%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP099^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:04:21 AM UTC 2026
% Result : Theorem 0.89s 0.49s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 18 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 295 ( 23 ~; 14 |; 6 &; 241 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_sort3,type,
list_a: $tType ).
thf(decl_23,type,
minus_minus_nat: nat > nat > nat ).
thf(decl_32,type,
listIn1312259492pend_a: list_a > ( nat > a ) > nat > a ).
thf(decl_34,type,
listIn1417627087drop_a: nat > ( nat > a ) > nat > a ).
thf(decl_40,type,
drop_a: nat > list_a > list_a ).
thf(decl_46,type,
size_size_list_a: list_a > nat ).
thf(decl_47,type,
ord_less_nat: nat > nat > $o ).
thf(decl_48,type,
ord_less_eq_nat: nat > nat > $o ).
thf(decl_49,type,
f: nat > a ).
thf(decl_50,type,
n: nat ).
thf(decl_51,type,
xs: list_a ).
thf(conj_0,conjecture,
( ( ( ord_less_nat @ n @ ( size_size_list_a @ xs ) )
=> ( ( listIn1417627087drop_a @ n @ ( listIn1312259492pend_a @ xs @ f ) )
= ( listIn1312259492pend_a @ ( drop_a @ n @ xs ) @ f ) ) )
& ( ~ ( ord_less_nat @ n @ ( size_size_list_a @ xs ) )
=> ( ( listIn1417627087drop_a @ n @ ( listIn1312259492pend_a @ xs @ f ) )
= ( listIn1417627087drop_a @ ( minus_minus_nat @ n @ ( size_size_list_a @ xs ) ) @ f ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jOUUHhc2kI/E---3.1_560125.p',conj_0) ).
thf(fact_33_i__append__i__drop__eq1,axiom,
! [X9: nat,X1: list_a,X2: nat > a] :
( ( ord_less_eq_nat @ X9 @ ( size_size_list_a @ X1 ) )
=> ( ( listIn1417627087drop_a @ X9 @ ( listIn1312259492pend_a @ X1 @ X2 ) )
= ( listIn1312259492pend_a @ ( drop_a @ X9 @ X1 ) @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jOUUHhc2kI/E---3.1_560125.p',fact_33_i__append__i__drop__eq1) ).
thf(fact_71_less__imp__le__nat,axiom,
! [X11: nat,X9: nat] :
( ( ord_less_nat @ X11 @ X9 )
=> ( ord_less_eq_nat @ X11 @ X9 ) ),
file('/export/starexec/sandbox/tmp/tmp.jOUUHhc2kI/E---3.1_560125.p',fact_71_less__imp__le__nat) ).
thf(fact_187_not__le__imp__less,axiom,
! [X24: nat,X23: nat] :
( ~ ( ord_less_eq_nat @ X24 @ X23 )
=> ( ord_less_nat @ X23 @ X24 ) ),
file('/export/starexec/sandbox/tmp/tmp.jOUUHhc2kI/E---3.1_560125.p',fact_187_not__le__imp__less) ).
thf(fact_35_i__append__i__drop__eq2,axiom,
! [X1: list_a,X9: nat,X2: nat > a] :
( ( ord_less_eq_nat @ ( size_size_list_a @ X1 ) @ X9 )
=> ( ( listIn1417627087drop_a @ X9 @ ( listIn1312259492pend_a @ X1 @ X2 ) )
= ( listIn1417627087drop_a @ ( minus_minus_nat @ X9 @ ( size_size_list_a @ X1 ) ) @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jOUUHhc2kI/E---3.1_560125.p',fact_35_i__append__i__drop__eq2) ).
