%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU612^2 : 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 : n014.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 08:26:55 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU612^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n014.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 13:57:54 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.22 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.z76eSb66rS/E---3.1_2703945.p
% 0.09/0.23 % Version: 3.5.1-ho
% 0.09/0.23 % Preprocessing class: HSSSSLSSSLMNSFA.
% 0.09/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.23 % Starting full_lambda_3 with 300s (1) cores
% 0.09/0.23 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.23 % Starting sh4l with 300s (1) cores
% 0.09/0.23 % new_ho_10 with pid 2703958 completed with status 0
% 0.09/0.23 % Result found by new_ho_10
% 0.09/0.23 % Preprocessing class: HSSSSLSSSLMNSFA.
% 0.09/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.23 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.23 % No SInE strategy applied
% 0.09/0.23 % Search class: HGHSF-FFSF22-SSFFMSBN
% 0.09/0.23 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.23 % Starting SubtermCWHack with 151s (1) cores
% 0.09/0.23 % Starting new_ho_10 with 901s (1) cores
% 0.09/0.23 % Starting new_bool_1 with 151s (1) cores
% 0.09/0.23 % Starting new_bool_2 with 151s (1) cores
% 0.09/0.23 % Starting new_bool_9 with 146s (1) cores
% 0.09/0.23 % SubtermCWHack with pid 2703962 completed with status 0
% 0.09/0.23 % Result found by SubtermCWHack
% 0.09/0.23 % Preprocessing class: HSSSSLSSSLMNSFA.
% 0.09/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.23 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.23 % No SInE strategy applied
% 0.09/0.23 % Search class: HGHSF-FFSF22-SSFFMSBN
% 0.09/0.23 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.23 % Starting SubtermCWHack with 151s (1) cores
% 0.09/0.23 % Preprocessing time : 0.001 s
% 0.09/0.23
% 0.09/0.23 % Proof found!
% 0.09/0.23 % SZS status Theorem
% 0.09/0.23 % SZS output start CNFRefutation
% 0.09/0.23 thf(decl_23, type, in: $i > $i > $o).
% 0.09/0.23 thf(decl_24, type, dsetconstr: $i > ($i > $o) > $i).
% 0.09/0.23 thf(decl_25, type, dsetconstrI: $o).
% 0.09/0.23 thf(decl_26, type, binunion: $i > $i > $i).
% 0.09/0.23 thf(decl_27, type, binunionIL: $o).
% 0.09/0.23 thf(decl_28, type, symdiff: $i > $i > $i).
% 0.09/0.23 thf(decl_29, type, esk1_0: $i).
% 0.09/0.23 thf(decl_30, type, esk2_0: $i).
% 0.09/0.23 thf(decl_31, type, esk3_0: $i).
% 0.09/0.23 thf(decl_32, type, epred1_2: $i > $i > $i > $o).
% 0.09/0.23 thf(symdiffI1, conjecture, ((dsetconstrI)=>((binunionIL)=>![X1:$i, X5:$i, X3:$i]:(((in @ X3 @ X1)=>(~((in @ X3 @ X5))=>(in @ X3 @ (symdiff @ X1 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.z76eSb66rS/E---3.1_2703945.p', symdiffI1)).
% 0.09/0.23 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X1:$i, X2:$i > $o, X3:$i]:(((in @ X3 @ X1)=>((X2 @ X3)=>(in @ X3 @ (dsetconstr @ X1 @ (^[X4:$i]:((X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.z76eSb66rS/E---3.1_2703945.p', dsetconstrI)).
% 0.09/0.23 thf(binunionIL, axiom, ((binunionIL)<=>![X1:$i, X5:$i, X3:$i]:(((in @ X3 @ X1)=>(in @ X3 @ (binunion @ X1 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.z76eSb66rS/E---3.1_2703945.p', binunionIL)).
% 0.09/0.23 thf(symdiff, axiom, ((symdiff)=(^[X1:$i, X5:$i]:(dsetconstr @ (binunion @ X1 @ X5) @ (^[X3:$i]:(((~((in @ X3 @ X1)))|(~((in @ X3 @ X5))))))))), file('/export/starexec/sandbox2/tmp/tmp.z76eSb66rS/E---3.1_2703945.p', symdiff)).
% 0.09/0.23 thf(c_0_4, negated_conjecture, ~(((dsetconstrI)=>((binunionIL)=>![X1:$i, X5:$i, X3:$i]:(((in @ X3 @ X1)=>(~((in @ X3 @ X5))=>(in @ X3 @ (symdiff @ X1 @ X5)))))))), inference(assume_negation,[status(cth)],[symdiffI1])).
