%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU697^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 08:27:26 AM UTC 2026
% Result : Theorem 0.23s 0.27s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU697^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:11:48 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.26 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.RrhVZGqzwp/E---3.1_832875.p
% 0.23/0.27 % Version: 3.5.1-ho
% 0.23/0.27 % partial match(1): HSSSSMSSSSMNSSN
% 0.23/0.27 % Preprocessing class: HSSSSMSSSSMNHSN.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting sh3 with 1500s (5) cores
% 0.23/0.27 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.23/0.27 % Starting sh2lt with 300s (1) cores
% 0.23/0.27 % Starting ho_unfolding_1 with 300s (1) cores
% 0.23/0.27 % sh2lt with pid 832890 completed with status 0
% 0.23/0.27 % Result found by sh2lt
% 0.23/0.27 % partial match(1): HSSSSMSSSSMNSSN
% 0.23/0.27 % Preprocessing class: HSSSSMSSSSMNHSN.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting sh3 with 1500s (5) cores
% 0.23/0.27 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.23/0.27 % Starting sh2lt with 300s (1) cores
% 0.23/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.23/0.27 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.23/0.27 % Search class: HHHSF-FFSF00-SHSFFFNN
% 0.23/0.27 % partial match(2): HHHNF-FFSF00-SSSFFFNN
% 0.23/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.27 % SubtermCWHack with pid 832895 completed with status 0
% 0.23/0.27 % Result found by SubtermCWHack
% 0.23/0.27 % partial match(1): HSSSSMSSSSMNSSN
% 0.23/0.27 % Preprocessing class: HSSSSMSSSSMNHSN.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting sh3 with 1500s (5) cores
% 0.23/0.27 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.23/0.27 % Starting sh2lt with 300s (1) cores
% 0.23/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.23/0.27 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.23/0.27 % Search class: HHHSF-FFSF00-SHSFFFNN
% 0.23/0.27 % partial match(2): HHHNF-FFSF00-SSSFFFNN
% 0.23/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.27 % Preprocessing time : 0.001 s
% 0.23/0.27
% 0.23/0.27 % Proof found!
% 0.23/0.27 % SZS status Theorem
% 0.23/0.27 % SZS output start CNFRefutation
% 0.23/0.27 thf(decl_23, type, in: $i > $i > $o).
% 0.23/0.27 thf(decl_24, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.23/0.27 thf(decl_25, type, lam: $i > $i > ($i > $i) > $i).
% 0.23/0.27 thf(decl_26, type, esk1_0: $i).
% 0.23/0.27 thf(decl_27, type, esk2_0: $i).
% 0.23/0.27 thf(decl_28, type, esk3_0: $i > $i).
% 0.23/0.27 thf(decl_29, type, epred1_0: $i > $i > $o).
% 0.23/0.27 thf(lam2lamEq, conjecture, ![X1:$i, X2:$i, X3:$i > $i]:((![X4:$i]:(((in @ X4 @ X1)=>(in @ (X3 @ X4) @ X2)))=>((lam @ X1 @ X2 @ (^[X4:$i]:(X3 @ X4)))=(lam @ X1 @ X2 @ (^[X4:$i]:(X3 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.RrhVZGqzwp/E---3.1_832875.p', lam2lamEq)).
% 0.23/0.27 thf(lam, axiom, ((lam)=(^[X1:$i, X2:$i, X3:$i > $i]:(dpsetconstr @ X1 @ X2 @ (^[X4:$i, X5:$i]:(((X3 @ X4)=(X5))))))), file('/export/starexec/sandbox2/tmp/tmp.RrhVZGqzwp/E---3.1_832875.p', lam)).
% 0.23/0.27 thf(c_0_2, negated_conjecture, ~(![X1:$i, X2:$i, X3:$i > $i]:((![X4:$i]:(((in @ X4 @ X1)=>(in @ (X3 @ X4) @ X2)))=>((lam @ X1 @ X2 @ (^[X4:$i]:(X3 @ X4)))=(lam @ X1 @ X2 @ (^[X4:$i]:(X3 @ X4))))))), inference(assume_negation,[status(cth)],[lam2lamEq])).
% 0.23/0.27 thf(c_0_3, plain, ((lam)=(^[Z0:$i, Z1:$i, Z2:$i > $i]:(dpsetconstr @ Z0 @ Z1 @ (^[Z3:$i, Z4:$i]:(((Z2 @ Z3)=(Z4))))))), inference(fof_simplification,[status(thm)],[lam])).
% 0.23/0.27 thf(c_0_4, negated_conjecture, ~(![X1:$i, X2:$i, X3:$i > $i]:((![X4:$i]:(((in @ X4 @ X1)=>(in @ (X3 @ X4) @ X2)))=>((dpsetconstr @ X1 @ X2 @ (^[Z0:$i]:($eq @ (X3 @ Z0))))=(dpsetconstr @ X1 @ X2 @ (^[Z0:$i]:($eq @ (X3 @ Z0)))))))), inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2]), c_0_3])])).
