%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP262^1 : 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 : 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 08:04:58 AM UTC 2026
% Result : Theorem 61.34s 24.54s
% Output : CNFRefutation 61.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 14 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 241 ( 18 ~; 10 |; 4 &; 205 @)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 27 ( 0 ^; 24 !; 3 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
num: $tType ).
thf(decl_sort3,type,
list_VEBT_VEBT: $tType ).
thf(decl_sort4,type,
vEBT_VEBT: $tType ).
thf(decl_342,type,
list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(decl_359,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(decl_446,type,
bit0: num > num ).
thf(decl_448,type,
one: num ).
thf(decl_456,type,
numeral_numeral_nat: num > nat ).
thf(decl_493,type,
ord_less_nat: nat > nat > $o ).
thf(decl_553,type,
power_power_nat: nat > nat > nat ).
thf(decl_768,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(decl_769,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(decl_771,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(decl_782,type,
vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
thf(decl_837,type,
m: nat ).
thf(decl_839,type,
maxs: nat ).
thf(decl_841,type,
na: nat ).
thf(decl_842,type,
summary: vEBT_VEBT ).
thf(decl_843,type,
treeList: list_VEBT_VEBT ).
thf(decl_844,type,
xa: nat ).
thf(decl_1181,type,
esk303_1: nat > nat ).
thf(conj_0,conjecture,
? [X27: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ X27 ),
file('/export/starexec/sandbox/tmp/tmp.VKjDD2mw5n/E---3.1_330545.p',conj_0) ).
thf(fact_22_nth__list__update__neq,axiom,
! [X6: nat,X17: nat,X20: list_VEBT_VEBT,X21: vEBT_VEBT] :
( ( X6 != X17 )
=> ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ X20 @ X6 @ X21 ) @ X17 )
= ( nth_VEBT_VEBT @ X20 @ X17 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VKjDD2mw5n/E---3.1_330545.p',fact_22_nth__list__update__neq) ).
thf(fact_10_bb,axiom,
( ( maxs
!= ( vEBT_VEBT_high @ xa @ na ) )
& ( ord_less_nat @ maxs @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VKjDD2mw5n/E---3.1_330545.p',fact_10_bb) ).
thf(fact_13__C4_C,axiom,
! [X7: nat] :
( ( ord_less_nat @ X7 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
=> ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X7 ) @ X8 )
<=> ( vEBT_V8194947554948674370ptions @ summary @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VKjDD2mw5n/E---3.1_330545.p',fact_13__C4_C) ).
thf(fact_2__C8_C,axiom,
na = m,
file('/export/starexec/sandbox/tmp/tmp.VKjDD2mw5n/E---3.1_330545.p',fact_2__C8_C) ).
thf(fact_1__092_060open_062both__member__options_Asummary_Amaxs_092_060close_062,axiom,
vEBT_V8194947554948674370ptions @ summary @ maxs,
file('/export/starexec/sandbox/tmp/tmp.VKjDD2mw5n/E---3.1_330545.p',fact_1__092_060open_062both__member__options_Asummary_Amaxs_092_060close_062) ).
thf(c_0_6,negated_conjecture,
~ ? [X27: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ X27 ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_7,plain,
! [X6: nat,X17: nat,X20: list_VEBT_VEBT,X21: vEBT_VEBT] :
( ( X6 != X17 )
=> ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ X20 @ X6 @ X21 ) @ X17 )
= ( nth_VEBT_VEBT @ X20 @ X17 ) ) ),
inference(fof_simplification,[status(thm)],[fact_22_nth__list__update__neq]) ).
thf(c_0_8,plain,
( ( maxs
!= ( vEBT_VEBT_high @ xa @ na ) )
& ( ord_less_nat @ maxs @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ),
inference(fof_simplification,[status(thm)],[fact_10_bb]) ).
thf(c_0_9,negated_conjecture,
! [X26703: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ X26703 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_10,plain,
! [X26831: nat,X26832: nat,X26833: list_VEBT_VEBT,X26834: vEBT_VEBT] :
( ( X26831 = X26832 )
| ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ X26833 @ X26831 @ X26834 ) @ X26832 )
= ( nth_VEBT_VEBT @ X26833 @ X26832 ) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
thf(c_0_11,plain,
( ( maxs
!= ( vEBT_VEBT_high @ xa @ na ) )
& ( ord_less_nat @ maxs @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ),
inference(fof_nnf,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X29032: nat,X29033: nat] :
( ( ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X29032 ) @ X29033 )
| ( vEBT_V8194947554948674370ptions @ summary @ X29032 )
| ~ ( ord_less_nat @ X29032 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) )
& ( ~ ( vEBT_V8194947554948674370ptions @ summary @ X29032 )
| ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X29032 ) @ ( esk303_1 @ X29032 ) )
| ~ ( ord_less_nat @ X29032 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ) ),
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)],[fact_13__C4_C])])])])])]) ).