thf(c_0_5,negated_conjecture,
~ ( ( ( ord_less_nat @ n @ ( size_size_list_a @ xs ) )
=> ( ( listIn1417627087drop_a @ n @ ( listIn1312259492pend_a @ xs @ f ) )
= ( listIn1312259492pend_a @ ( drop_a @ n @ xs ) @ f ) ) )
& ( ~ ( ord_less_nat @ n @ ( size_size_list_a @ xs ) )
=> ( ( listIn1417627087drop_a @ n @ ( listIn1312259492pend_a @ xs @ f ) )
= ( listIn1417627087drop_a @ ( minus_minus_nat @ n @ ( size_size_list_a @ xs ) ) @ f ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_6,negated_conjecture,
~ ( ( ( ord_less_nat @ n @ ( size_size_list_a @ xs ) )
=> ( ( listIn1417627087drop_a @ n @ ( listIn1312259492pend_a @ xs @ f ) )
= ( listIn1312259492pend_a @ ( drop_a @ n @ xs ) @ f ) ) )
& ( ~ ( ord_less_nat @ n @ ( size_size_list_a @ xs ) )
=> ( ( listIn1417627087drop_a @ n @ ( listIn1312259492pend_a @ xs @ f ) )
= ( listIn1417627087drop_a @ ( minus_minus_nat @ n @ ( size_size_list_a @ xs ) ) @ f ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
( ( ~ ( ord_less_nat @ n @ ( size_size_list_a @ xs ) )
| ( ord_less_nat @ n @ ( size_size_list_a @ xs ) ) )
& ( ( ( listIn1417627087drop_a @ n @ ( listIn1312259492pend_a @ xs @ f ) )
!= ( listIn1417627087drop_a @ ( minus_minus_nat @ n @ ( size_size_list_a @ xs ) ) @ f ) )
| ( ord_less_nat @ n @ ( size_size_list_a @ xs ) ) )
& ( ~ ( ord_less_nat @ n @ ( size_size_list_a @ xs ) )
| ( ( listIn1417627087drop_a @ n @ ( listIn1312259492pend_a @ xs @ f ) )
!= ( listIn1312259492pend_a @ ( drop_a @ n @ xs ) @ f ) ) )
& ( ( ( listIn1417627087drop_a @ n @ ( listIn1312259492pend_a @ xs @ f ) )
!= ( listIn1417627087drop_a @ ( minus_minus_nat @ n @ ( size_size_list_a @ xs ) ) @ f ) )
| ( ( listIn1417627087drop_a @ n @ ( listIn1312259492pend_a @ xs @ f ) )
!= ( listIn1312259492pend_a @ ( drop_a @ n @ xs ) @ f ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_8,plain,
! [X984: nat,X985: list_a,X986: nat > a] :
( ~ ( ord_less_eq_nat @ X984 @ ( size_size_list_a @ X985 ) )
| ( ( listIn1417627087drop_a @ X984 @ ( listIn1312259492pend_a @ X985 @ X986 ) )
= ( listIn1312259492pend_a @ ( drop_a @ X984 @ X985 ) @ X986 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_33_i__append__i__drop__eq1])])]) ).
thf(c_0_9,plain,
! [X1204: nat,X1205: nat] :
( ~ ( ord_less_nat @ X1204 @ X1205 )
| ( ord_less_eq_nat @ X1204 @ X1205 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_71_less__imp__le__nat])])]) ).
thf(c_0_10,plain,
! [X24: nat,X23: nat] :
( ~ ( ord_less_eq_nat @ X24 @ X23 )
=> ( ord_less_nat @ X23 @ X24 ) ),
inference(fof_simplification,[status(thm)],[fact_187_not__le__imp__less]) ).
thf(c_0_11,negated_conjecture,
( ~ ( ord_less_nat @ n @ ( size_size_list_a @ xs ) )
| ( ( listIn1417627087drop_a @ n @ ( listIn1312259492pend_a @ xs @ f ) )
!= ( listIn1312259492pend_a @ ( drop_a @ n @ xs ) @ f ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X9: nat,X2: nat > a,X1: list_a] :
( ( ( listIn1417627087drop_a @ X9 @ ( listIn1312259492pend_a @ X1 @ X2 ) )
= ( listIn1312259492pend_a @ ( drop_a @ X9 @ X1 ) @ X2 ) )
| ~ ( ord_less_eq_nat @ X9 @ ( size_size_list_a @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
! [X9: nat,X11: nat] :
( ( ord_less_eq_nat @ X9 @ X11 )
| ~ ( ord_less_nat @ X9 @ X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X1331: nat,X1332: nat] :
( ( ord_less_eq_nat @ X1331 @ X1332 )
| ( ord_less_nat @ X1332 @ X1331 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
thf(c_0_15,plain,
! [X987: list_a,X988: nat,X989: nat > a] :
( ~ ( ord_less_eq_nat @ ( size_size_list_a @ X987 ) @ X988 )
| ( ( listIn1417627087drop_a @ X988 @ ( listIn1312259492pend_a @ X987 @ X989 ) )
= ( listIn1417627087drop_a @ ( minus_minus_nat @ X988 @ ( size_size_list_a @ X987 ) ) @ X989 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_35_i__append__i__drop__eq2])])]) ).
