%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU669^2 : 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 : n026.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 08:27:09 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
% 0.00/0.02 % Problem : SEU669^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n026.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 14:09:27 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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.vhm2yjPfCA/E---3.1_654672.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.08/0.26 % Starting additional_ho_6 with 300s (1) cores
% 0.08/0.26 % additional_ho_6 with pid 654688 completed with status 0
% 0.08/0.26 % Result found by additional_ho_6
% 0.08/0.26 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.08/0.26 % Starting additional_ho_6 with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4.0,,2,20000,1.0))
% 0.08/0.26 % SinE strategy is GSinE(CountFormulas,hypos,4.0,,2,20000,1.0)
% 0.08/0.26 % Search class: HHUSF-FFSF32-SHSFMSBN
% 0.08/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.26 % SubtermCWHack with pid 654689 completed with status 0
% 0.08/0.26 % Result found by SubtermCWHack
% 0.08/0.26 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.08/0.26 % Starting additional_ho_6 with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4.0,,2,20000,1.0))
% 0.08/0.26 % SinE strategy is GSinE(CountFormulas,hypos,4.0,,2,20000,1.0)
% 0.08/0.26 % Search class: HHUSF-FFSF32-SHSFMSBN
% 0.08/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 28s (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, in: $i > $i > $o).
% 0.08/0.26 thf(decl_24, type, dsetconstr: $i > ($i > $o) > $i).
% 0.08/0.26 thf(decl_25, type, dsetconstrEL: $o).
% 0.08/0.26 thf(decl_26, type, kpair: $i > $i > $i).
% 0.08/0.26 thf(decl_27, type, cartprod: $i > $i > $i).
% 0.08/0.26 thf(decl_28, type, cartprodpairmemEL: $o).
% 0.08/0.26 thf(decl_29, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.08/0.26 thf(decl_30, type, esk1_0: $i).
% 0.08/0.26 thf(decl_31, type, esk2_0: $i).
% 0.08/0.26 thf(decl_32, type, epred1_0: $i > $i > $o).
% 0.08/0.26 thf(decl_33, type, esk3_0: $i).
% 0.08/0.26 thf(decl_34, type, esk4_0: $i).
% 0.08/0.26 thf(decl_35, type, epred2_3: ($i > $i > $o) > $i > $i > $i > $o).
% 0.08/0.26 thf(dpsetconstrEL1, conjecture, ((dsetconstrEL)=>((cartprodpairmemEL)=>![X1:$i, X5:$i, X8:$i > $i > $o, X3:$i, X4:$i]:(((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X5 @ (^[X9:$i, X7:$i]:((X8 @ X9 @ X7)))))=>(in @ X3 @ X1))))), file('/export/starexec/sandbox2/tmp/tmp.vhm2yjPfCA/E---3.1_654672.p', dpsetconstrEL1)).
% 0.08/0.26 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X1:$i, X2:$i > $o, X3:$i]:(((in @ X3 @ (dsetconstr @ X1 @ (^[X4:$i]:((X2 @ X4)))))=>(in @ X3 @ X1)))), file('/export/starexec/sandbox2/tmp/tmp.vhm2yjPfCA/E---3.1_654672.p', dsetconstrEL)).
% 0.08/0.26 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X1:$i, X5:$i, X3:$i, X4:$i]:(((in @ (kpair @ X3 @ X4) @ (cartprod @ X1 @ X5))=>(in @ X3 @ X1)))), file('/export/starexec/sandbox2/tmp/tmp.vhm2yjPfCA/E---3.1_654672.p', cartprodpairmemEL)).
% 0.08/0.26 thf(dpsetconstr, axiom, ((dpsetconstr)=(^[X1:$i, X5:$i, X6:$i > $i > $o]:(dsetconstr @ (cartprod @ X1 @ X5) @ (^[X7:$i]:(?[X3:$i]:((((in @ X3 @ X1))&(?[X4:$i]:((((((in @ X4 @ X5))&((X6 @ X3 @ X4))))&(((X7)=(kpair @ X3 @ X4))))))))))))), file('/export/starexec/sandbox2/tmp/tmp.vhm2yjPfCA/E---3.1_654672.p', dpsetconstr)).