thf(c_0_13,negated_conjecture,
! [X1: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X1: nat,X10: list_VEBT_VEBT,X3: vEBT_VEBT,X2: nat] :
( ( X1 = X2 )
| ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ X10 @ X1 @ X3 ) @ X2 )
= ( nth_VEBT_VEBT @ X10 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
( maxs
!= ( vEBT_VEBT_high @ xa @ na ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
! [X1: nat] :
( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X1 ) @ ( esk303_1 @ X1 ) )
| ~ ( vEBT_V8194947554948674370ptions @ summary @ X1 )
| ~ ( ord_less_nat @ X1 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,plain,
na = m,
inference(split_conjunct,[status(thm)],[fact_2__C8_C]) ).
thf(c_0_18,plain,
ord_less_nat @ maxs @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_19,negated_conjecture,
! [X1: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_20,plain,
! [X1: nat] :
( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ X1 ) @ ( esk303_1 @ X1 ) )
| ~ ( ord_less_nat @ X1 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
| ~ ( vEBT_V8194947554948674370ptions @ summary @ X1 ) ),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_21,plain,
ord_less_nat @ maxs @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ),
inference(rw,[status(thm)],[c_0_18,c_0_17]) ).
thf(c_0_22,plain,
vEBT_V8194947554948674370ptions @ summary @ maxs,
inference(split_conjunct,[status(thm)],[fact_1__092_060open_062both__member__options_Asummary_Amaxs_092_060close_062]) ).
thf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP262^1 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 20:42:30 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 4.44/4.53 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.VKjDD2mw5n/E---3.1_330545.p
% 61.34/24.54 % Version: 3.5.1-ho
% 61.34/24.54 % partial match(1): HMLMSMSMSSLCHFA
% 61.34/24.54 % Preprocessing class: HMLMSMLMSSLCHFA.
% 61.34/24.54 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 61.34/24.54 % Starting new_ho_10 with 1495s (5) cores
% 61.34/24.54 % Starting sh5l with 299s (1) cores
% 61.34/24.54 % Starting new_bool_1 with 299s (1) cores
% 61.34/24.54 % Starting new_bool_2 with 299s (1) cores
% 61.34/24.54 % new_bool_1 with pid 330565 completed with status 0
% 61.34/24.54 % Result found by new_bool_1
% 61.34/24.54 % partial match(1): HMLMSMSMSSLCHFA
% 61.34/24.54 % Preprocessing class: HMLMSMLMSSLCHFA.
% 61.34/24.54 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 61.34/24.54 % Starting new_ho_10 with 1495s (5) cores
% 61.34/24.54 % Starting sh5l with 299s (1) cores
% 61.34/24.54 % Starting new_bool_1 with 299s (1) cores
% 61.34/24.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 61.34/24.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 61.34/24.54 % Search class: HGHSM-SMLM32-DHFFFSBN
% 61.34/24.54 % Scheduled 5 strats onto 1 cores with 298 seconds (298 total)
% 61.34/24.54 % Starting SubtermCWHack with 30s (1) cores
% 61.34/24.54 % SubtermCWHack with pid 330568 completed with status 0
% 61.34/24.54 % Result found by SubtermCWHack
% 61.34/24.54 % partial match(1): HMLMSMSMSSLCHFA
% 61.34/24.54 % Preprocessing class: HMLMSMLMSSLCHFA.
% 61.34/24.54 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 61.34/24.54 % Starting new_ho_10 with 1495s (5) cores
% 61.34/24.54 % Starting sh5l with 299s (1) cores
% 61.34/24.54 % Starting new_bool_1 with 299s (1) cores
% 61.34/24.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 61.34/24.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 61.34/24.54 % Search class: HGHSM-SMLM32-DHFFFSBN
% 61.34/24.54 % Scheduled 5 strats onto 1 cores with 298 seconds (298 total)
% 61.34/24.54 % Starting SubtermCWHack with 30s (1) cores
% 61.34/24.54 % Preprocessing time : 0.084 s
% 61.34/24.54
% 61.34/24.54 % Proof found!
