%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP104^1 : 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 : n017.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 08:04:22 AM UTC 2026
% Result : Theorem 1.75s 0.55s
% Output : CNFRefutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 13 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 131 ( 8 ~; 4 |; 0 &; 117 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
list_list_a: $tType ).
thf(decl_sort2,type,
list_a: $tType ).
thf(decl_sort3,type,
nat: $tType ).
thf(decl_42,type,
listSl1174287072ice2_a: list_a > nat > list_list_a ).
thf(decl_47,type,
listSl97544552lice_a: list_a > nat > list_list_a ).
thf(decl_82,type,
nth_list_a: list_list_a > nat > list_a ).
thf(decl_97,type,
size_size_list_a: list_a > nat ).
thf(decl_98,type,
ord_less_nat: nat > nat > $o ).
thf(decl_106,type,
divide_divide_nat: nat > nat > nat ).
thf(decl_115,type,
k: nat ).
thf(decl_116,type,
m: nat ).
thf(decl_117,type,
xs: list_a ).
thf(conj_1,conjecture,
( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
= k ),
file('/export/starexec/sandbox/tmp/tmp.1OOc10X9KI/E---3.1_812333.p',conj_1) ).
thf(fact_19_list__slice2__list__slice__nth,axiom,
! [X48: nat,X52: list_a,X12: nat] :
( ( ord_less_nat @ X48 @ ( divide_divide_nat @ ( size_size_list_a @ X52 ) @ X12 ) )
=> ( ( nth_list_a @ ( listSl1174287072ice2_a @ X52 @ X12 ) @ X48 )
= ( nth_list_a @ ( listSl97544552lice_a @ X52 @ X12 ) @ X48 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1OOc10X9KI/E---3.1_812333.p',fact_19_list__slice2__list__slice__nth) ).
thf(fact_30_list__slice__nth__length,axiom,
! [X48: nat,X77: list_a,X12: nat] :
( ( ord_less_nat @ X48 @ ( divide_divide_nat @ ( size_size_list_a @ X77 ) @ X12 ) )
=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ X77 @ X12 ) @ X48 ) )
= X12 ) ),
file('/export/starexec/sandbox/tmp/tmp.1OOc10X9KI/E---3.1_812333.p',fact_30_list__slice__nth__length) ).
thf(conj_0,hypothesis,
ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ),
file('/export/starexec/sandbox/tmp/tmp.1OOc10X9KI/E---3.1_812333.p',conj_0) ).
thf(c_0_4,negated_conjecture,
( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
!= k ),
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(c_0_5,negated_conjecture,
( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
!= k ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_6,plain,
! [X1643: nat,X1644: list_a,X1645: nat] :
( ~ ( ord_less_nat @ X1643 @ ( divide_divide_nat @ ( size_size_list_a @ X1644 ) @ X1645 ) )
| ( ( nth_list_a @ ( listSl1174287072ice2_a @ X1644 @ X1645 ) @ X1643 )
= ( nth_list_a @ ( listSl97544552lice_a @ X1644 @ X1645 ) @ X1643 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_19_list__slice2__list__slice__nth])])]) ).
thf(c_0_7,plain,
! [X1684: nat,X1685: list_a,X1686: nat] :
( ~ ( ord_less_nat @ X1684 @ ( divide_divide_nat @ ( size_size_list_a @ X1685 ) @ X1686 ) )
| ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ X1685 @ X1686 ) @ X1684 ) )
= X1686 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_30_list__slice__nth__length])])]) ).
thf(c_0_8,negated_conjecture,
( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
!= k ),
inference(fof_nnf,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
! [X3: nat,X10: list_a,X12: nat] :
( ( ( nth_list_a @ ( listSl1174287072ice2_a @ X10 @ X12 ) @ X3 )
= ( nth_list_a @ ( listSl97544552lice_a @ X10 @ X12 ) @ X3 ) )
| ~ ( ord_less_nat @ X3 @ ( divide_divide_nat @ ( size_size_list_a @ X10 ) @ X12 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,hypothesis,
ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ),
inference(split_conjunct,[status(thm)],[conj_0]) ).
thf(c_0_11,plain,
! [X3: nat,X10: list_a,X12: nat] :
( ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ X10 @ X12 ) @ X3 ) )
= X12 )
| ~ ( ord_less_nat @ X3 @ ( divide_divide_nat @ ( size_size_list_a @ X10 ) @ X12 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,negated_conjecture,
( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
!= k ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,hypothesis,
( ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m )
= ( nth_list_a @ ( listSl97544552lice_a @ xs @ k ) @ m ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,hypothesis,
( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ xs @ k ) @ m ) )
= k ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
thf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP104^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n017.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 19:49:22 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.24 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.1OOc10X9KI/E---3.1_812333.p
% 1.75/0.55 % Version: 3.5.1-ho
% 1.75/0.55 % Preprocessing class: HSLSSMSSSSMNHFA.
% 1.75/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.75/0.55 % Starting pre_casc_2 with 1500s (5) cores
% 1.75/0.55 % Starting sh3 with 300s (1) cores
% 1.75/0.55 % Starting new_ho_10_cnf2 with 300s (1) cores
% 1.75/0.55 % Starting new_bool_3 with 300s (1) cores
% 1.75/0.55 % pre_casc_2 with pid 812346 completed with status 0
% 1.75/0.55 % Result found by pre_casc_2
% 1.75/0.55 % Preprocessing class: HSLSSMSSSSMNHFA.
