%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP056^1 : 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 : n013.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 08:04:13 AM UTC 2026
% Result : Theorem 0.23s 0.32s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 17 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 87 ( 10 ~; 2 |; 0 &; 73 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
list_c1059388851t_unit: $tType ).
thf(decl_sort3,type,
config256849571t_unit: $tType ).
thf(decl_23,type,
minus_minus_nat: nat > nat > nat ).
thf(decl_24,type,
one_one_nat: nat ).
thf(decl_27,type,
last_c571238084t_unit: list_c1059388851t_unit > config256849571t_unit ).
thf(decl_28,type,
nil_co1338500125t_unit: list_c1059388851t_unit ).
thf(decl_29,type,
nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
thf(decl_30,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(decl_33,type,
fe: nat > list_c1059388851t_unit ).
thf(decl_35,type,
n: nat ).
thf(conj_0,conjecture,
( ( last_c571238084t_unit @ ( fe @ n ) )
= ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WRLkj0q8pi/E---3.1_2564410.p',conj_0) ).
thf(fact_1_LastIsLastIndex,axiom,
! [X1: list_c1059388851t_unit] :
( ( X1 != nil_co1338500125t_unit )
=> ( ( last_c571238084t_unit @ X1 )
= ( nth_co1649820636t_unit @ X1 @ ( minus_minus_nat @ ( size_s1406904903t_unit @ X1 ) @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WRLkj0q8pi/E---3.1_2564410.p',fact_1_LastIsLastIndex) ).
thf(fact_0_FeNNotEmpty,axiom,
( ( fe @ n )
!= nil_co1338500125t_unit ),
file('/export/starexec/sandbox/tmp/tmp.WRLkj0q8pi/E---3.1_2564410.p',fact_0_FeNNotEmpty) ).
thf(c_0_3,negated_conjecture,
( ( last_c571238084t_unit @ ( fe @ n ) )
!= ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_4,negated_conjecture,
( ( last_c571238084t_unit @ ( fe @ n ) )
!= ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
thf(c_0_5,plain,
! [X1: list_c1059388851t_unit] :
( ( X1 != nil_co1338500125t_unit )
=> ( ( last_c571238084t_unit @ X1 )
= ( nth_co1649820636t_unit @ X1 @ ( minus_minus_nat @ ( size_s1406904903t_unit @ X1 ) @ one_one_nat ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_1_LastIsLastIndex]) ).
thf(c_0_6,plain,
( ( fe @ n )
!= nil_co1338500125t_unit ),
inference(fof_simplification,[status(thm)],[fact_0_FeNNotEmpty]) ).
thf(c_0_7,negated_conjecture,
( ( last_c571238084t_unit @ ( fe @ n ) )
!= ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) ),
inference(fof_nnf,[status(thm)],[c_0_4]) ).
thf(c_0_8,plain,
! [X769: list_c1059388851t_unit] :
( ( X769 = nil_co1338500125t_unit )
| ( ( last_c571238084t_unit @ X769 )
= ( nth_co1649820636t_unit @ X769 @ ( minus_minus_nat @ ( size_s1406904903t_unit @ X769 ) @ one_one_nat ) ) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])]) ).
thf(c_0_9,plain,
( ( fe @ n )
!= nil_co1338500125t_unit ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
( ( last_c571238084t_unit @ ( fe @ n ) )
!= ( nth_co1649820636t_unit @ ( fe @ n ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ n ) ) @ one_one_nat ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X1: list_c1059388851t_unit] :
( ( X1 = nil_co1338500125t_unit )
| ( ( last_c571238084t_unit @ X1 )
= ( nth_co1649820636t_unit @ X1 @ ( minus_minus_nat @ ( size_s1406904903t_unit @ X1 ) @ one_one_nat ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
( ( fe @ n )
!= nil_co1338500125t_unit ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP056^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:43:36 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.26 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.WRLkj0q8pi/E---3.1_2564410.p
% 0.23/0.32 % Version: 3.5.1-ho
% 0.23/0.32 % Preprocessing class: HSLSSMSSSSSNHFA.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.32 % Starting new_ho_10_unif with 300s (1) cores
% 0.23/0.32 % Starting sh10 with 300s (1) cores
% 0.23/0.32 % Starting lpo5_rw_fix with 300s (1) cores
% 0.23/0.32 % new_ho_10 with pid 2564426 completed with status 0
% 0.23/0.32 % Result found by new_ho_10
% 0.23/0.32 % Preprocessing class: HSLSSMSSSSSNHFA.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.32 % No SInE strategy applied
% 0.23/0.32 % Search class: HGHSM-FSLS32-MHFFFSBC
% 0.23/0.32 % partial match(1): HGHSM-FSLM32-MHFFFSBC
% 0.23/0.32 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.32 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.32 % Starting new_ho_10 with 151s (1) cores
% 0.23/0.32 % Starting lpo6_lambda_fix with 136s (1) cores
% 0.23/0.32 % Starting new_ho_3 with 136s (1) cores
% 0.23/0.32 % Starting sh3 with 136s (1) cores
% 0.23/0.32 % lpo6_lambda_fix with pid 2564432 completed with status 0
% 0.23/0.32 % Result found by lpo6_lambda_fix
% 0.23/0.32 % Preprocessing class: HSLSSMSSSSSNHFA.
