true @ (s @ zero) @ (ite @ $true @ zero @ (s @ zero))))|((X25)!=(zero))|~(epred1_0))&(((X25)=(s @ zero))|((h @ X25)=(ite @ $true @ (s @ zero) @ (ite @ $false @ zero @ (s @ zero))))|((X25)!=(zero))|~(epred1_0)))&((((X25)!=(s @ zero))|((h @ X25)=(ite @ $false @ (s @ zero) @ (ite @ $true @ zero @ (s @ zero))))|((X25)=(zero))|~(epred1_0))&(((X25)=(s @ zero))|((h @ X25)=(ite @ $false @ (s @ zero) @ (ite @ $false @ zero @ (s @ zero))))|((X25)=(zero))|~(epred1_0)))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])])).
% 0.08/0.26 thf(c_0_6, negated_conjecture, ![X16:$i > $i]:(((epred1_0)&(((X16 @ zero)!=(s @ zero))|((X16 @ (s @ zero))!=(zero))|((X16 @ (s @ (s @ zero)))!=(s @ zero))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])).
% 0.08/0.26 thf(c_0_7, plain, ![X2:$i, X3:$i]:((((ite @ (~($true)) @ X2 @ X3)=(X3))|~((epred1_0)))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_5])])])).
% 0.08/0.26 thf(c_0_8, negated_conjecture, (epred1_0), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.08/0.26 thf(c_0_9, plain, ![X2:$i]:((((X2)=(s @ zero))|((h @ X2)=(ite @ (~($true)) @ (s @ zero) @ (ite @ (~($true)) @ zero @ (s @ zero))))|((X2)=(zero))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.08/0.26 thf(c_0_10, plain, ![X2:$i, X3:$i]:(((ite @ (~($true)) @ X2 @ X3)=(X3))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_7, c_0_8])])).
% 0.08/0.26 thf(c_0_11, plain, ![X2:$i]:((((s @ X2)!=(X2))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.08/0.26 thf(c_0_12, plain, ![X2:$i]:((((s @ X2)!=(zero))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.08/0.26 thf(c_0_13, plain, ![X3:$i, X2:$i]:((((ite @ (($true)) @ X2 @ X3)=(X2))|~((epred1_0)))), inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_5])])])).
% 0.08/0.26 thf(c_0_14, negated_conjecture, ![X5:$i > $i]:((((X5 @ zero)!=(s @ zero))|((X5 @ (s @ zero))!=(zero))|((X5 @ (s @ (s @ zero)))!=(s @ zero)))), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.08/0.26 thf(c_0_15, plain, ![X2:$i]:((((h @ X2)=(s @ zero))|((X2)=(s @ zero))|((X2)=(zero)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9, c_0_10]), c_0_10]), c_0_8])])).
% 0.08/0.26 thf(c_0_16, plain, ![X2:$i]:(((s @ X2)!=(X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11, c_0_8])])).
% 0.08/0.26 thf(c_0_17, plain, ![X2:$i]:(((s @ X2)!=(zero))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_8])])).
% 0.08/0.26 thf(c_0_18, plain, ![X2:$i]:((((h @ X2)=(ite @ (~($true)) @ (s @ zero) @ (ite @ (($true)) @ zero @ (s @ zero))))|((X2)=(zero))|((X2)!=(s @ zero))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.08/0.26 thf(c_0_19, plain, ![X3:$i, X2:$i]:(((ite @ (($true)) @ X2 @ X3)=(X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13, c_0_8])])).
% 0.08/0.26 thf(c_0_20, negated_conjecture, (((h @ zero)!=(s @ zero))|((h @ (s @ zero))!=(zero))), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14, c_0_15]), c_0_16]), c_0_17])).
% 0.08/0.26 thf(c_0_21, plain, ((h @ (s @ zero))=(zero)), inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18, c_0_19]), c_0_10]), c_0_8])])]), c_0_16])).
