%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP246^1 : 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 : n008.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 08:04:54 AM UTC 2026
% Result : Theorem 54.97s 22.51s
% Output : CNFRefutation 54.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 11 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 164 ( 12 ~; 8 |; 0 &; 144 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
num: $tType ).
thf(decl_528,type,
bit0: num > num ).
thf(decl_530,type,
one: num ).
thf(decl_538,type,
numeral_numeral_nat: num > nat ).
thf(decl_594,type,
ord_less_eq_nat: nat > nat > $o ).
thf(decl_712,type,
divide_divide_nat: nat > nat > nat ).
thf(decl_843,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(decl_904,type,
deg: nat ).
thf(decl_909,type,
na: nat ).
thf(decl_914,type,
xa: nat ).
thf(decl_915,type,
za: nat ).
thf(conj_0,conjecture,
( ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
= ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LqPqYad7EU/E---3.1_3694240.p',conj_0) ).
thf(fact_49_verit__la__disequality,axiom,
! [X36: nat,X37: nat] :
( ( X36 = X37 )
| ~ ( ord_less_eq_nat @ X36 @ X37 )
| ~ ( ord_less_eq_nat @ X37 @ X36 ) ),
file('/export/starexec/sandbox2/tmp/tmp.LqPqYad7EU/E---3.1_3694240.p',fact_49_verit__la__disequality) ).
thf(fact_0_bbbb,axiom,
ord_less_eq_nat @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LqPqYad7EU/E---3.1_3694240.p',fact_0_bbbb) ).
thf(fact_5__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062,axiom,
( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= na ),
file('/export/starexec/sandbox2/tmp/tmp.LqPqYad7EU/E---3.1_3694240.p',fact_5__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062) ).
thf(fact_2_aaaa,axiom,
ord_less_eq_nat @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LqPqYad7EU/E---3.1_3694240.p',fact_2_aaaa) ).
thf(c_0_5,negated_conjecture,
( ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
!= ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_6,plain,
! [X36: nat,X37: nat] :
( ( X36 = X37 )
| ~ ( ord_less_eq_nat @ X36 @ X37 )
| ~ ( ord_less_eq_nat @ X37 @ X36 ) ),
inference(fof_simplification,[status(thm)],[fact_49_verit__la__disequality]) ).
thf(c_0_7,negated_conjecture,
( ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
!= ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
! [X28209: nat,X28210: nat] :
( ( X28209 = X28210 )
| ~ ( ord_less_eq_nat @ X28209 @ X28210 )
| ~ ( ord_less_eq_nat @ X28210 @ X28209 ) ),
inference(variable_rename,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
ord_less_eq_nat @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ),
inference(split_conjunct,[status(thm)],[fact_0_bbbb]) ).
thf(c_0_10,plain,
( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= na ),
inference(split_conjunct,[status(thm)],[fact_5__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062]) ).
thf(c_0_11,plain,
ord_less_eq_nat @ ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ),
inference(split_conjunct,[status(thm)],[fact_2_aaaa]) ).
thf(c_0_12,negated_conjecture,
( ( vEBT_VEBT_high @ xa @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
!= ( vEBT_VEBT_high @ za @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_13,plain,
! [X3: nat,X2: nat] :
( ( X2 = X3 )
| ~ ( ord_less_eq_nat @ X2 @ X3 )
| ~ ( ord_less_eq_nat @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,plain,
ord_less_eq_nat @ ( vEBT_VEBT_high @ za @ na ) @ ( vEBT_VEBT_high @ xa @ na ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
thf(c_0_15,plain,
ord_less_eq_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_VEBT_high @ za @ na ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10]),c_0_10]) ).
thf(c_0_16,negated_conjecture,
( ( vEBT_VEBT_high @ za @ na )
!= ( vEBT_VEBT_high @ xa @ na ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_10]),c_0_10]) ).
thf(c_0_17,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP246^1 : 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 : n008.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 20:32:39 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 4.44/4.53 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.LqPqYad7EU/E---3.1_3694240.p
% 54.97/22.51 % Version: 3.5.1-ho
% 54.97/22.51 % partial match(1): HMLMSMSMSSLCHFA
% 54.97/22.51 % Preprocessing class: HMLMSMLMSSLCHFA.
% 54.97/22.51 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 54.97/22.51 % Starting new_ho_10 with 1495s (5) cores
% 54.97/22.51 % Starting sh5l with 299s (1) cores
% 54.97/22.51 % Starting new_bool_1 with 299s (1) cores
% 54.97/22.51 % Starting new_bool_2 with 299s (1) cores
% 54.97/22.51 % new_bool_2 with pid 3694256 completed with status 0
% 54.97/22.51 % Result found by new_bool_2
% 54.97/22.51 % partial match(1): HMLMSMSMSSLCHFA
% 54.97/22.51 % Preprocessing class: HMLMSMLMSSLCHFA.
% 54.97/22.51 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 54.97/22.51 % Starting new_ho_10 with 1495s (5) cores
% 54.97/22.51 % Starting sh5l with 299s (1) cores
% 54.97/22.51 % Starting new_bool_1 with 299s (1) cores
% 54.97/22.51 % Starting new_bool_2 with 299s (1) cores
% 54.97/22.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 54.97/22.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 54.97/22.51 % Search class: HGHSM-SMLM32-DHFFFSBN
% 54.97/22.51 % Scheduled 5 strats onto 1 cores with 298 seconds (298 total)
% 54.97/22.51 % Starting SubtermCWHack with 30s (1) cores
% 54.97/22.51 % SubtermCWHack with pid 3694257 completed with status 0
% 54.97/22.51 % Result found by SubtermCWHack
% 54.97/22.51 % partial match(1): HMLMSMSMSSLCHFA
% 54.97/22.51 % Preprocessing class: HMLMSMLMSSLCHFA.