thf(c_0_16,negated_conjecture,
~ ( ord_less_nat @ n @ ( size_size_list_a @ xs ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
thf(c_0_17,plain,
! [X11: nat,X9: nat] :
( ( ord_less_eq_nat @ X9 @ X11 )
| ( ord_less_nat @ X11 @ X9 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,negated_conjecture,
( ( ord_less_nat @ n @ ( size_size_list_a @ xs ) )
| ( ( listIn1417627087drop_a @ n @ ( listIn1312259492pend_a @ xs @ f ) )
!= ( listIn1417627087drop_a @ ( minus_minus_nat @ n @ ( size_size_list_a @ xs ) ) @ f ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_19,plain,
! [X1: list_a,X2: nat > a,X9: nat] :
( ( ( listIn1417627087drop_a @ X9 @ ( listIn1312259492pend_a @ X1 @ X2 ) )
= ( listIn1417627087drop_a @ ( minus_minus_nat @ X9 @ ( size_size_list_a @ X1 ) ) @ X2 ) )
| ~ ( ord_less_eq_nat @ ( size_size_list_a @ X1 ) @ X9 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_20,negated_conjecture,
ord_less_eq_nat @ ( size_size_list_a @ xs ) @ n,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP099^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n011.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 19:53:31 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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.jOUUHhc2kI/E---3.1_560125.p
% 0.89/0.49 % Version: 3.5.1-ho
% 0.89/0.49 % Preprocessing class: HSLSSMSSSSSNHSA.
% 0.89/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.89/0.49 % Starting full_lambda_9 with 1500s (5) cores
% 0.89/0.49 % Starting new_ho_11 with 300s (1) cores
% 0.89/0.49 % Starting sh2l with 300s (1) cores
% 0.89/0.49 % Starting new_bool_6 with 300s (1) cores
% 0.89/0.49 % full_lambda_9 with pid 560138 completed with status 0
% 0.89/0.49 % Result found by full_lambda_9
% 0.89/0.49 % Preprocessing class: HSLSSMSSSSSNHSA.
% 0.89/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.89/0.49 % Starting full_lambda_9 with 1500s (5) cores
% 0.89/0.49 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.89/0.49 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.89/0.49 % Search class: HGHSM-FSLM32-DHSFFSBN
% 0.89/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.89/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.89/0.49 % Starting full_lambda_9 with 151s (1) cores
% 0.89/0.49 % Starting sh4l with 214s (1) cores
% 0.89/0.49 % Starting pre_casc_4 with 204s (1) cores
% 0.89/0.49 % Starting lpo5_fix with 136s (1) cores
% 0.89/0.49 % sh4l with pid 560146 completed with status 0
% 0.89/0.49 % Result found by sh4l
% 0.89/0.49 % Preprocessing class: HSLSSMSSSSSNHSA.
% 0.89/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.89/0.49 % Starting full_lambda_9 with 1500s (5) cores
% 0.89/0.49 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.89/0.49 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.89/0.49 % Search class: HGHSM-FSLM32-DHSFFSBN
% 0.89/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.89/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.89/0.49 % Starting full_lambda_9 with 151s (1) cores
% 0.89/0.49 % Starting sh4l with 214s (1) cores
% 0.89/0.49 % Preprocessing time : 0.009 s
% 0.89/0.49
% 0.89/0.49 % Proof found!
