%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP233^3 : 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 : n004.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 4.02s 13.21s
% Output : CNFRefutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 14 ( 5 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 181 ( 4 ~; 0 |; 0 &; 177 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 5 ( 0 ^; 3 !; 2 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
list_VEBT_VEBT: $tType ).
thf(decl_sort3,type,
vEBT_VEBT: $tType ).
thf(decl_507,type,
list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(decl_540,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(decl_1059,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(decl_1062,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(decl_1064,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(decl_1075,type,
vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
thf(decl_1136,type,
i: nat ).
thf(decl_1140,type,
na: nat ).
thf(decl_1142,type,
treeList: list_VEBT_VEBT ).
thf(decl_1143,type,
xa: nat ).
thf(conj_0,conjecture,
? [X234: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i ) @ X234 ),
file('/export/starexec/sandbox/tmp/tmp.3v41kWDfRX/E---3.1_1797526.p',conj_0) ).
thf(fact_3__C164_C,axiom,
( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i )
= ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3v41kWDfRX/E---3.1_1797526.p',fact_3__C164_C) ).
thf(fact_0_True,axiom,
( i
= ( vEBT_VEBT_high @ xa @ na ) ),
file('/export/starexec/sandbox/tmp/tmp.3v41kWDfRX/E---3.1_1797526.p',fact_0_True) ).
thf(fact_1__C166_C,axiom,
vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ),
file('/export/starexec/sandbox/tmp/tmp.3v41kWDfRX/E---3.1_1797526.p',fact_1__C166_C) ).
thf(c_0_4,negated_conjecture,
~ ? [X234: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i ) @ X234 ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_5,negated_conjecture,
! [X22586: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i ) @ X22586 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).
thf(c_0_6,plain,
( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i )
= ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ),
inference(split_conjunct,[status(thm)],[fact_3__C164_C]) ).
thf(c_0_7,plain,
( i
= ( vEBT_VEBT_high @ xa @ na ) ),
inference(split_conjunct,[status(thm)],[fact_0_True]) ).
thf(c_0_8,plain,
vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ),
inference(split_conjunct,[status(thm)],[fact_1__C166_C]) ).
thf(c_0_9,negated_conjecture,
! [X1: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i ) @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,plain,
( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ i @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ i ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ i )
= ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ i ) @ ( vEBT_VEBT_low @ xa @ na ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_7]),c_0_7]) ).
thf(c_0_11,plain,
vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ i ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ),
inference(rw,[status(thm)],[c_0_8,c_0_7]) ).
thf(c_0_12,negated_conjecture,
! [X1: nat] :
~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ i ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_7]),c_0_7]),c_0_10]) ).
thf(c_0_13,plain,
$false,
inference(sr,[status(thm)],[c_0_11,c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP233^3 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n004.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 20:25:07 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 3.98/4.06 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.3v41kWDfRX/E---3.1_1797526.p
% 4.02/13.21 % Version: 3.5.1-ho
% 4.02/13.21 % partial match(2): HMLMSMSMSSLCHFA
% 4.02/13.21 % Preprocessing class: HMLLSMLMSSLCHFA.
% 4.02/13.21 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 4.02/13.21 % Starting new_ho_10 with 1495s (5) cores
% 4.02/13.21 % Starting sh5l with 299s (1) cores
% 4.02/13.21 % Starting new_bool_1 with 299s (1) cores
% 4.02/13.21 % Starting new_bool_2 with 299s (1) cores
% 4.02/13.21 % new_bool_2 with pid 1797542 completed with status 0
% 4.02/13.21 % Result found by new_bool_2
% 4.02/13.21 % partial match(2): HMLMSMSMSSLCHFA
% 4.02/13.21 % Preprocessing class: HMLLSMLMSSLCHFA.
% 4.02/13.21 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 4.02/13.21 % Starting new_ho_10 with 1495s (5) cores
% 4.02/13.21 % Starting sh5l with 299s (1) cores
% 4.02/13.21 % Starting new_bool_1 with 299s (1) cores
% 4.02/13.21 % Starting new_bool_2 with 299s (1) cores
% 4.02/13.21 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 4.02/13.21 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.02/13.21 % Search class: HGHSM-SMLM32-DHFFFSBN
% 4.02/13.21 % Scheduled 5 strats onto 1 cores with 299 seconds (299 total)
% 4.02/13.21 % Starting SubtermCWHack with 30s (1) cores
% 4.02/13.21 % SubtermCWHack with pid 1797543 completed with status 0
% 4.02/13.21 % Result found by SubtermCWHack
% 4.02/13.21 % partial match(2): HMLMSMSMSSLCHFA
% 4.02/13.21 % Preprocessing class: HMLLSMLMSSLCHFA.
