%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP232^1 : TPTP v9.3.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 9.98s 6.77s
% Output : CNFRefutation 9.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 71 ( 9 ~; 2 |; 0 &; 58 @)
% ( 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/sandbox2/tmp/tmp.E8aUPfxQmg/E---3.1_3886537.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/sandbox2/tmp/tmp.E8aUPfxQmg/E---3.1_3886537.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/sandbox2/tmp/tmp.E8aUPfxQmg/E---3.1_3886537.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,plain,
~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ),
inference(fof_simplification,[status(thm)],[fact_1_False]) ).
thf(c_0_6,negated_conjecture,
! [X22942: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X22942 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
thf(c_0_7,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_8,plain,
~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ),
inference(fof_nnf,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
! [X2: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
! [X1: vEBT_VEBT] :
( ( vEBT_VEBT_minNull @ X1 )
| ( vEBT_V8194947554948674370ptions @ X1 @ ( esk221_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
~ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP232^1 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 20:22:40 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 3.99/4.06 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.E8aUPfxQmg/E---3.1_3886537.p
% 9.98/6.77 % Version: 3.5.1-ho
% 9.98/6.77 % partial match(1): HMLMSMSMSSLCHFA
% 9.98/6.77 % Preprocessing class: HMLMSMLMSSLCHFA.
% 9.98/6.77 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 9.98/6.77 % Starting new_ho_10 with 1495s (5) cores
% 9.98/6.77 % Starting sh5l with 299s (1) cores
% 9.98/6.77 % Starting new_bool_1 with 299s (1) cores
% 9.98/6.77 % Starting new_bool_2 with 299s (1) cores
% 9.98/6.77 % new_bool_1 with pid 3886584 completed with status 0
% 9.98/6.77 % Result found by new_bool_1
% 9.98/6.77 % partial match(1): HMLMSMSMSSLCHFA
% 9.98/6.77 % Preprocessing class: HMLMSMLMSSLCHFA.
% 9.98/6.77 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 9.98/6.77 % Starting new_ho_10 with 1495s (5) cores
% 9.98/6.77 % Starting sh5l with 299s (1) cores
% 9.98/6.77 % Starting new_bool_1 with 299s (1) cores
% 9.98/6.77 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 9.98/6.77 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.98/6.77 % Search class: HGHSM-SMLM32-DHFFFSBN
% 9.98/6.77 % Scheduled 5 strats onto 1 cores with 298 seconds (298 total)
% 9.98/6.77 % Starting SubtermCWHack with 30s (1) cores
% 9.98/6.77 % SubtermCWHack with pid 3886587 completed with status 0
% 9.98/6.77 % Result found by SubtermCWHack
% 9.98/6.77 % partial match(1): HMLMSMSMSSLCHFA
% 9.98/6.77 % Preprocessing class: HMLMSMLMSSLCHFA.
% 9.98/6.77 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 9.98/6.77 % Starting new_ho_10 with 1495s (5) cores
% 9.98/6.77 % Starting sh5l with 299s (1) cores
% 9.98/6.77 % Starting new_bool_1 with 299s (1) cores
% 9.98/6.77 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 9.98/6.77 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.98/6.77 % Search class: HGHSM-SMLM32-DHFFFSBN
% 9.98/6.77 % Scheduled 5 strats onto 1 cores with 298 seconds (298 total)
% 9.98/6.77 % Starting SubtermCWHack with 30s (1) cores
% 9.98/6.77 % Preprocessing time : 0.064 s
% 9.98/6.77
% 9.98/6.77 % Proof found!