% 0.08/0.26 thf(c_0_4, negated_conjecture, ~(((dsetconstrEL)=>((cartprodpairmemEL)=>![X1:$i, X5:$i, X8:$i > $i > $o, X3:$i, X4:$i]:(((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X5 @ (^[X9:$i, X7:$i]:((X8 @ X9 @ X7)))))=>(in @ X3 @ X1)))))), inference(assume_negation,[status(cth)],[dpsetconstrEL1])).
% 0.08/0.26 thf(c_0_5, plain, ((dsetconstrEL)<=>![X1:$i, X2:$i > $o, X3:$i]:(((in @ X3 @ (dsetconstr @ X1 @ (^[Z0:$i]:((X2 @ Z0)))))=>(in @ X3 @ X1)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.08/0.26 thf(c_0_6, negated_conjecture, ~((![X22:$i, X23:$i > $o, X24:$i]:(((in @ X24 @ (dsetconstr @ X22 @ X23))=>(in @ X24 @ X22)))=>(![X25:$i, X26:$i, X27:$i, X28:$i]:(((in @ (kpair @ X27 @ X28) @ (cartprod @ X25 @ X26))=>(in @ X27 @ X25)))=>![X1:$i, X5:$i, X8:$i > $i > $o, X3:$i, X4:$i]:(((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X5 @ X8))=>(in @ X3 @ X1)))))), inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_4]), cartprodpairmemEL]), c_0_5])])).
% 0.08/0.26 thf(c_0_7, plain, ![X29:$i, X30:$i, X31:$i > $i > $o]:(((dpsetconstr @ X29 @ X30 @ X31)=(dsetconstr @ (cartprod @ X29 @ X30) @ (^[Z0:$i]:(?[X3:$i]:((((in @ X3 @ X29))&(?[X4:$i]:((((((in @ X4 @ X30))&(X31 @ X3 @ X4)))&(((Z0)=(kpair @ X3 @ X4))))))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[dpsetconstr])])).
% 0.08/0.26 thf(c_0_8, negated_conjecture, ![X32:$i, X33:$i > $o, X34:$i, X35:$i, X36:$i, X37:$i, X38:$i]:(((~(in @ X34 @ (dsetconstr @ X32 @ X33))|(in @ X34 @ X32))&((~(in @ (kpair @ X37 @ X38) @ (cartprod @ X35 @ X36))|(in @ X37 @ X35))&((in @ (kpair @ esk3_0 @ esk4_0) @ (dpsetconstr @ esk1_0 @ esk2_0 @ epred1_0))&~(in @ esk3_0 @ esk1_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])])])])])).
% 0.08/0.26 thf(c_0_9, plain, ![X44:$i, X45:$i, X46:$i > $i > $o]:(((dpsetconstr @ X44 @ X45 @ X46)=(dsetconstr @ (cartprod @ X44 @ X45) @ (^[Z0:$i]:(?[X3:$i]:((((in @ X3 @ X44))&(?[X4:$i]:((((((in @ X4 @ X45))&(X46 @ X3 @ X4)))&(((Z0)=(kpair @ X3 @ X4))))))))))))), inference(variable_rename,[status(thm)],[c_0_7])).
% 0.08/0.26 thf(c_0_10, plain, ![X49:$i, X1:$i, X3:$i, X6:$i > $i > $o]:(((epred2_3 @ X6 @ X3 @ X1 @ X49)<=>?[X47:$i]:(((in @ X47 @ X1)&?[X48:$i]:((((in @ X48 @ X3)&(X6 @ X47 @ X48))&((X49)=(kpair @ X47 @ X48)))))))), introduced(definition)).
% 0.08/0.26 thf(c_0_11, negated_conjecture, ![X1:$i, X3:$i, X2:$i > $o]:(((in @ X1 @ X3)|~((in @ X1 @ (dsetconstr @ X3 @ X2))))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 0.08/0.26 thf(c_0_12, plain, ![X6:$i > $i > $o, X3:$i, X1:$i]:(((dpsetconstr @ X1 @ X3 @ X6)=(dsetconstr @ (cartprod @ X1 @ X3) @ (epred2_3 @ X6 @ X3 @ X1)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_9]), c_0_10])).