% 0.09/0.23 thf(c_0_5, plain, ((dsetconstrI)<=>![X1:$i, X2:$i > $o, X3:$i]:(((in @ X3 @ X1)=>((X2 @ X3)=>(in @ X3 @ (dsetconstr @ X1 @ (^[Z0:$i]:((X2 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.09/0.23 thf(c_0_6, negated_conjecture, ~((![X15:$i, X16:$i > $o, X17:$i]:(((in @ X17 @ X15)=>((X16 @ X17)=>(in @ X17 @ (dsetconstr @ X15 @ X16)))))=>(![X18:$i, X19:$i, X20:$i]:(((in @ X20 @ X18)=>(in @ X20 @ (binunion @ X18 @ X19))))=>![X1:$i, X5:$i, X3:$i]:(((in @ X3 @ X1)=>(~(in @ X3 @ X5)=>(in @ X3 @ (symdiff @ X1 @ X5)))))))), inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4, c_0_5]), binunionIL])])])).
% 0.09/0.23 thf(c_0_7, plain, ![X21:$i, X22:$i]:(((symdiff @ X21 @ X22)=(dsetconstr @ (binunion @ X21 @ X22) @ (^[Z0:$i]:(((~((in @ Z0 @ X21)))|(~((in @ Z0 @ X22))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[symdiff])])).
% 0.09/0.23 thf(c_0_8, negated_conjecture, ![X25:$i, X26:$i > $o, X27:$i, X28:$i, X29:$i, X30:$i]:(((~(in @ X27 @ X25)|(~(X26 @ X27)|(in @ X27 @ (dsetconstr @ X25 @ X26))))&((~(in @ X30 @ X28)|(in @ X30 @ (binunion @ X28 @ X29)))&((in @ esk3_0 @ esk1_0)&(~(in @ esk3_0 @ esk2_0)&~(in @ esk3_0 @ (symdiff @ esk1_0 @ esk2_0))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])])).
% 0.09/0.23 thf(c_0_9, plain, ![X23:$i, X24:$i]:(((symdiff @ X23 @ X24)=(dsetconstr @ (binunion @ X23 @ X24) @ (^[Z0:$i]:(((~((in @ Z0 @ X23)))|(~((in @ Z0 @ X24))))))))), inference(variable_rename,[status(thm)],[c_0_7])).
% 0.09/0.23 thf(c_0_10, plain, ![X34:$i, X1:$i, X3:$i]:(((epred1_2 @ X3 @ X1 @ X34)<=>(~((in @ X34 @ X1))|~((in @ X34 @ X3))))), introduced(definition)).
% 0.09/0.23 thf(c_0_11, negated_conjecture, ![X3:$i, X2:$i > $o, X1:$i]:(((in @ X1 @ (dsetconstr @ X3 @ X2))|~((in @ X1 @ X3))|~((X2 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 0.09/0.23 thf(c_0_12, plain, ![X3:$i, X1:$i]:(((symdiff @ X1 @ X3)=(dsetconstr @ (binunion @ X1 @ X3) @ (epred1_2 @ X3 @ X1)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_9]), c_0_10])).
% 0.09/0.23 thf(c_0_13, negated_conjecture, ![X4:$i, X3:$i, X1:$i]:(((in @ X1 @ (symdiff @ X3 @ X4))|~((in @ X1 @ (binunion @ X3 @ X4)))|~((epred1_2 @ X4 @ X3 @ X1)))), inference(spm,[status(thm)],[c_0_11, c_0_12])).
% 0.09/0.23 thf(c_0_14, negated_conjecture, ![X1:$i, X4:$i, X3:$i]:(((in @ X1 @ (binunion @ X3 @ X4))|~((in @ X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 0.09/0.23 thf(c_0_15, negated_conjecture, ~((in @ esk3_0 @ (symdiff @ esk1_0 @ esk2_0))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 0.09/0.23 thf(c_0_16, negated_conjecture, ![X1:$i, X4:$i, X3:$i]:(((in @ X1 @ (symdiff @ X3 @ X4))|~((epred1_2 @ X4 @ X3 @ X1))|~((in @ X1 @ X3)))), inference(spm,[status(thm)],[c_0_13, c_0_14])).
% 0.09/0.23 thf(c_0_17, negated_conjecture, (in @ esk3_0 @ esk1_0), inference(split_conjunct,[status(thm)],[c_0_8])).
% 0.09/0.23 thf(c_0_18, plain, ![X35:$i, X36:$i, X37:$i]:(((~(epred1_2 @ X37 @ X36 @ X35)|(~(in @ X35 @ X36)|~(in @ X35 @ X37)))&(((in @ X35 @ X36)|(epred1_2 @ X37 @ X36 @ X35))&((in @ X35 @ X37)|(epred1_2 @ X37 @ X36 @ X35))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[])])])])])).
% 0.09/0.23 thf(c_0_19, negated_conjecture, ~((epred1_2 @ esk2_0 @ esk1_0 @ esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16]), c_0_17])])).