% 54.97/22.51 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 54.97/22.51 % Starting new_ho_10 with 1495s (5) cores
% 54.97/22.51 % Starting sh5l with 299s (1) cores
% 54.97/22.51 % Starting new_bool_1 with 299s (1) cores
% 54.97/22.51 % Starting new_bool_2 with 299s (1) cores
% 54.97/22.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 54.97/22.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 54.97/22.51 % Search class: HGHSM-SMLM32-DHFFFSBN
% 54.97/22.51 % Scheduled 5 strats onto 1 cores with 298 seconds (298 total)
% 54.97/22.51 % Starting SubtermCWHack with 30s (1) cores
% 54.97/22.51 % Preprocessing time : 0.135 s
% 54.97/22.51
% 54.97/22.51 % Proof found!
% 54.97/22.51 % SZS status Theorem
% 54.97/22.51 % SZS output start CNFRefutation
% See solution above
% 54.97/22.51 % Parsed axioms : 11234
% 54.97/22.51 % Removed by relevancy pruning/SinE : 7424
% 54.97/22.51 % Initial clauses : 9458
% 54.97/22.51 % Removed in clause preprocessing : 1911
% 54.97/22.51 % Initial clauses in saturation : 7547
% 54.97/22.51 % Processed clauses : 52118
% 54.97/22.51 % ...of these trivial : 11633
% 54.97/22.51 % ...subsumed : 26034
% 54.97/22.51 % ...remaining for further processing : 14451
% 54.97/22.51 % Other redundant clauses eliminated : 2155
% 54.97/22.51 % Clauses deleted for lack of memory : 0
% 54.97/22.51 % Backward-subsumed : 288
% 54.97/22.51 % Backward-rewritten : 510
% 54.97/22.51 % Generated clauses : 340344
% 54.97/22.51 % ...of the previous two non-redundant : 283121
% 54.97/22.51 % ...aggressively subsumed : 0
% 54.97/22.51 % Contextual simplify-reflections : 52
% 54.97/22.51 % Paramodulations : 338000
% 54.97/22.51 % Factorizations : 32
% 54.97/22.51 % NegExts : 0
% 54.97/22.51 % Equation resolutions : 2251
% 54.97/22.51 % Disequality decompositions : 0
% 54.97/22.51 % Total rewrite steps : 128225
% 54.97/22.51 % ...of those cached : 109243
% 54.97/22.51 % Propositional unsat checks : 0
% 54.97/22.51 % Propositional check models : 0
% 54.97/22.51 % Propositional check unsatisfiable : 0
% 54.97/22.51 % Propositional clauses : 0
% 54.97/22.51 % Propositional clauses after purity: 0
% 54.97/22.51 % Propositional unsat core size : 0
% 54.97/22.51 % Propositional preprocessing time : 0.000
% 54.97/22.51 % Propositional encoding time : 0.000
% 54.97/22.51 % Propositional solver time : 0.000
% 54.97/22.51 % Success case prop preproc time : 0.000
% 54.97/22.51 % Success case prop encoding time : 0.000
% 54.97/22.51 % Success case prop solver time : 0.000
% 54.97/22.51 % Current number of processed clauses : 13011
% 54.97/22.51 % Positive orientable unit clauses : 5410
% 54.97/22.51 % Positive unorientable unit clauses: 45
% 54.97/22.51 % Negative unit clauses : 4440
% 54.97/22.51 % Non-unit-clauses : 3116
% 54.97/22.51 % Current number of unprocessed clauses: 237641
% 54.97/22.51 % ...number of literals in the above : 592297
% 54.97/22.51 % Current number of archived formulas : 0
% 54.97/22.51 % Current number of archived clauses : 802
% 54.97/22.51 % Clause-clause subsumption calls (NU) : 1903690
% 54.97/22.51 % Rec. Clause-clause subsumption calls : 1295850
% 54.97/22.51 % Non-unit clause-clause subsumptions : 4103
% 54.97/22.51 % Unit Clause-clause subsumption calls : 6324787
% 54.97/22.51 % Rewrite failures with RHS unbound : 0
% 54.97/22.51 % BW rewrite match attempts : 22259
% 54.97/22.51 % BW rewrite match successes : 690
% 54.97/22.51 % Condensation attempts : 0
% 54.97/22.51 % Condensation successes : 0
% 54.97/22.51 % Termbank termtop insertions : 4703628
% 54.97/22.51 % Search garbage collected termcells : 175949
% 54.97/22.51
% 54.97/22.51 % -------------------------------------------------
% 54.97/22.51 % User time : 15.968 s
% 54.97/22.51 % System time : 0.346 s
% 54.97/22.51 % Total time : 16.314 s
% 54.97/22.51 % Maximum resident set size: 47556 pages
% 54.97/22.51
% 54.97/22.51 % -------------------------------------------------
% 54.97/22.51 % User time : 17.313 s
% 54.97/22.51 % System time : 0.399 s
% 54.97/22.51 % Total time : 17.712 s
% 54.97/22.51 % Maximum resident set size: 27904 pages
% 54.97/22.51 % E exiting
%------------------------------------------------------------------------------