% 61.34/24.54 % SZS status Theorem
% 61.34/24.54 % SZS output start CNFRefutation
% See solution above
% 61.34/24.54 % Parsed axioms : 11165
% 61.34/24.54 % Removed by relevancy pruning/SinE : 7640
% 61.34/24.54 % Initial clauses : 10277
% 61.34/24.54 % Removed in clause preprocessing : 2661
% 61.34/24.54 % Initial clauses in saturation : 7616
% 61.34/24.54 % Processed clauses : 59610
% 61.34/24.54 % ...of these trivial : 10861
% 61.34/24.54 % ...subsumed : 30683
% 61.34/24.54 % ...remaining for further processing : 18066
% 61.34/24.54 % Other redundant clauses eliminated : 3601
% 61.34/24.54 % Clauses deleted for lack of memory : 0
% 61.34/24.54 % Backward-subsumed : 534
% 61.34/24.54 % Backward-rewritten : 762
% 61.34/24.54 % Generated clauses : 545534
% 61.34/24.54 % ...of the previous two non-redundant : 457357
% 61.34/24.54 % ...aggressively subsumed : 0
% 61.34/24.54 % Contextual simplify-reflections : 86
% 61.34/24.54 % Paramodulations : 541678
% 61.34/24.54 % Factorizations : 31
% 61.34/24.54 % NegExts : 0
% 61.34/24.54 % Equation resolutions : 3679
% 61.34/24.54 % Disequality decompositions : 0
% 61.34/24.54 % Total rewrite steps : 186217
% 61.34/24.54 % ...of those cached : 150098
% 61.34/24.54 % Propositional unsat checks : 0
% 61.34/24.54 % Propositional check models : 0
% 61.34/24.54 % Propositional check unsatisfiable : 0
% 61.34/24.54 % Propositional clauses : 0
% 61.34/24.54 % Propositional clauses after purity: 0
% 61.34/24.54 % Propositional unsat core size : 0
% 61.34/24.54 % Propositional preprocessing time : 0.000
% 61.34/24.54 % Propositional encoding time : 0.000
% 61.34/24.54 % Propositional solver time : 0.000
% 61.34/24.54 % Success case prop preproc time : 0.000
% 61.34/24.54 % Success case prop encoding time : 0.000
% 61.34/24.54 % Success case prop solver time : 0.000
% 61.34/24.54 % Current number of processed clauses : 16147
% 61.34/24.54 % Positive orientable unit clauses : 6471
% 61.34/24.54 % Positive unorientable unit clauses: 36
% 61.34/24.54 % Negative unit clauses : 5779
% 61.34/24.54 % Non-unit-clauses : 3861
% 61.34/24.54 % Current number of unprocessed clauses: 403872
% 61.34/24.54 % ...number of literals in the above : 1101547
% 61.34/24.54 % Current number of archived formulas : 0
% 61.34/24.54 % Current number of archived clauses : 1300
% 61.34/24.54 % Clause-clause subsumption calls (NU) : 4955370
% 61.34/24.54 % Rec. Clause-clause subsumption calls : 1637222
% 61.34/24.54 % Non-unit clause-clause subsumptions : 3746
% 61.34/24.54 % Unit Clause-clause subsumption calls : 19226951
% 61.34/24.54 % Rewrite failures with RHS unbound : 0
% 61.34/24.54 % BW rewrite match attempts : 41034
% 61.34/24.54 % BW rewrite match successes : 916
% 61.34/24.54 % Condensation attempts : 0
% 61.34/24.54 % Condensation successes : 0
% 61.34/24.54 % Termbank termtop insertions : 8375128
% 61.34/24.54 % Search garbage collected termcells : 215918
% 61.34/24.54
% 61.34/24.54 % -------------------------------------------------
% 61.34/24.54 % User time : 18.098 s
% 61.34/24.54 % System time : 0.348 s
% 61.34/24.54 % Total time : 18.446 s
% 61.34/24.54 % Maximum resident set size: 49192 pages
% 61.34/24.54
% 61.34/24.54 % -------------------------------------------------
% 61.34/24.54 % User time : 19.497 s
% 61.34/24.54 % System time : 0.403 s
% 61.34/24.54 % Total time : 19.900 s
% 61.34/24.54 % Maximum resident set size: 29184 pages
% 61.34/24.54 % E exiting
%------------------------------------------------------------------------------