% 9.98/6.77 % SZS status Theorem
% 9.98/6.77 % SZS output start CNFRefutation
% See solution above
% 9.98/6.77 % Parsed axioms : 10550
% 9.98/6.77 % Removed by relevancy pruning/SinE : 8377
% 9.98/6.77 % Initial clauses : 7639
% 9.98/6.77 % Removed in clause preprocessing : 2517
% 9.98/6.77 % Initial clauses in saturation : 5122
% 9.98/6.77 % Processed clauses : 2961
% 9.98/6.77 % ...of these trivial : 206
% 9.98/6.77 % ...subsumed : 1359
% 9.98/6.77 % ...remaining for further processing : 1396
% 9.98/6.77 % Other redundant clauses eliminated : 239
% 9.98/6.77 % Clauses deleted for lack of memory : 0
% 9.98/6.77 % Backward-subsumed : 17
% 9.98/6.77 % Backward-rewritten : 48
% 9.98/6.77 % Generated clauses : 5920
% 9.98/6.77 % ...of the previous two non-redundant : 4500
% 9.98/6.77 % ...aggressively subsumed : 0
% 9.98/6.77 % Contextual simplify-reflections : 4
% 9.98/6.77 % Paramodulations : 5643
% 9.98/6.77 % Factorizations : 12
% 9.98/6.77 % NegExts : 0
% 9.98/6.77 % Equation resolutions : 248
% 9.98/6.77 % Disequality decompositions : 0
% 9.98/6.77 % Total rewrite steps : 2158
% 9.98/6.77 % ...of those cached : 1593
% 9.98/6.77 % Propositional unsat checks : 0
% 9.98/6.77 % Propositional check models : 0
% 9.98/6.77 % Propositional check unsatisfiable : 0
% 9.98/6.77 % Propositional clauses : 0
% 9.98/6.77 % Propositional clauses after purity: 0
% 9.98/6.77 % Propositional unsat core size : 0
% 9.98/6.77 % Propositional preprocessing time : 0.000
% 9.98/6.77 % Propositional encoding time : 0.000
% 9.98/6.77 % Propositional solver time : 0.000
% 9.98/6.77 % Success case prop preproc time : 0.000
% 9.98/6.77 % Success case prop encoding time : 0.000
% 9.98/6.77 % Success case prop solver time : 0.000
% 9.98/6.77 % Current number of processed clauses : 1170
% 9.98/6.77 % Positive orientable unit clauses : 529
% 9.98/6.77 % Positive unorientable unit clauses: 0
% 9.98/6.77 % Negative unit clauses : 443
% 9.98/6.77 % Non-unit-clauses : 198
% 9.98/6.77 % Current number of unprocessed clauses: 6652
% 9.98/6.77 % ...number of literals in the above : 25621
% 9.98/6.77 % Current number of archived formulas : 0
% 9.98/6.77 % Current number of archived clauses : 65
% 9.98/6.77 % Clause-clause subsumption calls (NU) : 14184
% 9.98/6.77 % Rec. Clause-clause subsumption calls : 11992
% 9.98/6.77 % Non-unit clause-clause subsumptions : 253
% 9.98/6.77 % Unit Clause-clause subsumption calls : 68705
% 9.98/6.77 % Rewrite failures with RHS unbound : 0
% 9.98/6.77 % BW rewrite match attempts : 502
% 9.98/6.77 % BW rewrite match successes : 22
% 9.98/6.77 % Condensation attempts : 0
% 9.98/6.77 % Condensation successes : 0
% 9.98/6.77 % Termbank termtop insertions : 716498
% 9.98/6.77 % Search garbage collected termcells : 181117
% 9.98/6.77
% 9.98/6.77 % -------------------------------------------------
% 9.98/6.77 % User time : 1.194 s
% 9.98/6.77 % System time : 0.098 s
% 9.98/6.77 % Total time : 1.292 s
% 9.98/6.77 % Maximum resident set size: 41964 pages
% 9.98/6.77
% 9.98/6.77 % -------------------------------------------------
% 9.98/6.77 % User time : 2.528 s
% 9.98/6.77 % System time : 0.147 s
% 9.98/6.77 % Total time : 2.676 s
% 9.98/6.77 % Maximum resident set size: 28672 pages
% 9.98/6.77 % E exiting
%------------------------------------------------------------------------------