%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU679^2 : 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 : n016.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 08:25:00 AM UTC 2026
% Result : Theorem 0.24s 0.31s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU679^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n016.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:12:49 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.24/0.27 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.e3XqhvZgRY/E---3.1_413496.p
% 0.24/0.31 % Version: 3.5.1-ho
% 0.24/0.31 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.24/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.31 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.24/0.31 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.24/0.31 % Starting sh2l with 300s (1) cores
% 0.24/0.31 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.24/0.31 % sh2l with pid 413511 completed with status 0
% 0.24/0.31 % Result found by sh2l
% 0.24/0.31 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.24/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.31 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.24/0.31 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.24/0.31 % Starting sh2l with 300s (1) cores
% 0.24/0.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf120_gu_RUU_F100_L01000)
% 0.24/0.31 % SinE strategy is gf120_gu_RUU_F100_L01000
% 0.24/0.31 % Search class: HGUSS-FFSF33-MHSFMFNN
% 0.24/0.31 % partial match(3): HGUSF-FFSF32-MHFFMFNN
% 0.24/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.31 % SubtermCWHack with pid 413518 completed with status 10
% 0.24/0.31 % Starting sh2l with 31s (1) cores
% 0.24/0.31 % sh2l with pid 413519 completed with status 0
% 0.24/0.31 % Result found by sh2l
% 0.24/0.31 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.24/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.31 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.24/0.31 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.24/0.31 % Starting sh2l with 300s (1) cores
% 0.24/0.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf120_gu_RUU_F100_L01000)
% 0.24/0.31 % SinE strategy is gf120_gu_RUU_F100_L01000
% 0.24/0.31 % Search class: HGUSS-FFSF33-MHSFMFNN
% 0.24/0.31 % partial match(3): HGUSF-FFSF32-MHFFMFNN
% 0.24/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.31 % SubtermCWHack with pid 413518 completed with status 10
% 0.24/0.31 % Starting sh2l with 31s (1) cores
% 0.24/0.31 % Preprocessing time : 0.001 s
% 0.24/0.31 % Presaturation interreduction done
% 0.24/0.31
% 0.24/0.31 % Proof found!
% 0.24/0.31 % SZS status Theorem
% 0.24/0.31 % SZS output start CNFRefutation
% 0.24/0.31 thf(decl_23, type, in: $i > $i > $o).
% 0.24/0.31 thf(decl_33, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.24/0.31 thf(decl_34, type, func: $i > $i > $i > $o).
% 0.24/0.31 thf(decl_35, type, lamProp: $o).
% 0.24/0.31 thf(decl_36, type, lam: $i > $i > ($i > $i) > $i).
% 0.24/0.31 thf(decl_37, type, esk1_3: $i > $i > ($i > $i) > $i).
% 0.24/0.31 thf(decl_38, type, esk2_0: $i).
% 0.24/0.31 thf(decl_39, type, esk3_0: $i).
% 0.24/0.31 thf(decl_40, type, esk4_0: $i > $i).
% 0.24/0.31 thf(decl_41, type, epred1_0: $i > $i > $o).
% 0.24/0.31 thf(decl_42, type, epred2_1: ($i > $i) > $i > $i > $o).
% 0.24/0.31 thf(lamp, conjecture, ((lamProp)=>![X1:$i, X4:$i, X8:$i > $i]:((![X2:$i]:(((in @ X2 @ X1)=>(in @ (X8 @ X2) @ X4)))=>(func @ X1 @ X4 @ (lam @ X1 @ X4 @ (^[X2:$i]:(X8 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.e3XqhvZgRY/E---3.1_413496.p', lamp)).
% 0.24/0.31 thf(lamProp, axiom, ((lamProp)<=>![X1:$i, X4:$i, X8:$i > $i]:((![X2:$i]:(((in @ X2 @ X1)=>(in @ (X8 @ X2) @ X4)))=>(func @ X1 @ X4 @ (dpsetconstr @ X1 @ X4 @ (^[X2:$i, X7:$i]:(((X8 @ X2)=(X7))))))))), file('/export/starexec/sandbox2/tmp/tmp.e3XqhvZgRY/E---3.1_413496.p', lamProp)).
