%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU777^2 : 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 : n013.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 08:27:45 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU777^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n013.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:27:21 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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.QsZfHjoc6G/E---3.1_2193941.p
% 0.07/0.26 % Version: 3.5.1-ho
% 0.07/0.26 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.26 % Starting sh4l with 300s (1) cores
% 0.07/0.26 % Starting lpo8_s with 300s (1) cores
% 0.07/0.26 % new_ho_10 with pid 2193975 completed with status 0
% 0.07/0.26 % Result found by new_ho_10
% 0.07/0.26 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.26 % No SInE strategy applied
% 0.07/0.26 % Search class: HHUSF-FFSS32-SSFFMSBN
% 0.07/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.07/0.26 % Starting new_ho_10 with 901s (1) cores
% 0.07/0.26 % Starting full_lambda_3 with 151s (1) cores
% 0.07/0.26 % Starting ho_unfolding_6 with 151s (1) cores
% 0.07/0.26 % Starting sh4l with 146s (1) cores
% 0.07/0.26 % SubtermCWHack with pid 2193979 completed with status 0
% 0.07/0.26 % Result found by SubtermCWHack
% 0.07/0.26 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.26 % No SInE strategy applied
% 0.07/0.26 % Search class: HHUSF-FFSS32-SSFFMSBN
% 0.07/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.07/0.26 % Preprocessing time : 0.001 s
% 0.07/0.26
% 0.07/0.26 % Proof found!
% 0.07/0.26 % SZS status Theorem
% 0.07/0.26 % SZS output start CNFRefutation
% 0.07/0.26 thf(decl_23, type, in: $i > $i > $o).
% 0.07/0.26 thf(decl_24, type, subset: $i > $i > $o).
% 0.07/0.26 thf(decl_25, type, kpair: $i > $i > $i).
% 0.07/0.26 thf(decl_26, type, cartprod: $i > $i > $i).
% 0.07/0.26 thf(decl_27, type, breln: $i > $i > $i > $o).
% 0.07/0.26 thf(decl_28, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.07/0.26 thf(decl_29, type, dpsetconstrER: $o).
% 0.07/0.26 thf(decl_30, type, breln1: $i > $i > $o).
% 0.07/0.26 thf(decl_31, type, breln1invset: $i > $i > $i).
% 0.07/0.26 thf(decl_32, type, esk1_0: $i).
% 0.07/0.26 thf(decl_33, type, esk2_0: $i).
% 0.07/0.26 thf(decl_34, type, esk3_0: $i).
% 0.07/0.26 thf(decl_35, type, esk4_0: $i).
% 0.07/0.26 thf(decl_36, type, epred1_1: $i > $i > $i > $o).
% 0.07/0.26 thf(breln1, axiom, ((breln1)=(^[X1:$i, X9:$i]:((breln @ X1 @ X1 @ X9)))), file('/export/starexec/sandbox2/tmp/tmp.QsZfHjoc6G/E---3.1_2193941.p', breln1)).
% 0.07/0.26 thf(breln, axiom, ((breln)=(^[X1:$i, X2:$i, X3:$i]:((subset @ X3 @ (cartprod @ X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.QsZfHjoc6G/E---3.1_2193941.p', breln)).
% 0.07/0.26 thf(breln1invE, conjecture, ((dpsetconstrER)=>![X1:$i, X9:$i]:(((breln1 @ X1 @ X9)=>![X5:$i]:(((in @ X5 @ X1)=>![X6:$i]:(((in @ X6 @ X1)=>((in @ (kpair @ X6 @ X5) @ (breln1invset @ X1 @ X9))=>(in @ (kpair @ X5 @ X6) @ X9))))))))), file('/export/starexec/sandbox2/tmp/tmp.QsZfHjoc6G/E---3.1_2193941.p', breln1invE)).
% 0.07/0.26 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X1:$i, X2:$i, X4:$i > $i > $o, X5:$i, X6:$i]:(((in @ (kpair @ X5 @ X6) @ (dpsetconstr @ X1 @ X2 @ (^[X7:$i, X8:$i]:((X4 @ X7 @ X8)))))=>(X4 @ X5 @ X6)))), file('/export/starexec/sandbox2/tmp/tmp.QsZfHjoc6G/E---3.1_2193941.p', dpsetconstrER)).
% 0.07/0.26 thf(breln1invset, axiom, ((breln1invset)=(^[X1:$i, X9:$i]:(dpsetconstr @ X1 @ X1 @ (^[X5:$i, X6:$i]:((in @ (kpair @ X6 @ X5) @ X9)))))), file('/export/starexec/sandbox2/tmp/tmp.QsZfHjoc6G/E---3.1_2193941.p', breln1invset)).
% 0.07/0.26 thf(c_0_5, plain, ((breln1)=(^[Z0:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(fof_simplification,[status(thm)],[breln1])).