% 0.08/0.26 thf(c_0_22, plain, ![X2:$i]:((((X2)=(s @ zero))|((h @ X2)=(ite @ (($true)) @ (s @ zero) @ (ite @ (~($true)) @ zero @ (s @ zero))))|((X2)!=(zero))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.08/0.26 thf(c_0_23, negated_conjecture, ((h @ zero)!=(s @ zero)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 0.08/0.26 thf(c_0_24, plain, ![X2:$i]:((((h @ X2)=(s @ zero))|((X2)=(s @ zero)))), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22, c_0_10]), c_0_19]), c_0_8])]), c_0_15])).
% 0.08/0.26 thf(c_0_25, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24]), c_0_16]), ['proof']).
% 0.08/0.26 % SZS output end CNFRefutation
% 0.08/0.26 % Parsed axioms : 5
% 0.08/0.26 % Removed by relevancy pruning/SinE : 4
% 0.08/0.26 % Initial clauses : 10
% 0.08/0.26 % Removed in clause preprocessing : 0
% 0.08/0.26 % Initial clauses in saturation : 10
% 0.08/0.26 % Processed clauses : 15
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 3
% 0.08/0.26 % ...remaining for further processing : 12
% 0.08/0.26 % Other redundant clauses eliminated : 2
% 0.08/0.26 % Clauses deleted for lack of memory : 0
% 0.08/0.26 % Backward-subsumed : 1
% 0.08/0.26 % Backward-rewritten : 1
% 0.08/0.26 % Generated clauses : 7
% 0.08/0.26 % ...of the previous two non-redundant : 6
% 0.08/0.26 % ...aggressively subsumed : 0
% 0.08/0.26 % Contextual simplify-reflections : 1
% 0.08/0.26 % Paramodulations : 5
% 0.08/0.26 % Factorizations : 0
% 0.08/0.26 % NegExts : 0
% 0.08/0.26 % Equation resolutions : 2
% 0.08/0.26 % Disequality decompositions : 0
% 0.08/0.26 % Total rewrite steps : 18
% 0.08/0.26 % ...of those cached : 7
% 0.08/0.26 % Propositional unsat checks : 0
% 0.08/0.26 % Propositional check models : 0
% 0.08/0.26 % Propositional check unsatisfiable : 0
% 0.08/0.26 % Propositional clauses : 0
% 0.08/0.26 % Propositional clauses after purity: 0
% 0.08/0.26 % Propositional unsat core size : 0
% 0.08/0.26 % Propositional preprocessing time : 0.000
% 0.08/0.26 % Propositional encoding time : 0.000
% 0.08/0.26 % Propositional solver time : 0.000
% 0.08/0.26 % Success case prop preproc time : 0.000
% 0.08/0.26 % Success case prop encoding time : 0.000
% 0.08/0.26 % Success case prop solver time : 0.000
% 0.08/0.26 % Current number of processed clauses : 9
% 0.08/0.26 % Positive orientable unit clauses : 4
% 0.08/0.26 % Positive unorientable unit clauses: 0
% 0.08/0.26 % Negative unit clauses : 3
% 0.08/0.26 % Non-unit-clauses : 2
% 0.08/0.26 % Current number of unprocessed clauses: 1
% 0.08/0.26 % ...number of literals in the above : 4
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 2
% 0.08/0.26 % Clause-clause subsumption calls (NU) : 4
% 0.08/0.26 % Rec. Clause-clause subsumption calls : 3
% 0.08/0.26 % Non-unit clause-clause subsumptions : 3
% 0.08/0.26 % Unit Clause-clause subsumption calls : 3
% 0.08/0.26 % Rewrite failures with RHS unbound : 0
% 0.08/0.26 % BW rewrite match attempts : 1
% 0.08/0.26 % BW rewrite match successes : 1
% 0.08/0.26 % Condensation attempts : 0
% 0.08/0.26 % Condensation successes : 0
% 0.08/0.26 % Termbank termtop insertions : 1229
% 0.08/0.26 % Search garbage collected termcells : 203
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.003 s
% 0.08/0.26 % System time : 0.000 s
% 0.08/0.26 % Total time : 0.004 s
% 0.08/0.26 % Maximum resident set size: 3840 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.006 s
% 0.08/0.26 % System time : 0.005 s
% 0.08/0.26 % Total time : 0.011 s
% 0.08/0.26 % Maximum resident set size: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------