% 0.24/0.31 thf(lam, axiom, ((lam)=(^[X1:$i, X4:$i, X8:$i > $i]:(dpsetconstr @ X1 @ X4 @ (^[X2:$i, X7:$i]:(((X8 @ X2)=(X7))))))), file('/export/starexec/sandbox2/tmp/tmp.e3XqhvZgRY/E---3.1_413496.p', lam)).
% 0.24/0.31 thf(c_0_3, negated_conjecture, ~(((lamProp)=>![X1:$i, X4:$i, X8:$i > $i]:((![X2:$i]:(((in @ X2 @ X1)=>(in @ (X8 @ X2) @ X4)))=>(func @ X1 @ X4 @ (lam @ X1 @ X4 @ (^[X2:$i]:(X8 @ X2)))))))), inference(assume_negation,[status(cth)],[lamp])).
% 0.24/0.31 thf(c_0_4, plain, ((lamProp)<=>![X1:$i, X4:$i, X8:$i > $i]:((![X2:$i]:(((in @ X2 @ X1)=>(in @ (X8 @ X2) @ X4)))=>(func @ X1 @ X4 @ (dpsetconstr @ X1 @ X4 @ (^[Z0:$i, Z1:$i]:(((X8 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 0.24/0.31 thf(c_0_5, plain, ((lam)=(^[Z0:$i, Z1:$i, Z2:$i > $i]:(dpsetconstr @ Z0 @ Z1 @ (^[Z3:$i, Z4:$i]:(((Z2 @ Z3)=(Z4))))))), inference(fof_simplification,[status(thm)],[lam])).
% 0.24/0.31 thf(c_0_6, negated_conjecture, ~((![X17:$i, X18:$i, X19:$i > $i]:((![X20:$i]:(((in @ X20 @ X17)=>(in @ (X19 @ X20) @ X18)))=>(func @ X17 @ X18 @ (dpsetconstr @ X17 @ X18 @ (^[Z0:$i]:($eq @ (X19 @ Z0)))))))=>![X1:$i, X4:$i, X8:$i > $i]:((![X2:$i]:(((in @ X2 @ X1)=>(in @ (X8 @ X2) @ X4)))=>(func @ X1 @ X4 @ (dpsetconstr @ X1 @ X4 @ (^[Z0:$i]:($eq @ (X8 @ Z0))))))))), inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_3]), c_0_4]), c_0_5])])).
% 0.24/0.31 thf(c_0_7, negated_conjecture, ![X21:$i, X22:$i, X23:$i > $i, X28:$i]:(((((in @ (esk1_3 @ X21 @ X22 @ X23) @ X21)|(func @ X21 @ X22 @ (dpsetconstr @ X21 @ X22 @ (^[Z0:$i]:($eq @ (X23 @ Z0))))))&(~(in @ (X23 @ (esk1_3 @ X21 @ X22 @ X23)) @ X22)|(func @ X21 @ X22 @ (dpsetconstr @ X21 @ X22 @ (^[Z0:$i]:($eq @ (X23 @ Z0)))))))&((~(in @ X28 @ esk2_0)|(in @ (esk4_0 @ X28) @ esk3_0))&~(func @ esk2_0 @ esk3_0 @ (dpsetconstr @ esk2_0 @ esk3_0 @ (^[Z0:$i]:($eq @ (esk4_0 @ Z0)))))))), 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_6])])])])])])).
% 0.24/0.31 thf(c_0_8, plain, ![X29:$i]:(((epred1_0 @ X29)=($eq @ (esk4_0 @ X29)))), introduced(definition)).
% 0.24/0.31 thf(c_0_9, plain, ![X30:$i, X8:$i > $i]:(((epred2_1 @ X8 @ X30)=($eq @ (X8 @ X30)))), introduced(definition)).
% 0.24/0.31 thf(c_0_10, negated_conjecture, ~((((func @ esk2_0 @ esk3_0 @ (dpsetconstr @ esk2_0 @ esk3_0 @ epred1_0)))=(($true)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7]), c_0_8])).