% 0.07/0.26 thf(c_0_6, plain, ((breln)=(^[Z0:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 0.07/0.26 thf(c_0_7, negated_conjecture, ~(((dpsetconstrER)=>![X1:$i, X9:$i]:(((breln1 @ X1 @ X9)=>![X5:$i]:(((in @ X5 @ X1)=>![X6:$i]:(((in @ X6 @ X1)=>((in @ (kpair @ X6 @ X5) @ (breln1invset @ X1 @ X9))=>(in @ (kpair @ X5 @ X6) @ X9)))))))))), inference(assume_negation,[status(cth)],[breln1invE])).
% 0.07/0.26 thf(c_0_8, plain, ((dpsetconstrER)<=>![X1:$i, X2:$i, X4:$i > $i > $o, X5:$i, X6:$i]:(((in @ (kpair @ X5 @ X6) @ (dpsetconstr @ X1 @ X2 @ (^[Z0:$i, Z1:$i]:((X4 @ Z0 @ Z1)))))=>(X4 @ X5 @ X6)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 0.07/0.26 thf(c_0_9, plain, ((breln1)=(^[Z0:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(apply_def,[status(thm)],[c_0_5, c_0_6])).
% 0.07/0.26 thf(c_0_10, negated_conjecture, ~((![X19:$i, X20:$i, X21:$i > $i > $o, X22:$i, X23:$i]:(((in @ (kpair @ X22 @ X23) @ (dpsetconstr @ X19 @ X20 @ X21))=>(X21 @ X22 @ X23)))=>![X1:$i, X9:$i]:(((subset @ X9 @ (cartprod @ X1 @ X1))=>![X5:$i]:(((in @ X5 @ X1)=>![X6:$i]:(((in @ X6 @ X1)=>((in @ (kpair @ X6 @ X5) @ (breln1invset @ X1 @ X9))=>(in @ (kpair @ X5 @ X6) @ X9)))))))))), inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7, c_0_8]), c_0_9])])).
% 0.07/0.26 thf(c_0_11, plain, ![X24:$i, X25:$i]:(((breln1invset @ X24 @ X25)=(dpsetconstr @ X24 @ X24 @ (^[Z0:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X25)))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[breln1invset])])).
% 0.07/0.26 thf(c_0_12, negated_conjecture, ![X28:$i, X29:$i, X30:$i > $i > $o, X31:$i, X32:$i]:(((~(in @ (kpair @ X31 @ X32) @ (dpsetconstr @ X28 @ X29 @ X30))|(X30 @ X31 @ X32))&((subset @ esk2_0 @ (cartprod @ esk1_0 @ esk1_0))&((in @ esk3_0 @ esk1_0)&((in @ esk4_0 @ esk1_0)&((in @ (kpair @ esk4_0 @ esk3_0) @ (breln1invset @ esk1_0 @ esk2_0))&~(in @ (kpair @ esk3_0 @ esk4_0) @ esk2_0))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])])).
% 0.07/0.26 thf(c_0_13, plain, ![X26:$i, X27:$i]:(((breln1invset @ X26 @ X27)=(dpsetconstr @ X26 @ X26 @ (^[Z0:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X27)))))), inference(variable_rename,[status(thm)],[c_0_11])).
% 0.07/0.26 thf(c_0_14, plain, ![X38:$i, X37:$i, X2:$i]:(((epred1_1 @ X2 @ X37 @ X38)<=>(in @ (kpair @ X38 @ X37) @ X2))), introduced(definition)).
% 0.07/0.26 thf(c_0_15, negated_conjecture, ![X1:$i, X2:$i, X3:$i, X5:$i, X4:$i > $i > $o]:(((X4 @ X1 @ X2)|~((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X5 @ X4))))), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.07/0.26 thf(c_0_16, plain, ![X1:$i, X2:$i]:(((breln1invset @ X1 @ X2)=(dpsetconstr @ X1 @ X1 @ (epred1_1 @ X2)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_13]), c_0_14])).
% 0.07/0.26 thf(c_0_17, plain, ![X39:$i, X40:$i, X41:$i]:(((~(epred1_1 @ X41 @ X40 @ X39)|(in @ (kpair @ X39 @ X40) @ X41))&(~(in @ (kpair @ X39 @ X40) @ X41)|(epred1_1 @ X41 @ X40 @ X39)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])).
% 0.07/0.26 thf(c_0_18, negated_conjecture, ![X2:$i, X5:$i, X3:$i, X1:$i]:(((epred1_1 @ X1 @ X2 @ X3)|~((in @ (kpair @ X2 @ X3) @ (breln1invset @ X5 @ X1))))), inference(spm,[status(thm)],[c_0_15, c_0_16])).