% 0.08/0.26 thf(c_0_13, negated_conjecture, ![X1:$i, X3:$i, X4:$i, X6:$i > $i > $o]:(((in @ X1 @ (cartprod @ X3 @ X4))|~((in @ X1 @ (dpsetconstr @ X3 @ X4 @ X6))))), inference(spm,[status(thm)],[c_0_11, c_0_12])).
% 0.08/0.26 thf(c_0_14, negated_conjecture, (in @ (kpair @ esk3_0 @ esk4_0) @ (dpsetconstr @ esk1_0 @ esk2_0 @ epred1_0)), inference(split_conjunct,[status(thm)],[c_0_8])).
% 0.08/0.26 thf(c_0_15, negated_conjecture, ![X1:$i, X3:$i, X4:$i, X5:$i]:(((in @ X1 @ X4)|~((in @ (kpair @ X1 @ X3) @ (cartprod @ X4 @ X5))))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 0.08/0.26 thf(c_0_16, negated_conjecture, (in @ (kpair @ esk3_0 @ esk4_0) @ (cartprod @ esk1_0 @ esk2_0)), inference(spm,[status(thm)],[c_0_13, c_0_14])).
% 0.08/0.26 thf(c_0_17, negated_conjecture, ~((in @ esk3_0 @ esk1_0)), inference(split_conjunct,[status(thm)],[c_0_8])).
% 0.08/0.26 thf(c_0_18, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16]), c_0_17]), ['proof']).
% 0.08/0.26 % SZS output end CNFRefutation
% 0.08/0.26 % Parsed axioms : 11
% 0.08/0.26 % Removed by relevancy pruning/SinE : 7
% 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 : 9
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 0
% 0.08/0.26 % ...remaining for further processing : 9
% 0.08/0.26 % Other redundant clauses eliminated : 0
% 0.08/0.26 % Clauses deleted for lack of memory : 0
% 0.08/0.26 % Backward-subsumed : 0
% 0.08/0.26 % Backward-rewritten : 0
% 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 : 0
% 0.08/0.26 % Paramodulations : 7
% 0.08/0.26 % Factorizations : 0
% 0.08/0.26 % NegExts : 0
% 0.08/0.26 % Equation resolutions : 0
% 0.08/0.26 % Disequality decompositions : 0
% 0.08/0.26 % Total rewrite steps : 0
% 0.08/0.26 % ...of those cached : 0
% 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 : 3
% 0.08/0.26 % Positive unorientable unit clauses: 0
% 0.08/0.26 % Negative unit clauses : 1
% 0.08/0.26 % Non-unit-clauses : 5
% 0.08/0.26 % Current number of unprocessed clauses: 7
% 0.08/0.26 % ...number of literals in the above : 17
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 0
% 0.08/0.26 % Clause-clause subsumption calls (NU) : 2
% 0.08/0.26 % Rec. Clause-clause subsumption calls : 2
% 0.08/0.26 % Non-unit clause-clause subsumptions : 0
% 0.08/0.26 % Unit Clause-clause subsumption calls : 0
% 0.08/0.26 % Rewrite failures with RHS unbound : 0
% 0.08/0.26 % BW rewrite match attempts : 0
% 0.08/0.26 % BW rewrite match successes : 0
% 0.08/0.26 % Condensation attempts : 0
% 0.08/0.26 % Condensation successes : 0
% 0.08/0.26 % Termbank termtop insertions : 1267
% 0.08/0.26 % Search garbage collected termcells : 456
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.002 s
% 0.08/0.26 % System time : 0.002 s
% 0.08/0.26 % Total time : 0.004 s
% 0.08/0.26 % Maximum resident set size: 3644 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.002 s
% 0.08/0.26 % System time : 0.005 s
% 0.08/0.26 % Total time : 0.008 s
% 0.08/0.26 % Maximum resident set size: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------