% 0.24/0.31 thf(c_0_11, negated_conjecture, ![X1:$i, X8:$i > $i, X2:$i]:(((((func @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (epred2_1 @ X8))))=(($true)))|~((in @ (X8 @ (esk1_3 @ X1 @ X2 @ X8)) @ X2)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7]), c_0_9])).
% 0.24/0.31 thf(c_0_12, negated_conjecture, ~((func @ esk2_0 @ esk3_0 @ (dpsetconstr @ esk2_0 @ esk3_0 @ epred1_0))), inference(cn,[status(thm)],[c_0_10])).
% 0.24/0.31 thf(c_0_13, negated_conjecture, ![X1:$i, X8:$i > $i, X2:$i]:(((func @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (epred2_1 @ X8)))|~((in @ (X8 @ (esk1_3 @ X1 @ X2 @ X8)) @ X2)))), inference(cn,[status(thm)],[c_0_11])).
% 0.24/0.31 thf(c_0_14, plain, ![X8:$i > $i]:((((epred2_1 @ X8)!=(epred1_0))|~((in @ (X8 @ (esk1_3 @ esk2_0 @ esk3_0 @ X8)) @ esk3_0)))), inference(er,[status(thm)],[inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_12, c_0_13])])])).
% 0.24/0.31 thf(c_0_15, negated_conjecture, ![X1:$i]:(((in @ (esk4_0 @ X1) @ esk3_0)|~((in @ X1 @ esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_7])).
% 0.24/0.31 thf(c_0_16, plain, ![X32:$i, X33:$i > $i]:(((epred2_1 @ X33 @ X32)=($eq @ (X33 @ X32)))), inference(variable_rename,[status(thm)],[])).
% 0.24/0.31 thf(c_0_17, plain, ![X34:$i]:(((epred1_0 @ X34)=($eq @ (esk4_0 @ X34)))), inference(variable_rename,[status(thm)],[])).
% 0.24/0.31 thf(c_0_18, negated_conjecture, ![X1:$i, X2:$i, X8:$i > $i]:(((in @ (esk1_3 @ X1 @ X2 @ X8) @ X1)|(((func @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (epred2_1 @ X8))))=(($true))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7]), c_0_9])).
% 0.24/0.31 thf(c_0_19, negated_conjecture, (((epred2_1 @ esk4_0)!=(epred1_0))|~((in @ (esk1_3 @ esk2_0 @ esk3_0 @ esk4_0) @ esk2_0))), inference(spm,[status(thm)],[c_0_14, c_0_15])).
% 0.24/0.31 thf(c_0_20, plain, ![X8:$i > $i, X1:$i]:(((epred2_1 @ X8 @ X1)=($eq @ (X8 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_16])).
% 0.24/0.31 thf(c_0_21, plain, ![X1:$i]:(((epred1_0 @ X1)=($eq @ (esk4_0 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_17])).
% 0.24/0.31 thf(c_0_22, negated_conjecture, ![X8:$i > $i, X2:$i, X1:$i]:(((func @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (epred2_1 @ X8)))|(in @ (esk1_3 @ X1 @ X2 @ X8) @ X1))), inference(cn,[status(thm)],[c_0_18])).
% 0.24/0.31 thf(c_0_23, negated_conjecture, ~((in @ (esk1_3 @ esk2_0 @ esk3_0 @ esk4_0) @ esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_19]), c_0_20]), c_0_21])])).
% 0.24/0.31 thf(c_0_24, plain, ![X8:$i > $i]:(((in @ (esk1_3 @ esk2_0 @ esk3_0 @ X8) @ esk2_0)|((epred2_1 @ X8)!=(epred1_0)))), inference(er,[status(thm)],[inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_12, c_0_22])])])).
% 0.24/0.31 thf(c_0_25, negated_conjecture, ((epred2_1 @ esk4_0)!=(epred1_0)), inference(spm,[status(thm)],[c_0_23, c_0_24])).
% 0.24/0.31 thf(c_0_26, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_25]), c_0_20]), c_0_21])]), ['proof']).