% 0.09/0.23 thf(c_0_20, plain, ![X4:$i, X3:$i, X1:$i]:(((in @ X1 @ X3)|(epred1_2 @ X3 @ X4 @ X1))), inference(split_conjunct,[status(thm)],[c_0_18])).
% 0.09/0.23 thf(c_0_21, negated_conjecture, ~((in @ esk3_0 @ esk2_0)), inference(split_conjunct,[status(thm)],[c_0_8])).
% 0.09/0.23 thf(c_0_22, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_20]), c_0_21]), ['proof']).
% 0.09/0.23 % SZS output end CNFRefutation
% 0.09/0.23 % Parsed axioms : 10
% 0.09/0.23 % Removed by relevancy pruning/SinE : 0
% 0.09/0.23 % Initial clauses : 15
% 0.09/0.23 % Removed in clause preprocessing : 6
% 0.09/0.23 % Initial clauses in saturation : 9
% 0.09/0.23 % Processed clauses : 12
% 0.09/0.23 % ...of these trivial : 0
% 0.09/0.23 % ...subsumed : 0
% 0.09/0.23 % ...remaining for further processing : 12
% 0.09/0.23 % Other redundant clauses eliminated : 0
% 0.09/0.23 % Clauses deleted for lack of memory : 0
% 0.09/0.23 % Backward-subsumed : 0
% 0.09/0.23 % Backward-rewritten : 0
% 0.09/0.23 % Generated clauses : 7
% 0.09/0.23 % ...of the previous two non-redundant : 3
% 0.09/0.23 % ...aggressively subsumed : 0
% 0.09/0.23 % Contextual simplify-reflections : 0
% 0.09/0.23 % Paramodulations : 7
% 0.09/0.23 % Factorizations : 0
% 0.09/0.23 % NegExts : 0
% 0.09/0.23 % Equation resolutions : 0
% 0.09/0.23 % Disequality decompositions : 0
% 0.09/0.23 % Total rewrite steps : 2
% 0.09/0.23 % ...of those cached : 1
% 0.09/0.23 % Propositional unsat checks : 0
% 0.09/0.23 % Propositional check models : 0
% 0.09/0.23 % Propositional check unsatisfiable : 0
% 0.09/0.23 % Propositional clauses : 0
% 0.09/0.23 % Propositional clauses after purity: 0
% 0.09/0.23 % Propositional unsat core size : 0
% 0.09/0.23 % Propositional preprocessing time : 0.000
% 0.09/0.23 % Propositional encoding time : 0.000
% 0.09/0.23 % Propositional solver time : 0.000
% 0.09/0.23 % Success case prop preproc time : 0.000
% 0.09/0.23 % Success case prop encoding time : 0.000
% 0.09/0.23 % Success case prop solver time : 0.000
% 0.09/0.23 % Current number of processed clauses : 12
% 0.09/0.23 % Positive orientable unit clauses : 2
% 0.09/0.23 % Positive unorientable unit clauses: 0
% 0.09/0.23 % Negative unit clauses : 3
% 0.09/0.23 % Non-unit-clauses : 7
% 0.09/0.23 % Current number of unprocessed clauses: 0
% 0.09/0.23 % ...number of literals in the above : 0
% 0.09/0.23 % Current number of archived formulas : 0
% 0.09/0.23 % Current number of archived clauses : 0
% 0.09/0.23 % Clause-clause subsumption calls (NU) : 10
% 0.09/0.23 % Rec. Clause-clause subsumption calls : 9
% 0.09/0.23 % Non-unit clause-clause subsumptions : 0
% 0.09/0.23 % Unit Clause-clause subsumption calls : 0
% 0.09/0.23 % Rewrite failures with RHS unbound : 0
% 0.09/0.23 % BW rewrite match attempts : 0
% 0.09/0.23 % BW rewrite match successes : 0
% 0.09/0.23 % Condensation attempts : 0
% 0.09/0.23 % Condensation successes : 0
% 0.09/0.23 % Termbank termtop insertions : 1108
% 0.09/0.23 % Search garbage collected termcells : 312
% 0.09/0.23
% 0.09/0.23 % -------------------------------------------------
% 0.09/0.23 % User time : 0.004 s
% 0.09/0.23 % System time : 0.002 s
% 0.09/0.23 % Total time : 0.006 s
% 0.09/0.23 % Maximum resident set size: 3636 pages
% 0.09/0.23
% 0.09/0.23 % -------------------------------------------------
% 0.09/0.23 % User time : 0.015 s
% 0.09/0.23 % System time : 0.012 s
% 0.09/0.23 % Total time : 0.027 s
% 0.09/0.23 % Maximum resident set size: 4864 pages
% 0.09/0.23 % E exiting
%------------------------------------------------------------------------------