%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU575^2 : 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 : n009.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 08:24:34 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 9 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 64 ( 8 ~; 4 |; 3 &; 34 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
emptyset: $i ).
thf(decl_24,type,
subset: $i > $i > $o ).
thf(decl_25,type,
emptysetsubset: $o ).
thf(decl_26,type,
setextsub: $o ).
thf(decl_27,type,
esk1_0: $i ).
thf(subsetemptysetimpeq,conjecture,
( emptysetsubset
=> ( setextsub
=> ! [X1: $i] :
( ( subset @ X1 @ emptyset )
=> ( X1 = emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TKg4SKo4Nv/E---3.1_4030913.p',subsetemptysetimpeq) ).
thf(emptysetsubset,axiom,
( emptysetsubset
<=> ! [X1: $i] : ( subset @ emptyset @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.TKg4SKo4Nv/E---3.1_4030913.p',emptysetsubset) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X1 )
=> ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TKg4SKo4Nv/E---3.1_4030913.p',setextsub) ).
thf(c_0_3,negated_conjecture,
~ ( emptysetsubset
=> ( setextsub
=> ! [X1: $i] :
( ( subset @ X1 @ emptyset )
=> ( X1 = emptyset ) ) ) ),
inference(assume_negation,[status(cth)],[subsetemptysetimpeq]) ).
thf(c_0_4,negated_conjecture,
~ ( ! [X7: $i] : ( subset @ emptyset @ X7 )
=> ( ! [X8: $i,X9: $i] :
( ( subset @ X8 @ X9 )
=> ( ( subset @ X9 @ X8 )
=> ( X8 = X9 ) ) )
=> ! [X1: $i] :
( ( subset @ X1 @ emptyset )
=> ( X1 = emptyset ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,emptysetsubset]),setextsub]) ).
thf(c_0_5,negated_conjecture,
! [X10: $i,X11: $i,X12: $i] :
( ( subset @ emptyset @ X10 )
& ( ~ ( subset @ X11 @ X12 )
| ~ ( subset @ X12 @ X11 )
| ( X11 = X12 ) )
& ( subset @ esk1_0 @ emptyset )
& ( esk1_0 != emptyset ) ),
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_4])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ~ ( subset @ X1 @ X2 )
| ~ ( subset @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
subset @ esk1_0 @ emptyset,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i] : ( subset @ emptyset @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
esk1_0 != emptyset,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]),c_0_9]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU575^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n009.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:51:45 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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.TKg4SKo4Nv/E---3.1_4030913.p
% 0.09/0.26 % Version: 3.5.1-ho
% 0.09/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.09/0.26 % Starting post_as_ho8 with 300s (1) cores
% 0.09/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.26 % Starting post_as_ho2 with 300s (1) cores
% 0.09/0.26 % lpo6_lambda_fix with pid 4030926 completed with status 0
% 0.09/0.26 % Result found by lpo6_lambda_fix
% 0.09/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HHUSF-FFSF00-SFFFMFNN
% 0.09/0.26 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.26 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.26 % Starting lpo6_lambda_fix with 151s (1) cores
% 0.09/0.26 % Starting sh5l with 136s (1) cores
% 0.09/0.26 % Starting new_bool_1 with 136s (1) cores
% 0.09/0.26 % Starting new_bool_2 with 136s (1) cores
% 0.09/0.26 % lpo6_lambda_fix with pid 4030931 completed with status 0
% 0.09/0.26 % Result found by lpo6_lambda_fix
% 0.09/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HHUSF-FFSF00-SFFFMFNN
% 0.09/0.26 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.26 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.26 % Starting lpo6_lambda_fix with 151s (1) cores
% 0.09/0.26 % Preprocessing time : 0.001 s
% 0.09/0.26
% 0.09/0.26 % Proof found!
