%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU563^2 : 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 : n020.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 08:24:31 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 3 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 114 ( 13 ~; 6 |; 4 &; 70 @)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 29 ( 4 ^; 25 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
emptysetimpfalse: $o ).
thf(decl_26,type,
subset: $i > $i > $o ).
thf(decl_27,type,
subsetI2: $o ).
thf(decl_28,type,
esk1_2: $i > $i > $i ).
thf(decl_29,type,
esk2_0: $i ).
thf(decl_30,type,
esk3_0: $i ).
thf(subset,axiom,
( subset
= ( ^ [X2: $i,X3: $i] :
! [X1: $i] :
( ( in @ X1 @ X2 )
=> ( in @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3XW8yGlJ0E/E---3.1_1087257.p',subset) ).
thf(emptysetsubset,conjecture,
( emptysetimpfalse
=> ( subsetI2
=> ! [X2: $i] : ( subset @ emptyset @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3XW8yGlJ0E/E---3.1_1087257.p',emptysetsubset) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X2: $i,X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X2 )
=> ( in @ X1 @ X3 ) )
=> ( subset @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3XW8yGlJ0E/E---3.1_1087257.p',subsetI2) ).
thf(emptysetimpfalse,axiom,
( emptysetimpfalse
<=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ~ $true ) ),
file('/export/starexec/sandbox2/tmp/tmp.3XW8yGlJ0E/E---3.1_1087257.p',emptysetimpfalse) ).
thf(c_0_4,plain,
( subset
= ( ^ [Z0: $i,Z1: $i] :
! [X1: $i] :
( ( in @ X1 @ Z0 )
=> ( in @ X1 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[subset]) ).
thf(c_0_5,negated_conjecture,
~ ( emptysetimpfalse
=> ( subsetI2
=> ! [X2: $i] : ( subset @ emptyset @ X2 ) ) ),
inference(assume_negation,[status(cth)],[emptysetsubset]) ).
thf(c_0_6,axiom,
( subsetI2
= ( ! [X2: $i,X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X2 )
=> ( in @ X1 @ X3 ) )
=> ! [X9: $i] :
( ( in @ X9 @ X2 )
=> ( in @ X9 @ X3 ) ) ) ) ),
inference(apply_def,[status(thm)],[subsetI2,c_0_4]) ).
thf(c_0_7,negated_conjecture,
~ ( ! [X10: $i] :
( ( in @ X10 @ emptyset )
=> ~ $true )
=> ( ! [X11: $i,X12: $i] :
( ! [X13: $i] :
( ( in @ X13 @ X11 )
=> ( in @ X13 @ X12 ) )
=> ! [X14: $i] :
( ( in @ X14 @ X11 )
=> ( in @ X14 @ X12 ) ) )
=> ! [X2: $i,X15: $i] :
( ( in @ X15 @ emptyset )
=> ( in @ X15 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6]),c_0_4]),emptysetimpfalse]) ).
thf(c_0_8,negated_conjecture,
! [X16: $i,X17: $i,X18: $i,X20: $i] :
( ( ~ ( in @ X16 @ emptyset )
| ~ $true )
& ( ( in @ ( esk1_2 @ X17 @ X18 ) @ X17 )
| ~ ( in @ X20 @ X17 )
| ( in @ X20 @ X18 ) )
& ( ~ ( in @ ( esk1_2 @ X17 @ X18 ) @ X18 )
| ~ ( in @ X20 @ X17 )
| ( in @ X20 @ X18 ) )
& ( in @ esk3_0 @ emptyset )
& ~ ( in @ esk3_0 @ esk2_0 ) ),
inference(distribute,[status(thm)],[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_7])])])])])]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ emptyset )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
in @ esk3_0 @ emptyset,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i] :
~ ( in @ X1 @ emptyset ),
inference(cn,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_10,c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU563^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n020.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:51:19 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 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.3XW8yGlJ0E/E---3.1_1087257.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.26 % Starting lpo1_def_fix with 300s (1) cores
% 0.08/0.26 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.08/0.26 % lpo1_def_fix with pid 1087294 completed with status 0
% 0.08/0.26 % Result found by lpo1_def_fix
% 0.08/0.26 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.26 % Starting lpo1_def_fix with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf600_gu_R05_F100_L20000)
% 0.08/0.26 % SinE strategy is gf600_gu_R05_F100_L20000
% 0.08/0.26 % Search class: HGUNF-FFSF22-SSFFMFNN
% 0.08/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.26 % SubtermCWHack with pid 1087300 completed with status 0
% 0.08/0.26 % Result found by SubtermCWHack
% 0.08/0.26 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.26 % Starting lpo1_def_fix with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf600_gu_R05_F100_L20000)
% 0.08/0.26 % SinE strategy is gf600_gu_R05_F100_L20000
% 0.08/0.26 % Search class: HGUNF-FFSF22-SSFFMFNN
% 0.08/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 31s (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
% See solution above
% 0.08/0.26 % Parsed axioms : 9
% 0.08/0.26 % Removed by relevancy pruning/SinE : 5
% 0.08/0.26 % Initial clauses : 5
% 0.08/0.26 % Removed in clause preprocessing : 0
% 0.08/0.26 % Initial clauses in saturation : 5
% 0.08/0.26 % Processed clauses : 3
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 0
% 0.08/0.26 % ...remaining for further processing : 3
% 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 : 1
% 0.08/0.26 % ...of the previous two non-redundant : 0
% 0.08/0.26 % ...aggressively subsumed : 0
% 0.08/0.26 % Contextual simplify-reflections : 0
% 0.08/0.26 % Paramodulations : 0
% 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 : 2
% 0.08/0.26 % Positive orientable unit clauses : 0
% 0.08/0.26 % Positive unorientable unit clauses: 0
% 0.08/0.26 % Negative unit clauses : 2
% 0.08/0.26 % Non-unit-clauses : 0
% 0.08/0.26 % Current number of unprocessed clauses: 2
% 0.08/0.26 % ...number of literals in the above : 6
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 1
% 0.08/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.26 % Rec. Clause-clause subsumption calls : 0
% 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 : 581
% 0.08/0.26 % Search garbage collected termcells : 218
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.002 s
% 0.08/0.26 % System time : 0.003 s
% 0.08/0.26 % Total time : 0.005 s
% 0.08/0.26 % Maximum resident set size: 3888 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.004 s
% 0.08/0.26 % System time : 0.006 s
% 0.08/0.26 % Total time : 0.010 s
% 0.08/0.26 % Maximum resident set size: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------