%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU561^2 : 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 : n002.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 0.25s 0.28s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 8 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 95 ( 7 ~; 4 |; 4 &; 62 @)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 27 ( 4 ^; 23 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
subset: $i > $i > $o ).
thf(decl_25,type,
subsetI1: $o ).
thf(decl_26,type,
esk1_2: $i > $i > $i ).
thf(decl_27,type,
esk2_0: $i ).
thf(decl_28,type,
esk3_0: $i ).
thf(decl_29,type,
esk4_0: $i ).
thf(subset,axiom,
( subset
= ( ^ [X1: $i,X2: $i] :
! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eUffsVzsnY/E---3.1_1319862.p',subset) ).
thf(eqimpsubset1,conjecture,
( subsetI1
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( subset @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eUffsVzsnY/E---3.1_1319862.p',eqimpsubset1) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eUffsVzsnY/E---3.1_1319862.p',subsetI1) ).
thf(c_0_3,plain,
( subset
= ( ^ [Z0: $i,Z1: $i] :
! [X3: $i] :
( ( in @ X3 @ Z0 )
=> ( in @ X3 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[subset]) ).
thf(c_0_4,negated_conjecture,
~ ( subsetI1
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( subset @ X1 @ X2 ) ) ),
inference(assume_negation,[status(cth)],[eqimpsubset1]) ).
thf(c_0_5,axiom,
( subsetI1
= ( ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ! [X9: $i] :
( ( in @ X9 @ X1 )
=> ( in @ X9 @ X2 ) ) ) ) ),
inference(apply_def,[status(thm)],[subsetI1,c_0_3]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X10: $i,X11: $i] :
( ! [X12: $i] :
( ( in @ X12 @ X10 )
=> ( in @ X12 @ X11 ) )
=> ! [X13: $i] :
( ( in @ X13 @ X10 )
=> ( in @ X13 @ X11 ) ) )
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X14: $i] :
( ( in @ X14 @ X1 )
=> ( in @ X14 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_3]),c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X15: $i,X16: $i,X18: $i] :
( ( ( in @ ( esk1_2 @ X15 @ X16 ) @ X15 )
| ~ ( in @ X18 @ X15 )
| ( in @ X18 @ X16 ) )
& ( ~ ( in @ ( esk1_2 @ X15 @ X16 ) @ X16 )
| ~ ( in @ X18 @ X15 )
| ( in @ X18 @ X16 ) )
& ( esk2_0 = esk3_0 )
& ( in @ esk4_0 @ esk2_0 )
& ~ ( in @ esk4_0 @ esk3_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_6])])])])])]) ).
thf(c_0_8,negated_conjecture,
~ ( in @ esk4_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
esk2_0 = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
in @ esk4_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU561^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n002.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 13:52:52 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.25 Running higher-order theorem proving
% 0.07/0.26 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.eUffsVzsnY/E---3.1_1319862.p
% 0.25/0.28 % Version: 3.5.1-ho
% 0.25/0.28 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.25/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.25/0.28 % Starting post_as_ho5 with 300s (1) cores
% 0.25/0.28 % Starting sh4l with 300s (1) cores
% 0.25/0.28 % Starting ho_unfolding_2 with 300s (1) cores
% 0.25/0.28 % post_as_ho5 with pid 1319877 completed with status 0
% 0.25/0.28 % Result found by post_as_ho5
% 0.25/0.28 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.25/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.25/0.28 % Starting post_as_ho5 with 300s (1) cores
% 0.25/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.25/0.28 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.25/0.28 % Search class: HGUSF-FFSF22-SSFFMFNN
% 0.25/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.28 % SubtermCWHack with pid 1319883 completed with status 0
% 0.25/0.28 % Result found by SubtermCWHack
% 0.25/0.28 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.25/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.25/0.28 % Starting post_as_ho5 with 300s (1) cores
% 0.25/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.25/0.28 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.25/0.28 % Search class: HGUSF-FFSF22-SSFFMFNN
% 0.25/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.28 % Preprocessing time : 0.002 s
% 0.25/0.28
% 0.25/0.28 % Proof found!