% 1.75/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.75/0.55 % Starting pre_casc_2 with 1500s (5) cores
% 1.75/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.75/0.55 % No SInE strategy applied
% 1.75/0.55 % Search class: HGHSM-FSLF32-MHFFFSBC
% 1.75/0.55 % partial match(1): HGHSM-FSLM32-MHFFFSBC
% 1.75/0.55 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 1.75/0.55 % Starting SubtermCWHack with 151s (1) cores
% 1.75/0.55 % Starting additional_ho_6 with 901s (1) cores
% 1.75/0.55 % Starting lpo6_lambda_fix with 151s (1) cores
% 1.75/0.55 % Starting new_ho_3 with 151s (1) cores
% 1.75/0.55 % Starting sh3 with 146s (1) cores
% 1.75/0.55 % additional_ho_6 with pid 812353 completed with status 0
% 1.75/0.55 % Result found by additional_ho_6
% 1.75/0.55 % Preprocessing class: HSLSSMSSSSMNHFA.
% 1.75/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.75/0.55 % Starting pre_casc_2 with 1500s (5) cores
% 1.75/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.75/0.55 % No SInE strategy applied
% 1.75/0.55 % Search class: HGHSM-FSLF32-MHFFFSBC
% 1.75/0.55 % partial match(1): HGHSM-FSLM32-MHFFFSBC
% 1.75/0.55 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 1.75/0.55 % Starting SubtermCWHack with 151s (1) cores
% 1.75/0.55 % Starting additional_ho_6 with 901s (1) cores
% 1.75/0.55 % Preprocessing time : 0.017 s
% 1.75/0.55 % Presaturation interreduction done
% 1.75/0.55
% 1.75/0.55 % Proof found!
% 1.75/0.55 % SZS status Theorem
% 1.75/0.55 % SZS output start CNFRefutation
% See solution above
% 1.75/0.55 % Parsed axioms : 462
% 1.75/0.55 % Removed by relevancy pruning/SinE : 0
% 1.75/0.55 % Initial clauses : 958
% 1.75/0.55 % Removed in clause preprocessing : 141
% 1.75/0.55 % Initial clauses in saturation : 817
% 1.75/0.55 % Processed clauses : 1413
% 1.75/0.55 % ...of these trivial : 9
% 1.75/0.55 % ...subsumed : 237
% 1.75/0.55 % ...remaining for further processing : 1167
% 1.75/0.55 % Other redundant clauses eliminated : 99
% 1.75/0.55 % Clauses deleted for lack of memory : 0
% 1.75/0.55 % Backward-subsumed : 25
% 1.75/0.55 % Backward-rewritten : 7
% 1.75/0.55 % Generated clauses : 1909
% 1.75/0.55 % ...of the previous two non-redundant : 1697
% 1.75/0.55 % ...aggressively subsumed : 0
% 1.75/0.55 % Contextual simplify-reflections : 4
% 1.75/0.55 % Paramodulations : 1801
% 1.75/0.55 % Factorizations : 4
% 1.75/0.55 % NegExts : 0
% 1.75/0.55 % Equation resolutions : 101
% 1.75/0.55 % Disequality decompositions : 0
% 1.75/0.55 % Total rewrite steps : 221
% 1.75/0.55 % ...of those cached : 125
% 1.75/0.55 % Propositional unsat checks : 0
% 1.75/0.55 % Propositional check models : 0
% 1.75/0.55 % Propositional check unsatisfiable : 0
% 1.75/0.55 % Propositional clauses : 0
% 1.75/0.55 % Propositional clauses after purity: 0
% 1.75/0.55 % Propositional unsat core size : 0
% 1.75/0.55 % Propositional preprocessing time : 0.000
% 1.75/0.55 % Propositional encoding time : 0.000
% 1.75/0.55 % Propositional solver time : 0.000
% 1.75/0.55 % Success case prop preproc time : 0.000
% 1.75/0.55 % Success case prop encoding time : 0.000
% 1.75/0.55 % Success case prop solver time : 0.000
% 1.75/0.55 % Current number of processed clauses : 436
% 1.75/0.55 % Positive orientable unit clauses : 78
% 1.75/0.55 % Positive unorientable unit clauses: 0
% 1.75/0.55 % Negative unit clauses : 90
% 1.75/0.55 % Non-unit-clauses : 268
% 1.75/0.55 % Current number of unprocessed clauses: 1704
% 1.75/0.55 % ...number of literals in the above : 4881
% 1.75/0.55 % Current number of archived formulas : 0
% 1.75/0.55 % Current number of archived clauses : 640
% 1.75/0.55 % Clause-clause subsumption calls (NU) : 135616
% 1.75/0.55 % Rec. Clause-clause subsumption calls : 41369
% 1.75/0.55 % Non-unit clause-clause subsumptions : 198
% 1.75/0.55 % Unit Clause-clause subsumption calls : 1571
% 1.75/0.55 % Rewrite failures with RHS unbound : 0
% 1.75/0.55 % BW rewrite match attempts : 29
% 1.75/0.55 % BW rewrite match successes : 9
% 1.75/0.55 % Condensation attempts : 0
% 1.75/0.55 % Condensation successes : 0
% 1.75/0.55 % Termbank termtop insertions : 121167
% 1.75/0.55 % Search garbage collected termcells : 18356
% 1.75/0.55
% 1.75/0.55 % -------------------------------------------------
% 1.75/0.55 % User time : 0.252 s
% 1.75/0.55 % System time : 0.018 s
% 1.75/0.55 % Total time : 0.270 s
% 1.75/0.55 % Maximum resident set size: 7916 pages
% 1.75/0.55
% 1.75/0.55 % -------------------------------------------------
% 1.75/0.55 % User time : 0.946 s
% 1.75/0.55 % System time : 0.069 s
% 1.75/0.55 % Total time : 1.015 s
% 1.75/0.55 % Maximum resident set size: 5888 pages
% 1.75/0.55 % E exiting
%------------------------------------------------------------------------------