% 0.07/0.26 thf(c_0_19, negated_conjecture, (in @ (kpair @ esk4_0 @ esk3_0) @ (breln1invset @ esk1_0 @ esk2_0)), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.07/0.26 thf(c_0_20, plain, ![X1:$i, X2:$i, X3:$i]:(((in @ (kpair @ X3 @ X2) @ X1)|~((epred1_1 @ X1 @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_17])).
% 0.07/0.26 thf(c_0_21, negated_conjecture, (epred1_1 @ esk2_0 @ esk4_0 @ esk3_0), inference(spm,[status(thm)],[c_0_18, c_0_19])).
% 0.07/0.26 thf(c_0_22, negated_conjecture, ~((in @ (kpair @ esk3_0 @ esk4_0) @ esk2_0)), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.07/0.26 thf(c_0_23, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_21]), c_0_22]), ['proof']).
% 0.07/0.26 % SZS output end CNFRefutation
% 0.07/0.26 % Parsed axioms : 14
% 0.07/0.26 % Removed by relevancy pruning/SinE : 0
% 0.07/0.26 % Initial clauses : 18
% 0.07/0.26 % Removed in clause preprocessing : 9
% 0.07/0.26 % Initial clauses in saturation : 9
% 0.07/0.26 % Processed clauses : 11
% 0.07/0.26 % ...of these trivial : 0
% 0.07/0.26 % ...subsumed : 0
% 0.07/0.26 % ...remaining for further processing : 11
% 0.07/0.26 % Other redundant clauses eliminated : 0
% 0.07/0.26 % Clauses deleted for lack of memory : 0
% 0.07/0.26 % Backward-subsumed : 0
% 0.07/0.26 % Backward-rewritten : 0
% 0.07/0.26 % Generated clauses : 4
% 0.07/0.26 % ...of the previous two non-redundant : 2
% 0.07/0.26 % ...aggressively subsumed : 0
% 0.07/0.26 % Contextual simplify-reflections : 0
% 0.07/0.26 % Paramodulations : 4
% 0.07/0.26 % Factorizations : 0
% 0.07/0.26 % NegExts : 0
% 0.07/0.26 % Equation resolutions : 0
% 0.07/0.26 % Disequality decompositions : 0
% 0.07/0.26 % Total rewrite steps : 0
% 0.07/0.26 % ...of those cached : 0
% 0.07/0.26 % Propositional unsat checks : 0
% 0.07/0.26 % Propositional check models : 0
% 0.07/0.26 % Propositional check unsatisfiable : 0
% 0.07/0.26 % Propositional clauses : 0
% 0.07/0.26 % Propositional clauses after purity: 0
% 0.07/0.26 % Propositional unsat core size : 0
% 0.07/0.26 % Propositional preprocessing time : 0.000
% 0.07/0.26 % Propositional encoding time : 0.000
% 0.07/0.26 % Propositional solver time : 0.000
% 0.07/0.26 % Success case prop preproc time : 0.000
% 0.07/0.26 % Success case prop encoding time : 0.000
% 0.07/0.26 % Success case prop solver time : 0.000
% 0.07/0.26 % Current number of processed clauses : 11
% 0.07/0.26 % Positive orientable unit clauses : 6
% 0.07/0.26 % Positive unorientable unit clauses: 0
% 0.07/0.26 % Negative unit clauses : 1
% 0.07/0.26 % Non-unit-clauses : 4
% 0.07/0.26 % Current number of unprocessed clauses: 0
% 0.07/0.26 % ...number of literals in the above : 0
% 0.07/0.26 % Current number of archived formulas : 0
% 0.07/0.26 % Current number of archived clauses : 0
% 0.07/0.26 % Clause-clause subsumption calls (NU) : 4
% 0.07/0.26 % Rec. Clause-clause subsumption calls : 2
% 0.07/0.26 % Non-unit clause-clause subsumptions : 0
% 0.07/0.26 % Unit Clause-clause subsumption calls : 0
% 0.07/0.26 % Rewrite failures with RHS unbound : 0
% 0.07/0.26 % BW rewrite match attempts : 0
% 0.07/0.26 % BW rewrite match successes : 0
% 0.07/0.26 % Condensation attempts : 0
% 0.07/0.26 % Condensation successes : 0
% 0.07/0.26 % Termbank termtop insertions : 1012
% 0.07/0.26 % Search garbage collected termcells : 275
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.004 s
% 0.07/0.26 % System time : 0.002 s
% 0.07/0.26 % Total time : 0.006 s
% 0.07/0.26 % Maximum resident set size: 3644 pages
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.014 s
% 0.07/0.26 % System time : 0.008 s
% 0.07/0.26 % Total time : 0.021 s
% 0.07/0.26 % Maximum resident set size: 4608 pages
% 0.07/0.26 % E exiting
%------------------------------------------------------------------------------