% 0.25/0.28 % SZS status Theorem
% 0.25/0.28 % SZS output start CNFRefutation
% See solution above
% 0.25/0.28 % Parsed axioms : 6
% 0.25/0.28 % Removed by relevancy pruning/SinE : 3
% 0.25/0.28 % Initial clauses : 5
% 0.25/0.28 % Removed in clause preprocessing : 0
% 0.25/0.28 % Initial clauses in saturation : 5
% 0.25/0.28 % Processed clauses : 3
% 0.25/0.28 % ...of these trivial : 0
% 0.25/0.28 % ...subsumed : 0
% 0.25/0.28 % ...remaining for further processing : 2
% 0.25/0.28 % Other redundant clauses eliminated : 0
% 0.25/0.28 % Clauses deleted for lack of memory : 0
% 0.25/0.28 % Backward-subsumed : 0
% 0.25/0.28 % Backward-rewritten : 0
% 0.25/0.28 % Generated clauses : 0
% 0.25/0.28 % ...of the previous two non-redundant : 0
% 0.25/0.28 % ...aggressively subsumed : 0
% 0.25/0.28 % Contextual simplify-reflections : 0
% 0.25/0.28 % Paramodulations : 0
% 0.25/0.28 % Factorizations : 0
% 0.25/0.28 % NegExts : 0
% 0.25/0.28 % Equation resolutions : 0
% 0.25/0.28 % Disequality decompositions : 0
% 0.25/0.28 % Total rewrite steps : 2
% 0.25/0.28 % ...of those cached : 0
% 0.25/0.28 % Propositional unsat checks : 0
% 0.25/0.28 % Propositional check models : 0
% 0.25/0.28 % Propositional check unsatisfiable : 0
% 0.25/0.28 % Propositional clauses : 0
% 0.25/0.28 % Propositional clauses after purity: 0
% 0.25/0.28 % Propositional unsat core size : 0
% 0.25/0.28 % Propositional preprocessing time : 0.000
% 0.25/0.28 % Propositional encoding time : 0.000
% 0.25/0.28 % Propositional solver time : 0.000
% 0.25/0.28 % Success case prop preproc time : 0.000
% 0.25/0.28 % Success case prop encoding time : 0.000
% 0.25/0.28 % Success case prop solver time : 0.000
% 0.25/0.28 % Current number of processed clauses : 2
% 0.25/0.28 % Positive orientable unit clauses : 2
% 0.25/0.28 % Positive unorientable unit clauses: 0
% 0.25/0.28 % Negative unit clauses : 0
% 0.25/0.28 % Non-unit-clauses : 0
% 0.25/0.29 % Current number of unprocessed clauses: 2
% 0.25/0.29 % ...number of literals in the above : 6
% 0.25/0.29 % Current number of archived formulas : 0
% 0.25/0.29 % Current number of archived clauses : 0
% 0.25/0.29 % Clause-clause subsumption calls (NU) : 0
% 0.25/0.29 % Rec. Clause-clause subsumption calls : 0
% 0.25/0.29 % Non-unit clause-clause subsumptions : 0
% 0.25/0.29 % Unit Clause-clause subsumption calls : 0
% 0.25/0.29 % Rewrite failures with RHS unbound : 0
% 0.25/0.29 % BW rewrite match attempts : 0
% 0.25/0.29 % BW rewrite match successes : 0
% 0.25/0.29 % Condensation attempts : 0
% 0.25/0.29 % Condensation successes : 0
% 0.25/0.29 % Termbank termtop insertions : 483
% 0.25/0.29 % Search garbage collected termcells : 193
% 0.25/0.29
% 0.25/0.29 % -------------------------------------------------
% 0.25/0.29 % User time : 0.004 s
% 0.25/0.29 % System time : 0.002 s
% 0.25/0.29 % Total time : 0.005 s
% 0.25/0.29 % Maximum resident set size: 3628 pages
% 0.25/0.29
% 0.25/0.29 % -------------------------------------------------
% 0.25/0.29 % User time : 0.005 s
% 0.25/0.29 % System time : 0.007 s
% 0.25/0.29 % Total time : 0.012 s
% 0.25/0.29 % Maximum resident set size: 4864 pages
% 0.25/0.29 % E exiting
%------------------------------------------------------------------------------