%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : QUA012^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:21:20 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : QUA012^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n019.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:29:32 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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.i98Lyi6a3L/E---3.1_756756.p
% 0.21/0.29 % Version: 3.5.1-ho
% 0.21/0.29 % Preprocessing class: HSSSSMSSSLSCHSN.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting sh2 with 1500s (5) cores
% 0.21/0.29 % Starting sh5l with 300s (1) cores
% 0.21/0.29 % Starting lpo1_def_fix with 300s (1) cores
% 0.21/0.29 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.21/0.29 % sh2 with pid 756769 completed with status 0
% 0.21/0.29 % Result found by sh2
% 0.21/0.29 % Preprocessing class: HSSSSMSSSLSCHSN.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting sh2 with 1500s (5) cores
% 0.21/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.29 % No SInE strategy applied
% 0.21/0.29 % Search class: HGUSM-FFSF32-SHSFMSBN
% 0.21/0.29 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.29 % Starting SubtermCWHack with 151s (1) cores
% 0.21/0.29 % Starting sh2 with 901s (1) cores
% 0.21/0.29 % Starting sh5l with 151s (1) cores
% 0.21/0.29 % Starting lpo1_def_fix with 151s (1) cores
% 0.21/0.29 % Starting ehoh_best8_lambda with 146s (1) cores
% 0.21/0.29 % sh2 with pid 756777 completed with status 0
% 0.21/0.29 % Result found by sh2
% 0.21/0.29 % Preprocessing class: HSSSSMSSSLSCHSN.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting sh2 with 1500s (5) cores
% 0.21/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.29 % No SInE strategy applied
% 0.21/0.29 % Search class: HGUSM-FFSF32-SHSFMSBN
% 0.21/0.29 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.29 % Starting SubtermCWHack with 151s (1) cores
% 0.21/0.29 % Starting sh2 with 901s (1) cores
% 0.21/0.29 % Preprocessing time : 0.002 s
% 0.21/0.29 % Presaturation interreduction done
% 0.21/0.29
% 0.21/0.29 % Proof found!
% 0.21/0.29 % SZS status Theorem
% 0.21/0.29 % SZS output start CNFRefutation
% 0.21/0.29 thf(decl_23, type, emptyset: $i > $o).
% 0.21/0.29 thf(decl_26, type, zero: $i).
% 0.21/0.29 thf(decl_27, type, sup: ($i > $o) > $i).
% 0.21/0.29 thf(decl_32, type, multiplication: $i > $i > $i).
% 0.21/0.29 thf(decl_33, type, crossmult: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.29 thf(decl_35, type, epred1_0: $i > $o).
% 0.21/0.29 thf(decl_36, type, epred2_0: $i > $o).
% 0.21/0.29 thf(decl_41, type, epred7_2: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.29 thf(decl_44, type, esk1_3: $i > ($i > $o) > ($i > $o) > $i).
% 0.21/0.29 thf(decl_45, type, esk2_3: $i > ($i > $o) > ($i > $o) > $i).
% 0.21/0.29 thf(decl_99, type, esk63_0: $i).
% 0.21/0.29 thf(crossmult_def, axiom, ((crossmult)=(^[X10:$i > $o, X3:$i > $o, X11:$i]:(?[X8:$i, X12:$i]:((((((X10 @ X8))&((X3 @ X12))))&(((X11)=(multiplication @ X8 @ X12)))))))), file('/export/starexec/sandbox/tmp/tmp.i98Lyi6a3L/E---3.1_756756.p', crossmult_def)).
% 0.21/0.29 thf(multiplication_def, axiom, ![X13:$i > $o, X3:$i > $o]:(((multiplication @ (sup @ X13) @ (sup @ X3))=(sup @ (crossmult @ X13 @ X3)))), file('/export/starexec/sandbox/tmp/tmp.i98Lyi6a3L/E---3.1_756756.p', multiplication_def)).
% 0.21/0.29 thf(emptyset_def, axiom, ((emptyset)=(^[X1:$i]:(~($true)))), file('/export/starexec/sandbox/tmp/tmp.i98Lyi6a3L/E---3.1_756756.p', emptyset_def)).
% 0.21/0.29 thf(sup_es, axiom, ((sup @ emptyset)=(zero)), file('/export/starexec/sandbox/tmp/tmp.i98Lyi6a3L/E---3.1_756756.p', sup_es)).
% 0.21/0.29 thf(multiplication_anni, conjecture, ![X14:$i > $o]:(((multiplication @ zero @ (sup @ X14))=(zero))), file('/export/starexec/sandbox/tmp/tmp.i98Lyi6a3L/E---3.1_756756.p', multiplication_anni)).
% 0.21/0.29 thf(c_0_5, plain, ((crossmult)=(^[Z0:$i > $o, Z1:$i > $o, Z2:$i]:(?[X8:$i, X12:$i]:((((((Z0 @ X8))&((Z1 @ X12))))&(((Z2)=(multiplication @ X8 @ X12)))))))), inference(fof_simplification,[status(thm)],[crossmult_def])).
