%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU589^2 : 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 : n010.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 08:24:37 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU589^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n010.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 13:53:33 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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.3vkwXu9mZ1/E---3.1_2895845.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.25 % Starting sh4l with 300s (1) cores
% 0.08/0.25 % Starting lpo8_s with 300s (1) cores
% 0.08/0.25 % lpo8_s with pid 2895861 completed with status 0
% 0.08/0.25 % Result found by lpo8_s
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.25 % Starting sh4l with 300s (1) cores
% 0.08/0.25 % Starting lpo8_s with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,4.0,,6,20000,1.0))
% 0.08/0.25 % SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.08/0.25 % Search class: HHUNF-FFSF22-SSFFMSBN
% 0.08/0.25 % partial match(1): HHUSF-FFSF22-SSFFMSBN
% 0.08/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 2895862 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.25 % Starting sh4l with 300s (1) cores
% 0.08/0.25 % Starting lpo8_s with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,4.0,,6,20000,1.0))
% 0.08/0.25 % SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.08/0.25 % Search class: HHUNF-FFSF22-SSFFMSBN
% 0.08/0.25 % partial match(1): HHUSF-FFSF22-SSFFMSBN
% 0.08/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.25 % Preprocessing time : 0.001 s
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% 0.08/0.25 thf(decl_23, type, in: $i > $i > $o).
% 0.08/0.25 thf(decl_24, type, dsetconstr: $i > ($i > $o) > $i).
% 0.08/0.25 thf(decl_25, type, dsetconstrI: $o).
% 0.08/0.25 thf(decl_26, type, binintersect: $i > $i > $i).
% 0.08/0.25 thf(decl_27, type, esk1_0: $i).
% 0.08/0.25 thf(decl_28, type, esk2_0: $i).
% 0.08/0.25 thf(decl_29, type, esk3_0: $i).
% 0.08/0.25 thf(decl_30, type, epred1_0: $i > $o).
% 0.08/0.25 thf(binintersectI, conjecture, ((dsetconstrI)=>![X1:$i, X5:$i, X3:$i]:(((in @ X3 @ X1)=>((in @ X3 @ X5)=>(in @ X3 @ (binintersect @ X1 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3vkwXu9mZ1/E---3.1_2895845.p', binintersectI)).
% 0.08/0.25 thf(binintersect, axiom, ((binintersect)=(^[X1:$i, X5:$i]:(dsetconstr @ X1 @ (^[X3:$i]:((in @ X3 @ X5)))))), file('/export/starexec/sandbox2/tmp/tmp.3vkwXu9mZ1/E---3.1_2895845.p', binintersect)).
% 0.08/0.25 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X1:$i, X2:$i > $o, X3:$i]:(((in @ X3 @ X1)=>((X2 @ X3)=>(in @ X3 @ (dsetconstr @ X1 @ (^[X4:$i]:((X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.3vkwXu9mZ1/E---3.1_2895845.p', dsetconstrI)).
% 0.08/0.25 thf(c_0_3, negated_conjecture, ~(((dsetconstrI)=>![X1:$i, X5:$i, X3:$i]:(((in @ X3 @ X1)=>((in @ X3 @ X5)=>(in @ X3 @ (binintersect @ X1 @ X5))))))), inference(assume_negation,[status(cth)],[binintersectI])).
% 0.08/0.25 thf(c_0_4, plain, ((binintersect)=(^[Z0:$i, Z1:$i]:(dsetconstr @ Z0 @ (^[Z2:$i]:((in @ Z2 @ Z1)))))), inference(fof_simplification,[status(thm)],[binintersect])).
% 0.08/0.25 thf(c_0_5, plain, ((dsetconstrI)<=>![X1:$i, X2:$i > $o, X3:$i]:(((in @ X3 @ X1)=>((X2 @ X3)=>(in @ X3 @ (dsetconstr @ X1 @ (^[Z0:$i]:((X2 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.08/0.25 thf(c_0_6, negated_conjecture, ~((![X12:$i, X13:$i > $o, X14:$i]:(((in @ X14 @ X12)=>((X13 @ X14)=>(in @ X14 @ (dsetconstr @ X12 @ X13)))))=>![X1:$i, X5:$i, X3:$i]:(((in @ X3 @ X1)=>((in @ X3 @ X5)=>(in @ X3 @ (dsetconstr @ X1 @ (^[Z0:$i]:((in @ Z0 @ X5)))))))))), inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3, c_0_4]), c_0_5])])).
