%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP104^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:05:32 AM UTC 2026
% Result : Theorem 2.90s 0.83s
% Output : CNFRefutation 2.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 12 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 124 ( 9 ~; 4 |; 0 &; 109 @)
% ( 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/sandbox2/tmp/tmp.dAnpKIpazQ/E---3.1_1512271.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/sandbox2/tmp/tmp.dAnpKIpazQ/E---3.1_1512271.p',fact_19_list__slice2__list__slice__nth) ).
thf(conj_0,hypothesis,
ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ),
file('/export/starexec/sandbox2/tmp/tmp.dAnpKIpazQ/E---3.1_1512271.p',conj_0) ).
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/sandbox2/tmp/tmp.dAnpKIpazQ/E---3.1_1512271.p',fact_30_list__slice__nth__length) ).
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,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_7,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_8,negated_conjecture,
( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
!= k ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
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_7]) ).
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,
! [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_12,negated_conjecture,
( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ xs @ k ) @ m ) )
!= k ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]) ).
thf(c_0_13,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_11]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP104^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n020.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 19:54:49 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 Running higher-order theorem proving
% 0.27/0.34 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.dAnpKIpazQ/E---3.1_1512271.p
% 2.90/0.83 % Version: 3.5.1-ho
% 2.90/0.83 % Preprocessing class: HSLSSMSSSSMNHFA.
% 2.90/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.90/0.83 % Starting pre_casc_2 with 1500s (5) cores
% 2.90/0.83 % Starting sh3 with 300s (1) cores
% 2.90/0.83 % Starting new_ho_10_cnf2 with 300s (1) cores
% 2.90/0.83 % Starting new_bool_3 with 300s (1) cores
% 2.90/0.83 % pre_casc_2 with pid 1512286 completed with status 0
% 2.90/0.83 % Result found by pre_casc_2
% 2.90/0.83 % Preprocessing class: HSLSSMSSSSMNHFA.
% 2.90/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.90/0.83 % Starting pre_casc_2 with 1500s (5) cores
% 2.90/0.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.90/0.83 % No SInE strategy applied
% 2.90/0.83 % Search class: HGHSM-FSLF32-MHFFFSBC
% 2.90/0.83 % partial match(1): HGHSM-FSLM32-MHFFFSBC
% 2.90/0.83 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 2.90/0.83 % Starting SubtermCWHack with 151s (1) cores
% 2.90/0.83 % Starting additional_ho_6 with 901s (1) cores
% 2.90/0.83 % Starting lpo6_lambda_fix with 151s (1) cores
% 2.90/0.83 % Starting new_ho_3 with 151s (1) cores
% 2.90/0.83 % Starting sh3 with 146s (1) cores
% 2.90/0.83 % sh3 with pid 1512297 completed with status 0
% 2.90/0.83 % Result found by sh3
% 2.90/0.83 % Preprocessing class: HSLSSMSSSSMNHFA.
% 2.90/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.90/0.83 % Starting pre_casc_2 with 1500s (5) cores
% 2.90/0.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.90/0.83 % No SInE strategy applied
% 2.90/0.83 % Search class: HGHSM-FSLF32-MHFFFSBC
% 2.90/0.83 % partial match(1): HGHSM-FSLM32-MHFFFSBC
% 2.90/0.83 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 2.90/0.83 % Starting SubtermCWHack with 151s (1) cores
% 2.90/0.83 % Starting additional_ho_6 with 901s (1) cores
% 2.90/0.83 % Starting lpo6_lambda_fix with 151s (1) cores
% 2.90/0.83 % Starting new_ho_3 with 151s (1) cores
% 2.90/0.83 % Starting sh3 with 146s (1) cores
% 2.90/0.83 % Preprocessing time : 0.028 s
% 2.90/0.83 % Presaturation interreduction done
% 2.90/0.83
% 2.90/0.83 % Proof found!