% 0.21/0.29 thf(c_0_6, plain, ![X13:$i > $o, X3:$i > $o]:(((multiplication @ (sup @ X13) @ (sup @ X3))=(sup @ (^[Z0:$i]:(?[X26:$i, X27:$i]:(((((X13 @ X26)&(X3 @ X27)))&(((Z0)=(multiplication @ X26 @ X27)))))))))), inference(apply_def,[status(thm)],[multiplication_def, c_0_5])).
% 0.21/0.29 thf(c_0_7, plain, ((emptyset)=(^[Z0:$i]:(~($true)))), inference(fof_simplification,[status(thm)],[emptyset_def])).
% 0.21/0.29 thf(c_0_8, plain, ![X36:$i > $o, X37:$i > $o]:(((multiplication @ (sup @ X36) @ (sup @ X37))=(sup @ (^[Z0:$i]:(?[X26:$i, X27:$i]:(((((X36 @ X26)&(X37 @ X27)))&(((Z0)=(multiplication @ X26 @ X27)))))))))), inference(variable_rename,[status(thm)],[c_0_6])).
% 0.21/0.29 thf(c_0_9, plain, ![X50:$i, X2:$i > $o, X3:$i > $o]:(((epred7_2 @ X3 @ X2 @ X50)<=>?[X48:$i, X49:$i]:((((X2 @ X48)&(X3 @ X49))&((X50)=(multiplication @ X48 @ X49)))))), introduced(definition)).
% 0.21/0.29 thf(c_0_10, plain, ((sup @ (^[Z0:$i]:(~($true))))=(zero)), inference(apply_def,[status(thm)],[sup_es, c_0_7])).
% 0.21/0.29 thf(c_0_11, plain, ![X41:$i]:(((epred2_0 @ X41)<=>~(($true)))), introduced(definition)).
% 0.21/0.29 thf(c_0_12, negated_conjecture, ~(![X14:$i > $o]:(((multiplication @ zero @ (sup @ X14))=(zero)))), inference(assume_negation,[status(cth)],[multiplication_anni])).
% 0.21/0.29 thf(c_0_13, plain, ![X3:$i > $o, X2:$i > $o]:(((multiplication @ (sup @ X2) @ (sup @ X3))=(sup @ (epred7_2 @ X3 @ X2)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_8]), c_0_9])).
% 0.21/0.29 thf(c_0_14, plain, ((sup @ epred2_0)=(zero)), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_10]), c_0_11])).
% 0.21/0.29 thf(c_0_15, negated_conjecture, ((multiplication @ zero @ (sup @ epred1_0))!=(zero)), inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])).
% 0.21/0.29 thf(c_0_16, plain, ![X2:$i > $o]:(((sup @ (epred7_2 @ X2 @ epred2_0))=(multiplication @ zero @ (sup @ X2)))), inference(spm,[status(thm)],[c_0_13, c_0_14])).
% 0.21/0.29 thf(c_0_17, plain, ![X2:$i > $o, X3:$i > $o]:((((sup @ (epred7_2 @ X2 @ X3))=(zero))|((epred7_2 @ X2 @ X3)!=(epred2_0)))), inference(rw,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_14, c_0_13]), c_0_13])).
% 0.21/0.29 thf(c_0_18, plain, ![X51:$i]:(((~(epred2_0 @ X51)|~($true))&(($true)|(epred2_0 @ X51)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])).
% 0.21/0.29 thf(c_0_19, negated_conjecture, ((multiplication @ zero @ (sup @ epred1_0))!=(zero)), inference(split_conjunct,[status(thm)],[c_0_15])).
% 0.21/0.29 thf(c_0_20, plain, ![X2:$i > $o]:((((multiplication @ zero @ (sup @ X2))=(zero))|((epred7_2 @ X2 @ epred2_0)!=(epred2_0)))), inference(spm,[status(thm)],[c_0_16, c_0_17])).
% 0.21/0.29 thf(c_0_21, plain, ![X1:$i]:((~((epred2_0 @ X1))|~(($true)))), inference(split_conjunct,[status(thm)],[c_0_18])).
% 0.21/0.29 thf(c_0_22, plain, ![X69:$i, X70:$i > $o, X71:$i > $o, X74:$i, X75:$i]:((((((X70 @ (esk1_3 @ X69 @ X70 @ X71))|~(epred7_2 @ X71 @ X70 @ X69))&((X71 @ (esk2_3 @ X69 @ X70 @ X71))|~(epred7_2 @ X71 @ X70 @ X69)))&(((X69)=(multiplication @ (esk1_3 @ X69 @ X70 @ X71) @ (esk2_3 @ X69 @ X70 @ X71)))|~(epred7_2 @ X71 @ X70 @ X69)))&(~(X70 @ X74)|~(X71 @ X75)|((X69)!=(multiplication @ X74 @ X75))|(epred7_2 @ X71 @ X70 @ X69)))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])).
% 0.21/0.29 thf(c_0_23, negated_conjecture, ((epred7_2 @ epred1_0 @ epred2_0)!=(epred2_0)), inference(spm,[status(thm)],[c_0_19, c_0_20])).
