%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP232^3 : TPTP v9.3.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:05:58 AM UTC 2026
% Result : Theorem 8.03s 6.31s
% Output : CNFRefutation 8.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 65 ( 8 ~; 2 |; 0 &; 53 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 6 !; 4 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
vEBT_VEBT: $tType ).
thf(decl_sort3,type,
list_VEBT_VEBT: $tType ).
thf(decl_418,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(decl_836,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(decl_837,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(decl_853,type,
vEBT_VEBT_minNull: vEBT_VEBT > $o ).
thf(decl_887,type,
mi: nat ).
thf(decl_888,type,
na: nat ).
thf(decl_890,type,
treeList: list_VEBT_VEBT ).
thf(decl_1128,type,
esk221_1: vEBT_VEBT > nat ).
thf(conj_0,conjecture,
? [X261: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X261 ),
file('/export/starexec/sandbox/tmp/tmp.wQG3LSG2VY/E---3.1_3362428.p',conj_0) ).
thf(fact_0_not__min__Null__member,axiom,
! [X1: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ X1 )
=> ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.wQG3LSG2VY/E---3.1_3362428.p',fact_0_not__min__Null__member) ).
thf(fact_1_False,axiom,
~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ),
file('/export/starexec/sandbox/tmp/tmp.wQG3LSG2VY/E---3.1_3362428.p',fact_1_False) ).
thf(c_0_3,negated_conjecture,
~ ? [X261: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X261 ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_4,plain,
! [X1: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ X1 )
=> ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X1 @ X2 ) ),
inference(fof_simplification,[status(thm)],[fact_0_not__min__Null__member]) ).
thf(c_0_5,negated_conjecture,
! [X22942: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X22942 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])]) ).
thf(c_0_6,plain,
! [X25015: vEBT_VEBT] :
( ( vEBT_VEBT_minNull @ X25015 )
| ( vEBT_V8194947554948674370ptions @ X25015 @ ( esk221_1 @ X25015 ) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
thf(c_0_7,plain,
~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ),
inference(fof_simplification,[status(thm)],[fact_1_False]) ).
thf(c_0_8,negated_conjecture,
! [X2: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
! [X1: vEBT_VEBT] :
( ( vEBT_VEBT_minNull @ X1 )
| ( vEBT_V8194947554948674370ptions @ X1 @ ( esk221_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP232^3 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n010.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % 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 20:25:33 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.25 Running higher-order theorem proving
% 3.97/4.05 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.wQG3LSG2VY/E---3.1_3362428.p
% 8.03/6.31 % Version: 3.5.1-ho
% 8.03/6.31 % partial match(1): HMLMSMSMSSLCHFA
% 8.03/6.31 % Preprocessing class: HMLMSMLMSSLCHFA.
% 8.03/6.31 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 8.03/6.31 % Starting new_ho_10 with 1495s (5) cores
% 8.03/6.31 % Starting sh5l with 299s (1) cores
% 8.03/6.31 % Starting new_bool_1 with 299s (1) cores
% 8.03/6.31 % Starting new_bool_2 with 299s (1) cores
% 8.03/6.31 % new_bool_2 with pid 3362444 completed with status 0
% 8.03/6.31 % Result found by new_bool_2
% 8.03/6.31 % partial match(1): HMLMSMSMSSLCHFA
% 8.03/6.31 % Preprocessing class: HMLMSMLMSSLCHFA.
% 8.03/6.31 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 8.03/6.31 % Starting new_ho_10 with 1495s (5) cores
% 8.03/6.31 % Starting sh5l with 299s (1) cores
% 8.03/6.31 % Starting new_bool_1 with 299s (1) cores
% 8.03/6.31 % Starting new_bool_2 with 299s (1) cores
% 8.03/6.31 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 8.03/6.31 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 8.03/6.31 % Search class: HGHSM-SMLM32-DHFFFSBN
% 8.03/6.31 % Scheduled 5 strats onto 1 cores with 299 seconds (299 total)
% 8.03/6.31 % Starting SubtermCWHack with 30s (1) cores
% 8.03/6.31 % SubtermCWHack with pid 3362445 completed with status 0
% 8.03/6.31 % Result found by SubtermCWHack
% 8.03/6.31 % partial match(1): HMLMSMSMSSLCHFA
% 8.03/6.31 % Preprocessing class: HMLMSMLMSSLCHFA.