% 2.90/0.83 % SZS status Theorem
% 2.90/0.83 % SZS output start CNFRefutation
% See solution above
% 2.90/0.83 % Parsed axioms : 462
% 2.90/0.83 % Removed by relevancy pruning/SinE : 0
% 2.90/0.83 % Initial clauses : 958
% 2.90/0.83 % Removed in clause preprocessing : 141
% 2.90/0.83 % Initial clauses in saturation : 817
% 2.90/0.83 % Processed clauses : 1316
% 2.90/0.83 % ...of these trivial : 7
% 2.90/0.83 % ...subsumed : 251
% 2.90/0.83 % ...remaining for further processing : 1058
% 2.90/0.83 % Other redundant clauses eliminated : 97
% 2.90/0.83 % Clauses deleted for lack of memory : 0
% 2.90/0.83 % Backward-subsumed : 4
% 2.90/0.83 % Backward-rewritten : 1
% 2.90/0.83 % Generated clauses : 1516
% 2.90/0.83 % ...of the previous two non-redundant : 1274
% 2.90/0.83 % ...aggressively subsumed : 0
% 2.90/0.83 % Contextual simplify-reflections : 4
% 2.90/0.83 % Paramodulations : 1412
% 2.90/0.83 % Factorizations : 4
% 2.90/0.83 % NegExts : 0
% 2.90/0.83 % Equation resolutions : 97
% 2.90/0.83 % Disequality decompositions : 0
% 2.90/0.83 % Total rewrite steps : 252
% 2.90/0.83 % ...of those cached : 150
% 2.90/0.83 % Propositional unsat checks : 0
% 2.90/0.83 % Propositional check models : 0
% 2.90/0.83 % Propositional check unsatisfiable : 0
% 2.90/0.83 % Propositional clauses : 0
% 2.90/0.83 % Propositional clauses after purity: 0
% 2.90/0.83 % Propositional unsat core size : 0
% 2.90/0.83 % Propositional preprocessing time : 0.000
% 2.90/0.83 % Propositional encoding time : 0.000
% 2.90/0.83 % Propositional solver time : 0.000
% 2.90/0.83 % Success case prop preproc time : 0.000
% 2.90/0.83 % Success case prop encoding time : 0.000
% 2.90/0.83 % Success case prop solver time : 0.000
% 2.90/0.83 % Current number of processed clauses : 354
% 2.90/0.83 % Positive orientable unit clauses : 66
% 2.90/0.83 % Positive unorientable unit clauses: 0
% 2.90/0.83 % Negative unit clauses : 44
% 2.90/0.83 % Non-unit-clauses : 244
% 2.90/0.83 % Current number of unprocessed clauses: 1380
% 2.90/0.83 % ...number of literals in the above : 4249
% 2.90/0.83 % Current number of archived formulas : 0
% 2.90/0.83 % Current number of archived clauses : 613
% 2.90/0.83 % Clause-clause subsumption calls (NU) : 135105
% 2.90/0.83 % Rec. Clause-clause subsumption calls : 40971
% 2.90/0.83 % Non-unit clause-clause subsumptions : 188
% 2.90/0.83 % Unit Clause-clause subsumption calls : 549
% 2.90/0.83 % Rewrite failures with RHS unbound : 0
% 2.90/0.83 % BW rewrite match attempts : 17
% 2.90/0.83 % BW rewrite match successes : 2
% 2.90/0.83 % Condensation attempts : 0
% 2.90/0.83 % Condensation successes : 0
% 2.90/0.83 % Termbank termtop insertions : 117572
% 2.90/0.83 % Search garbage collected termcells : 18356
% 2.90/0.83
% 2.90/0.83 % -------------------------------------------------
% 2.90/0.83 % User time : 0.411 s
% 2.90/0.83 % System time : 0.024 s
% 2.90/0.83 % Total time : 0.435 s
% 2.90/0.83 % Maximum resident set size: 7916 pages
% 2.90/0.83
% 2.90/0.83 % -------------------------------------------------
% 2.90/0.83 % User time : 1.650 s
% 2.90/0.83 % System time : 0.116 s
% 2.90/0.83 % Total time : 1.766 s
% 2.90/0.83 % Maximum resident set size: 5888 pages
% 2.90/0.83 % E exiting
%------------------------------------------------------------------------------