% 4.02/13.21 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 4.02/13.21 % Starting new_ho_10 with 1495s (5) cores
% 4.02/13.21 % Starting sh5l with 299s (1) cores
% 4.02/13.21 % Starting new_bool_1 with 299s (1) cores
% 4.02/13.21 % Starting new_bool_2 with 299s (1) cores
% 4.02/13.21 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 4.02/13.21 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.02/13.21 % Search class: HGHSM-SMLM32-DHFFFSBN
% 4.02/13.21 % Scheduled 5 strats onto 1 cores with 299 seconds (299 total)
% 4.02/13.21 % Starting SubtermCWHack with 30s (1) cores
% 4.02/13.21 % Preprocessing time : 0.103 s
% 4.02/13.21
% 4.02/13.21 % Proof found!
% 4.02/13.21 % SZS status Theorem
% 4.02/13.21 % SZS output start CNFRefutation
% See solution above
% 4.02/13.21 % Parsed axioms : 10382
% 4.02/13.21 % Removed by relevancy pruning/SinE : 8298
% 4.02/13.21 % Initial clauses : 6346
% 4.02/13.21 % Removed in clause preprocessing : 1815
% 4.02/13.21 % Initial clauses in saturation : 4531
% 4.02/13.21 % Processed clauses : 32560
% 4.02/13.21 % ...of these trivial : 7244
% 4.02/13.21 % ...subsumed : 17097
% 4.02/13.21 % ...remaining for further processing : 8219
% 4.02/13.21 % Other redundant clauses eliminated : 1702
% 4.02/13.21 % Clauses deleted for lack of memory : 0
% 4.02/13.21 % Backward-subsumed : 306
% 4.02/13.21 % Backward-rewritten : 468
% 4.02/13.21 % Generated clauses : 197355
% 4.02/13.21 % ...of the previous two non-redundant : 165318
% 4.02/13.21 % ...aggressively subsumed : 0
% 4.02/13.21 % Contextual simplify-reflections : 55
% 4.02/13.21 % Paramodulations : 195522
% 4.02/13.21 % Factorizations : 22
% 4.02/13.21 % NegExts : 0
% 4.02/13.21 % Equation resolutions : 1735
% 4.02/13.21 % Disequality decompositions : 0
% 4.02/13.21 % Total rewrite steps : 67671
% 4.02/13.21 % ...of those cached : 57921
% 4.02/13.21 % Propositional unsat checks : 0
% 4.02/13.21 % Propositional check models : 0
% 4.02/13.21 % Propositional check unsatisfiable : 0
% 4.02/13.21 % Propositional clauses : 0
% 4.02/13.21 % Propositional clauses after purity: 0
% 4.02/13.21 % Propositional unsat core size : 0
% 4.02/13.21 % Propositional preprocessing time : 0.000
% 4.02/13.21 % Propositional encoding time : 0.000
% 4.02/13.21 % Propositional solver time : 0.000
% 4.02/13.21 % Success case prop preproc time : 0.000
% 4.02/13.21 % Success case prop encoding time : 0.000
% 4.02/13.21 % Success case prop solver time : 0.000
% 4.02/13.21 % Current number of processed clauses : 7107
% 4.02/13.21 % Positive orientable unit clauses : 2732
% 4.02/13.21 % Positive unorientable unit clauses: 20
% 4.02/13.21 % Negative unit clauses : 2365
% 4.02/13.21 % Non-unit-clauses : 1990
% 4.02/13.21 % Current number of unprocessed clauses: 136510
% 4.02/13.21 % ...number of literals in the above : 362928
% 4.02/13.21 % Current number of archived formulas : 0
% 4.02/13.21 % Current number of archived clauses : 778
% 4.02/13.21 % Clause-clause subsumption calls (NU) : 1185880
% 4.02/13.21 % Rec. Clause-clause subsumption calls : 534228
% 4.02/13.21 % Non-unit clause-clause subsumptions : 2658
% 4.02/13.21 % Unit Clause-clause subsumption calls : 1880455
% 4.02/13.21 % Rewrite failures with RHS unbound : 0
% 4.02/13.21 % BW rewrite match attempts : 5845
% 4.02/13.21 % BW rewrite match successes : 542
% 4.02/13.21 % Condensation attempts : 0
% 4.02/13.21 % Condensation successes : 0
% 4.02/13.21 % Termbank termtop insertions : 3056897
% 4.02/13.21 % Search garbage collected termcells : 157622
% 4.02/13.21
% 4.02/13.21 % -------------------------------------------------
% 4.02/13.21 % User time : 7.546 s
% 4.02/13.21 % System time : 0.225 s
% 4.02/13.21 % Total time : 7.771 s
% 4.02/13.21 % Maximum resident set size: 38740 pages
% 4.02/13.21
% 4.02/13.21 % -------------------------------------------------
% 4.02/13.21 % User time : 8.799 s
% 4.02/13.21 % System time : 0.271 s
% 4.02/13.21 % Total time : 9.070 s
% 4.02/13.21 % Maximum resident set size: 28160 pages
% 4.02/13.21 % E exiting
%------------------------------------------------------------------------------