% 0.89/0.49 % SZS status Theorem
% 0.89/0.49 % SZS output start CNFRefutation
% See solution above
% 0.89/0.49 % Parsed axioms : 286
% 0.89/0.49 % Removed by relevancy pruning/SinE : 54
% 0.89/0.49 % Initial clauses : 541
% 0.89/0.49 % Removed in clause preprocessing : 24
% 0.89/0.49 % Initial clauses in saturation : 517
% 0.89/0.49 % Processed clauses : 532
% 0.89/0.49 % ...of these trivial : 8
% 0.89/0.49 % ...subsumed : 139
% 0.89/0.49 % ...remaining for further processing : 384
% 0.89/0.49 % Other redundant clauses eliminated : 92
% 0.89/0.49 % Clauses deleted for lack of memory : 0
% 0.89/0.49 % Backward-subsumed : 1
% 0.89/0.49 % Backward-rewritten : 0
% 0.89/0.49 % Generated clauses : 5456
% 0.89/0.49 % ...of the previous two non-redundant : 4938
% 0.89/0.49 % ...aggressively subsumed : 0
% 0.89/0.49 % Contextual simplify-reflections : 2
% 0.89/0.49 % Paramodulations : 4142
% 0.89/0.49 % Factorizations : 944
% 0.89/0.49 % NegExts : 19
% 0.89/0.49 % Equation resolutions : 117
% 0.89/0.49 % Disequality decompositions : 0
% 0.89/0.49 % Total rewrite steps : 199
% 0.89/0.49 % ...of those cached : 131
% 0.89/0.49 % Propositional unsat checks : 0
% 0.89/0.49 % Propositional check models : 0
% 0.89/0.49 % Propositional check unsatisfiable : 0
% 0.89/0.49 % Propositional clauses : 0
% 0.89/0.49 % Propositional clauses after purity: 0
% 0.89/0.49 % Propositional unsat core size : 0
% 0.89/0.49 % Propositional preprocessing time : 0.000
% 0.89/0.49 % Propositional encoding time : 0.000
% 0.89/0.49 % Propositional solver time : 0.000
% 0.89/0.49 % Success case prop preproc time : 0.000
% 0.89/0.49 % Success case prop encoding time : 0.000
% 0.89/0.49 % Success case prop solver time : 0.000
% 0.89/0.49 % Current number of processed clauses : 344
% 0.89/0.49 % Positive orientable unit clauses : 37
% 0.89/0.49 % Positive unorientable unit clauses: 1
% 0.89/0.49 % Negative unit clauses : 2
% 0.89/0.49 % Non-unit-clauses : 304
% 0.89/0.49 % Current number of unprocessed clauses: 4923
% 0.89/0.49 % ...number of literals in the above : 27033
% 0.89/0.49 % Current number of archived formulas : 0
% 0.89/0.49 % Current number of archived clauses : 1
% 0.89/0.49 % Clause-clause subsumption calls (NU) : 47364
% 0.89/0.49 % Rec. Clause-clause subsumption calls : 6516
% 0.89/0.49 % Non-unit clause-clause subsumptions : 140
% 0.89/0.49 % Unit Clause-clause subsumption calls : 266
% 0.89/0.49 % Rewrite failures with RHS unbound : 0
% 0.89/0.49 % BW rewrite match attempts : 10
% 0.89/0.49 % BW rewrite match successes : 4
% 0.89/0.49 % Condensation attempts : 532
% 0.89/0.49 % Condensation successes : 12
% 0.89/0.49 % Termbank termtop insertions : 479875
% 0.89/0.49 % Search garbage collected termcells : 9890
% 0.89/0.49
% 0.89/0.49 % -------------------------------------------------
% 0.89/0.49 % User time : 0.186 s
% 0.89/0.49 % System time : 0.013 s
% 0.89/0.49 % Total time : 0.199 s
% 0.89/0.49 % Maximum resident set size: 5680 pages
% 0.89/0.49
% 0.89/0.49 % -------------------------------------------------
% 0.89/0.49 % User time : 0.837 s
% 0.89/0.49 % System time : 0.062 s
% 0.89/0.49 % Total time : 0.899 s
% 0.89/0.49 % Maximum resident set size: 5376 pages
% 0.89/0.49 % E exiting
%------------------------------------------------------------------------------