% 0.21/0.29 thf(c_0_24, plain, ![X1:$i]:(~((epred2_0 @ X1))), inference(cn,[status(thm)],[c_0_21])).
% 0.21/0.29 thf(c_0_25, plain, ![X3:$i > $o, X2:$i > $o, X1:$i]:(((X2 @ (esk1_3 @ X1 @ X2 @ X3))|~((epred7_2 @ X3 @ X2 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_22])).
% 0.21/0.29 thf(c_0_26, negated_conjecture, ((epred7_2 @ epred1_0 @ epred2_0 @ esk63_0)<~>(epred2_0 @ esk63_0)), inference(neg_ext,[status(thm)],[c_0_23])).
% 0.21/0.29 thf(c_0_27, plain, ![X2:$i > $o, X1:$i]:(~((epred7_2 @ X2 @ epred2_0 @ X1))), inference(spm,[status(thm)],[c_0_24, c_0_25])).
% 0.21/0.29 thf(c_0_28, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_26]), c_0_27]), c_0_24]), ['proof']).
% 0.21/0.29 % SZS output end CNFRefutation
% 0.21/0.29 % Parsed axioms : 27
% 0.21/0.29 % Removed by relevancy pruning/SinE : 0
% 0.21/0.29 % Initial clauses : 39
% 0.21/0.29 % Removed in clause preprocessing : 13
% 0.21/0.29 % Initial clauses in saturation : 26
% 0.21/0.29 % Processed clauses : 162
% 0.21/0.29 % ...of these trivial : 0
% 0.21/0.29 % ...subsumed : 18
% 0.21/0.29 % ...remaining for further processing : 144
% 0.21/0.29 % Other redundant clauses eliminated : 5
% 0.21/0.29 % Clauses deleted for lack of memory : 0
% 0.21/0.29 % Backward-subsumed : 1
% 0.21/0.29 % Backward-rewritten : 0
% 0.21/0.29 % Generated clauses : 334
% 0.21/0.29 % ...of the previous two non-redundant : 328
% 0.21/0.29 % ...aggressively subsumed : 0
% 0.21/0.29 % Contextual simplify-reflections : 0
% 0.21/0.29 % Paramodulations : 223
% 0.21/0.29 % Factorizations : 0
% 0.21/0.29 % NegExts : 55
% 0.21/0.29 % Equation resolutions : 5
% 0.21/0.29 % Disequality decompositions : 0
% 0.21/0.29 % Total rewrite steps : 20
% 0.21/0.29 % ...of those cached : 13
% 0.21/0.29 % Propositional unsat checks : 0
% 0.21/0.29 % Propositional check models : 0
% 0.21/0.29 % Propositional check unsatisfiable : 0
% 0.21/0.29 % Propositional clauses : 0
% 0.21/0.29 % Propositional clauses after purity: 0
% 0.21/0.29 % Propositional unsat core size : 0
% 0.21/0.29 % Propositional preprocessing time : 0.000
% 0.21/0.29 % Propositional encoding time : 0.000
% 0.21/0.29 % Propositional solver time : 0.000
% 0.21/0.29 % Success case prop preproc time : 0.000
% 0.21/0.29 % Success case prop encoding time : 0.000
% 0.21/0.29 % Success case prop solver time : 0.000
% 0.21/0.29 % Current number of processed clauses : 101
% 0.21/0.29 % Positive orientable unit clauses : 12
% 0.21/0.29 % Positive unorientable unit clauses: 0
% 0.21/0.29 % Negative unit clauses : 16
% 0.21/0.29 % Non-unit-clauses : 73
% 0.21/0.29 % Current number of unprocessed clauses: 218
% 0.21/0.29 % ...number of literals in the above : 528
% 0.21/0.29 % Current number of archived formulas : 0
% 0.21/0.29 % Current number of archived clauses : 38
% 0.21/0.29 % Clause-clause subsumption calls (NU) : 1180
% 0.21/0.29 % Rec. Clause-clause subsumption calls : 924
% 0.21/0.29 % Non-unit clause-clause subsumptions : 5
% 0.21/0.29 % Unit Clause-clause subsumption calls : 94
% 0.21/0.29 % Rewrite failures with RHS unbound : 0
% 0.21/0.29 % BW rewrite match attempts : 8
% 0.21/0.29 % BW rewrite match successes : 0
% 0.21/0.29 % Condensation attempts : 0
% 0.21/0.29 % Condensation successes : 0
% 0.21/0.29 % Termbank termtop insertions : 7322
% 0.21/0.29 % Search garbage collected termcells : 581
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.016 s
% 0.21/0.29 % System time : 0.006 s
% 0.21/0.29 % Total time : 0.022 s
% 0.21/0.29 % Maximum resident set size: 3856 pages
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.121 s
% 0.21/0.29 % System time : 0.018 s
% 0.21/0.29 % Total time : 0.139 s
% 0.21/0.29 % Maximum resident set size: 4864 pages
% 0.21/0.29 % E exiting
%------------------------------------------------------------------------------