% 0.23/0.27 thf(c_0_5, negated_conjecture, ![X13:$i]:(((~(in @ X13 @ esk1_0)|(in @ (esk3_0 @ X13) @ esk2_0))&((dpsetconstr @ esk1_0 @ esk2_0 @ (^[Z0:$i]:($eq @ (esk3_0 @ Z0))))!=(dpsetconstr @ esk1_0 @ esk2_0 @ (^[Z0:$i]:($eq @ (esk3_0 @ Z0))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])).
% 0.23/0.27 thf(c_0_6, plain, ![X14:$i]:(((epred1_0 @ X14)=($eq @ (esk3_0 @ X14)))), introduced(definition)).
% 0.23/0.27 thf(c_0_7, negated_conjecture, ((dpsetconstr @ esk1_0 @ esk2_0 @ epred1_0)!=(dpsetconstr @ esk1_0 @ esk2_0 @ epred1_0)), inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_5]), c_0_6]), c_0_6])).
% 0.23/0.27 thf(c_0_8, negated_conjecture, ($false), inference(cn,[status(thm)],[c_0_7]), ['proof']).
% 0.23/0.27 % SZS output end CNFRefutation
% 0.23/0.27 % Parsed axioms : 5
% 0.23/0.27 % Removed by relevancy pruning/SinE : 3
% 0.23/0.27 % Initial clauses : 3
% 0.23/0.27 % Removed in clause preprocessing : 0
% 0.23/0.27 % Initial clauses in saturation : 3
% 0.23/0.27 % Processed clauses : 1
% 0.23/0.27 % ...of these trivial : 0
% 0.23/0.27 % ...subsumed : 0
% 0.23/0.27 % ...remaining for further processing : 0
% 0.23/0.27 % Other redundant clauses eliminated : 0
% 0.23/0.27 % Clauses deleted for lack of memory : 0
% 0.23/0.27 % Backward-subsumed : 0
% 0.23/0.27 % Backward-rewritten : 0
% 0.23/0.27 % Generated clauses : 0
% 0.23/0.27 % ...of the previous two non-redundant : 0
% 0.23/0.27 % ...aggressively subsumed : 0
% 0.23/0.27 % Contextual simplify-reflections : 0
% 0.23/0.27 % Paramodulations : 0
% 0.23/0.27 % Factorizations : 0
% 0.23/0.27 % NegExts : 0
% 0.23/0.27 % Equation resolutions : 0
% 0.23/0.27 % Disequality decompositions : 0
% 0.23/0.27 % Total rewrite steps : 0
% 0.23/0.27 % ...of those cached : 0
% 0.23/0.27 % Propositional unsat checks : 0
% 0.23/0.27 % Propositional check models : 0
% 0.23/0.27 % Propositional check unsatisfiable : 0
% 0.23/0.27 % Propositional clauses : 0
% 0.23/0.27 % Propositional clauses after purity: 0
% 0.23/0.27 % Propositional unsat core size : 0
% 0.23/0.27 % Propositional preprocessing time : 0.000
% 0.23/0.27 % Propositional encoding time : 0.000
% 0.23/0.27 % Propositional solver time : 0.000
% 0.23/0.27 % Success case prop preproc time : 0.000
% 0.23/0.27 % Success case prop encoding time : 0.000
% 0.23/0.27 % Success case prop solver time : 0.000
% 0.23/0.27 % Current number of processed clauses : 0
% 0.23/0.27 % Positive orientable unit clauses : 0
% 0.23/0.27 % Positive unorientable unit clauses: 0
% 0.23/0.27 % Negative unit clauses : 0
% 0.23/0.27 % Non-unit-clauses : 0
% 0.23/0.27 % Current number of unprocessed clauses: 2
% 0.23/0.27 % ...number of literals in the above : 3
% 0.23/0.27 % Current number of archived formulas : 0
% 0.23/0.27 % Current number of archived clauses : 0
% 0.23/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.23/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.23/0.27 % Non-unit clause-clause subsumptions : 0
% 0.23/0.27 % Unit Clause-clause subsumption calls : 0
% 0.23/0.27 % Rewrite failures with RHS unbound : 0
% 0.23/0.27 % BW rewrite match attempts : 0
% 0.23/0.27 % BW rewrite match successes : 0
% 0.23/0.27 % Condensation attempts : 0
% 0.23/0.27 % Condensation successes : 0
% 0.23/0.27 % Termbank termtop insertions : 339
% 0.23/0.27 % Search garbage collected termcells : 113
% 0.23/0.27
% 0.23/0.27 % -------------------------------------------------
% 0.23/0.27 % User time : 0.003 s
% 0.23/0.27 % System time : 0.001 s
% 0.23/0.27 % Total time : 0.004 s
% 0.23/0.27 % Maximum resident set size: 3632 pages
% 0.23/0.27
% 0.23/0.27 % -------------------------------------------------
% 0.23/0.27 % User time : 0.005 s
% 0.23/0.27 % System time : 0.005 s
% 0.23/0.27 % Total time : 0.010 s
% 0.23/0.27 % Maximum resident set size: 4864 pages
% 0.23/0.27 % E exiting
%------------------------------------------------------------------------------