% 0.09/0.26 % SZS status Theorem
% 0.09/0.26 % SZS output start CNFRefutation
% See solution above
% 0.09/0.26 % Parsed axioms : 7
% 0.09/0.26 % Removed by relevancy pruning/SinE : 0
% 0.09/0.26 % Initial clauses : 8
% 0.09/0.26 % Removed in clause preprocessing : 4
% 0.09/0.26 % Initial clauses in saturation : 4
% 0.09/0.26 % Processed clauses : 4
% 0.09/0.26 % ...of these trivial : 0
% 0.09/0.26 % ...subsumed : 0
% 0.09/0.26 % ...remaining for further processing : 4
% 0.09/0.26 % Other redundant clauses eliminated : 0
% 0.09/0.26 % Clauses deleted for lack of memory : 0
% 0.09/0.26 % Backward-subsumed : 0
% 0.09/0.26 % Backward-rewritten : 0
% 0.09/0.26 % Generated clauses : 2
% 0.09/0.26 % ...of the previous two non-redundant : 0
% 0.09/0.26 % ...aggressively subsumed : 0
% 0.09/0.26 % Contextual simplify-reflections : 0
% 0.09/0.26 % Paramodulations : 2
% 0.09/0.26 % Factorizations : 0
% 0.09/0.26 % NegExts : 0
% 0.09/0.26 % Equation resolutions : 0
% 0.09/0.26 % Disequality decompositions : 0
% 0.09/0.26 % Total rewrite steps : 1
% 0.09/0.26 % ...of those cached : 0
% 0.09/0.26 % Propositional unsat checks : 0
% 0.09/0.26 % Propositional check models : 0
% 0.09/0.26 % Propositional check unsatisfiable : 0
% 0.09/0.26 % Propositional clauses : 0
% 0.09/0.26 % Propositional clauses after purity: 0
% 0.09/0.26 % Propositional unsat core size : 0
% 0.09/0.26 % Propositional preprocessing time : 0.000
% 0.09/0.26 % Propositional encoding time : 0.000
% 0.09/0.26 % Propositional solver time : 0.000
% 0.09/0.26 % Success case prop preproc time : 0.000
% 0.09/0.26 % Success case prop encoding time : 0.000
% 0.09/0.26 % Success case prop solver time : 0.000
% 0.09/0.26 % Current number of processed clauses : 4
% 0.09/0.26 % Positive orientable unit clauses : 2
% 0.09/0.26 % Positive unorientable unit clauses: 0
% 0.09/0.26 % Negative unit clauses : 1
% 0.09/0.26 % Non-unit-clauses : 1
% 0.09/0.26 % Current number of unprocessed clauses: 0
% 0.09/0.26 % ...number of literals in the above : 0
% 0.09/0.26 % Current number of archived formulas : 0
% 0.09/0.26 % Current number of archived clauses : 0
% 0.09/0.26 % Clause-clause subsumption calls (NU) : 1
% 0.09/0.26 % Rec. Clause-clause subsumption calls : 1
% 0.09/0.26 % Non-unit clause-clause subsumptions : 0
% 0.09/0.26 % Unit Clause-clause subsumption calls : 0
% 0.09/0.26 % Rewrite failures with RHS unbound : 0
% 0.09/0.26 % BW rewrite match attempts : 0
% 0.09/0.26 % BW rewrite match successes : 0
% 0.09/0.26 % Condensation attempts : 4
% 0.09/0.26 % Condensation successes : 0
% 0.09/0.26 % Termbank termtop insertions : 405
% 0.09/0.26 % Search garbage collected termcells : 122
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.001 s
% 0.09/0.26 % System time : 0.002 s
% 0.09/0.26 % Total time : 0.004 s
% 0.09/0.26 % Maximum resident set size: 3628 pages
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.007 s
% 0.09/0.26 % System time : 0.010 s
% 0.09/0.26 % Total time : 0.018 s
% 0.09/0.26 % Maximum resident set size: 4864 pages
% 0.09/0.26 % E exiting
%------------------------------------------------------------------------------