% 8.03/6.31 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 8.03/6.31 % Starting new_ho_10 with 1495s (5) cores
% 8.03/6.31 % Starting sh5l with 299s (1) cores
% 8.03/6.31 % Starting new_bool_1 with 299s (1) cores
% 8.03/6.31 % Starting new_bool_2 with 299s (1) cores
% 8.03/6.31 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 8.03/6.31 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 8.03/6.31 % Search class: HGHSM-SMLM32-DHFFFSBN
% 8.03/6.31 % Scheduled 5 strats onto 1 cores with 299 seconds (299 total)
% 8.03/6.31 % Starting SubtermCWHack with 30s (1) cores
% 8.03/6.31 % Preprocessing time : 0.099 s
% 8.03/6.31
% 8.03/6.31 % Proof found!
% 8.03/6.31 % SZS status Theorem
% 8.03/6.31 % SZS output start CNFRefutation
% See solution above
% 8.03/6.31 % Parsed axioms : 10550
% 8.03/6.31 % Removed by relevancy pruning/SinE : 8377
% 8.03/6.31 % Initial clauses : 6516
% 8.03/6.31 % Removed in clause preprocessing : 1832
% 8.03/6.31 % Initial clauses in saturation : 4684
% 8.03/6.31 % Processed clauses : 3144
% 8.03/6.31 % ...of these trivial : 256
% 8.03/6.31 % ...subsumed : 1438
% 8.03/6.31 % ...remaining for further processing : 1450
% 8.03/6.31 % Other redundant clauses eliminated : 251
% 8.03/6.31 % Clauses deleted for lack of memory : 0
% 8.03/6.31 % Backward-subsumed : 11
% 8.03/6.31 % Backward-rewritten : 49
% 8.03/6.31 % Generated clauses : 6406
% 8.03/6.31 % ...of the previous two non-redundant : 4899
% 8.03/6.31 % ...aggressively subsumed : 0
% 8.03/6.31 % Contextual simplify-reflections : 5
% 8.03/6.31 % Paramodulations : 6117
% 8.03/6.31 % Factorizations : 12
% 8.03/6.31 % NegExts : 0
% 8.03/6.31 % Equation resolutions : 260
% 8.03/6.31 % Disequality decompositions : 0
% 8.03/6.31 % Total rewrite steps : 2266
% 8.03/6.31 % ...of those cached : 1668
% 8.03/6.31 % Propositional unsat checks : 0
% 8.03/6.31 % Propositional check models : 0
% 8.03/6.31 % Propositional check unsatisfiable : 0
% 8.03/6.31 % Propositional clauses : 0
% 8.03/6.31 % Propositional clauses after purity: 0
% 8.03/6.31 % Propositional unsat core size : 0
% 8.03/6.31 % Propositional preprocessing time : 0.000
% 8.03/6.31 % Propositional encoding time : 0.000
% 8.03/6.31 % Propositional solver time : 0.000
% 8.03/6.31 % Success case prop preproc time : 0.000
% 8.03/6.31 % Success case prop encoding time : 0.000
% 8.03/6.31 % Success case prop solver time : 0.000
% 8.03/6.31 % Current number of processed clauses : 1223
% 8.03/6.31 % Positive orientable unit clauses : 544
% 8.03/6.31 % Positive unorientable unit clauses: 0
% 8.03/6.31 % Negative unit clauses : 473
% 8.03/6.31 % Non-unit-clauses : 206
% 8.03/6.31 % Current number of unprocessed clauses: 6432
% 8.03/6.31 % ...number of literals in the above : 22334
% 8.03/6.31 % Current number of archived formulas : 0
% 8.03/6.31 % Current number of archived clauses : 60
% 8.03/6.31 % Clause-clause subsumption calls (NU) : 15021
% 8.03/6.31 % Rec. Clause-clause subsumption calls : 12772
% 8.03/6.31 % Non-unit clause-clause subsumptions : 260
% 8.03/6.31 % Unit Clause-clause subsumption calls : 74522
% 8.03/6.31 % Rewrite failures with RHS unbound : 0
% 8.03/6.31 % BW rewrite match attempts : 530
% 8.03/6.31 % BW rewrite match successes : 22
% 8.03/6.31 % Condensation attempts : 0
% 8.03/6.31 % Condensation successes : 0
% 8.03/6.31 % Termbank termtop insertions : 611047
% 8.03/6.31 % Search garbage collected termcells : 159781
% 8.03/6.31
% 8.03/6.31 % -------------------------------------------------
% 8.03/6.31 % User time : 0.815 s
% 8.03/6.31 % System time : 0.078 s
% 8.03/6.31 % Total time : 0.893 s
% 8.03/6.31 % Maximum resident set size: 38892 pages
% 8.03/6.31
% 8.03/6.31 % -------------------------------------------------
% 8.03/6.31 % User time : 2.119 s
% 8.03/6.31 % System time : 0.116 s
% 8.03/6.31 % Total time : 2.235 s
% 8.03/6.31 % Maximum resident set size: 28928 pages
% 8.03/6.31 % E exiting
%------------------------------------------------------------------------------