% 0.08/0.25 thf(c_0_7, negated_conjecture, ![X15:$i, X16:$i > $o, X17:$i]:(((~(in @ X17 @ X15)|(~(X16 @ X17)|(in @ X17 @ (dsetconstr @ X15 @ X16))))&((in @ esk3_0 @ esk1_0)&((in @ esk3_0 @ esk2_0)&~(in @ esk3_0 @ (dsetconstr @ esk1_0 @ (^[Z0:$i]:((in @ Z0 @ esk2_0))))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])).
% 0.08/0.25 thf(c_0_8, plain, ![X21:$i]:(((epred1_0 @ X21)<=>(in @ X21 @ esk2_0))), introduced(definition)).
% 0.08/0.25 thf(c_0_9, plain, ![X22:$i]:(((~(epred1_0 @ X22)|(in @ X22 @ esk2_0))&(~(in @ X22 @ esk2_0)|(epred1_0 @ X22)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])).
% 0.08/0.25 thf(c_0_10, negated_conjecture, ~((((in @ esk3_0 @ (dsetconstr @ esk1_0 @ epred1_0)))=(($true)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7]), c_0_8])).
% 0.08/0.25 thf(c_0_11, plain, ![X1:$i]:(((epred1_0 @ X1)|~((in @ X1 @ esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_9])).
% 0.08/0.25 thf(c_0_12, negated_conjecture, (in @ esk3_0 @ esk2_0), inference(split_conjunct,[status(thm)],[c_0_7])).
% 0.08/0.25 thf(c_0_13, negated_conjecture, ~((in @ esk3_0 @ (dsetconstr @ esk1_0 @ epred1_0))), inference(cn,[status(thm)],[c_0_10])).
% 0.08/0.25 thf(c_0_14, negated_conjecture, ![X3:$i, X2:$i > $o, X1:$i]:(((in @ X1 @ (dsetconstr @ X3 @ X2))|~((in @ X1 @ X3))|~((X2 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_7])).
% 0.08/0.25 thf(c_0_15, negated_conjecture, (in @ esk3_0 @ esk1_0), inference(split_conjunct,[status(thm)],[c_0_7])).
% 0.08/0.25 thf(c_0_16, negated_conjecture, (epred1_0 @ esk3_0), inference(spm,[status(thm)],[c_0_11, c_0_12])).
% 0.08/0.25 thf(c_0_17, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13, c_0_14]), c_0_15]), c_0_16])]), ['proof']).
% 0.08/0.25 % SZS output end CNFRefutation
% 0.08/0.25 % Parsed axioms : 7
% 0.08/0.25 % Removed by relevancy pruning/SinE : 4
% 0.08/0.25 % Initial clauses : 6
% 0.08/0.25 % Removed in clause preprocessing : 0
% 0.08/0.25 % Initial clauses in saturation : 6
% 0.08/0.25 % Processed clauses : 7
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 0
% 0.08/0.25 % ...remaining for further processing : 7
% 0.08/0.25 % Other redundant clauses eliminated : 0
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 0
% 0.08/0.25 % Backward-rewritten : 0
% 0.08/0.25 % Generated clauses : 3
% 0.08/0.25 % ...of the previous two non-redundant : 1
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 3
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 0
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 2
% 0.08/0.25 % ...of those cached : 0
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 7
% 0.08/0.25 % Positive orientable unit clauses : 3
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 1
% 0.08/0.25 % Non-unit-clauses : 3
% 0.08/0.25 % Current number of unprocessed clauses: 0
% 0.08/0.25 % ...number of literals in the above : 0
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 0
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.25 % Non-unit clause-clause subsumptions : 0
% 0.08/0.25 % Unit Clause-clause subsumption calls : 0
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 0
% 0.08/0.25 % BW rewrite match successes : 0
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 638
% 0.08/0.25 % Search garbage collected termcells : 198
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.002 s
% 0.08/0.25 % System time : 0.002 s
% 0.08/0.25 % Total time : 0.005 s
% 0.08/0.25 % Maximum resident set size: 3580 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.004 s
% 0.08/0.25 % System time : 0.007 s
% 0.08/0.25 % Total time : 0.011 s
% 0.08/0.25 % Maximum resident set size: 4864 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------