% 0.24/0.31 % SZS output end CNFRefutation
% 0.24/0.31 % Parsed axioms : 21
% 0.24/0.31 % Removed by relevancy pruning/SinE : 18
% 0.24/0.31 % Initial clauses : 6
% 0.24/0.31 % Removed in clause preprocessing : 0
% 0.24/0.31 % Initial clauses in saturation : 6
% 0.24/0.31 % Processed clauses : 25
% 0.24/0.31 % ...of these trivial : 0
% 0.24/0.31 % ...subsumed : 2
% 0.24/0.31 % ...remaining for further processing : 22
% 0.24/0.31 % Other redundant clauses eliminated : 5
% 0.24/0.31 % Clauses deleted for lack of memory : 0
% 0.24/0.31 % Backward-subsumed : 1
% 0.24/0.31 % Backward-rewritten : 0
% 0.24/0.31 % Generated clauses : 28
% 0.24/0.31 % ...of the previous two non-redundant : 23
% 0.24/0.31 % ...aggressively subsumed : 0
% 0.24/0.31 % Contextual simplify-reflections : 0
% 0.24/0.31 % Paramodulations : 4
% 0.24/0.31 % Factorizations : 0
% 0.24/0.31 % NegExts : 9
% 0.24/0.31 % Equation resolutions : 5
% 0.24/0.31 % Disequality decompositions : 0
% 0.24/0.31 % Total rewrite steps : 6
% 0.24/0.31 % ...of those cached : 0
% 0.24/0.31 % Propositional unsat checks : 0
% 0.24/0.31 % Propositional check models : 0
% 0.24/0.31 % Propositional check unsatisfiable : 0
% 0.24/0.31 % Propositional clauses : 0
% 0.24/0.31 % Propositional clauses after purity: 0
% 0.24/0.31 % Propositional unsat core size : 0
% 0.24/0.31 % Propositional preprocessing time : 0.000
% 0.24/0.31 % Propositional encoding time : 0.000
% 0.24/0.31 % Propositional solver time : 0.000
% 0.24/0.31 % Success case prop preproc time : 0.000
% 0.24/0.31 % Success case prop encoding time : 0.000
% 0.24/0.31 % Success case prop solver time : 0.000
% 0.24/0.31 % Current number of processed clauses : 12
% 0.24/0.31 % Positive orientable unit clauses : 1
% 0.24/0.31 % Positive unorientable unit clauses: 1
% 0.24/0.31 % Negative unit clauses : 3
% 0.24/0.31 % Non-unit-clauses : 7
% 0.24/0.31 % Current number of unprocessed clauses: 10
% 0.24/0.31 % ...number of literals in the above : 21
% 0.24/0.31 % Current number of archived formulas : 0
% 0.24/0.31 % Current number of archived clauses : 10
% 0.24/0.31 % Clause-clause subsumption calls (NU) : 9
% 0.24/0.31 % Rec. Clause-clause subsumption calls : 7
% 0.24/0.31 % Non-unit clause-clause subsumptions : 0
% 0.24/0.31 % Unit Clause-clause subsumption calls : 3
% 0.24/0.31 % Rewrite failures with RHS unbound : 0
% 0.24/0.31 % BW rewrite match attempts : 2
% 0.24/0.31 % BW rewrite match successes : 2
% 0.24/0.31 % Condensation attempts : 0
% 0.24/0.31 % Condensation successes : 0
% 0.24/0.31 % Termbank termtop insertions : 1989
% 0.24/0.31 % Search garbage collected termcells : 286
% 0.24/0.31
% 0.24/0.31 % -------------------------------------------------
% 0.24/0.31 % User time : 0.010 s
% 0.24/0.31 % System time : 0.003 s
% 0.24/0.31 % Total time : 0.013 s
% 0.24/0.31 % Maximum resident set size: 3904 pages
% 0.24/0.31
% 0.24/0.31 % -------------------------------------------------
% 0.24/0.31 % User time : 0.010 s
% 0.24/0.31 % System time : 0.010 s
% 0.24/0.31 % Total time : 0.020 s
% 0.24/0.31 % Maximum resident set size: 4864 pages
% 0.24/0.31 % E exiting
%------------------------------------------------------------------------------