% 0.23/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.32 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.32 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.32 % No SInE strategy applied
% 0.23/0.32 % Search class: HGHSM-FSLS32-MHFFFSBC
% 0.23/0.32 % partial match(1): HGHSM-FSLM32-MHFFFSBC
% 0.23/0.32 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.32 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.32 % Starting new_ho_10 with 151s (1) cores
% 0.23/0.32 % Starting lpo6_lambda_fix with 136s (1) cores
% 0.23/0.32 % Preprocessing time : 0.012 s
% 0.23/0.32
% 0.23/0.32 % Proof found!
% 0.23/0.32 % SZS status Theorem
% 0.23/0.32 % SZS output start CNFRefutation
% See solution above
% 0.23/0.32 % Parsed axioms : 231
% 0.23/0.32 % Removed by relevancy pruning/SinE : 0
% 0.23/0.32 % Initial clauses : 516
% 0.23/0.32 % Removed in clause preprocessing : 33
% 0.23/0.32 % Initial clauses in saturation : 483
% 0.23/0.32 % Processed clauses : 44
% 0.23/0.32 % ...of these trivial : 2
% 0.23/0.32 % ...subsumed : 4
% 0.23/0.32 % ...remaining for further processing : 38
% 0.23/0.32 % Other redundant clauses eliminated : 23
% 0.23/0.32 % Clauses deleted for lack of memory : 0
% 0.23/0.32 % Backward-subsumed : 1
% 0.23/0.32 % Backward-rewritten : 1
% 0.23/0.32 % Generated clauses : 28
% 0.23/0.32 % ...of the previous two non-redundant : 19
% 0.23/0.32 % ...aggressively subsumed : 0
% 0.23/0.32 % Contextual simplify-reflections : 0
% 0.23/0.32 % Paramodulations : 5
% 0.23/0.32 % Factorizations : 0
% 0.23/0.32 % NegExts : 0
% 0.23/0.32 % Equation resolutions : 23
% 0.23/0.32 % Disequality decompositions : 0
% 0.23/0.32 % Total rewrite steps : 10
% 0.23/0.32 % ...of those cached : 8
% 0.23/0.32 % Propositional unsat checks : 0
% 0.23/0.32 % Propositional check models : 0
% 0.23/0.32 % Propositional check unsatisfiable : 0
% 0.23/0.32 % Propositional clauses : 0
% 0.23/0.32 % Propositional clauses after purity: 0
% 0.23/0.32 % Propositional unsat core size : 0
% 0.23/0.32 % Propositional preprocessing time : 0.000
% 0.23/0.32 % Propositional encoding time : 0.000
% 0.23/0.32 % Propositional solver time : 0.000
% 0.23/0.32 % Success case prop preproc time : 0.000
% 0.23/0.32 % Success case prop encoding time : 0.000
% 0.23/0.32 % Success case prop solver time : 0.000
% 0.23/0.32 % Current number of processed clauses : 13
% 0.23/0.32 % Positive orientable unit clauses : 6
% 0.23/0.32 % Positive unorientable unit clauses: 0
% 0.23/0.32 % Negative unit clauses : 5
% 0.23/0.32 % Non-unit-clauses : 2
% 0.23/0.32 % Current number of unprocessed clauses: 458
% 0.23/0.32 % ...number of literals in the above : 1950
% 0.23/0.32 % Current number of archived formulas : 0
% 0.23/0.32 % Current number of archived clauses : 2
% 0.23/0.32 % Clause-clause subsumption calls (NU) : 1
% 0.23/0.32 % Rec. Clause-clause subsumption calls : 1
% 0.23/0.32 % Non-unit clause-clause subsumptions : 1
% 0.23/0.32 % Unit Clause-clause subsumption calls : 4
% 0.23/0.32 % Rewrite failures with RHS unbound : 0
% 0.23/0.32 % BW rewrite match attempts : 1
% 0.23/0.32 % BW rewrite match successes : 1
% 0.23/0.32 % Condensation attempts : 44
% 0.23/0.32 % Condensation successes : 0
% 0.23/0.32 % Termbank termtop insertions : 43686
% 0.23/0.32 % Search garbage collected termcells : 8339
% 0.23/0.32
% 0.23/0.32 % -------------------------------------------------
% 0.23/0.32 % User time : 0.029 s
% 0.23/0.32 % System time : 0.007 s
% 0.23/0.32 % Total time : 0.036 s
% 0.23/0.32 % Maximum resident set size: 5532 pages
% 0.23/0.32
% 0.23/0.32 % -------------------------------------------------
% 0.23/0.32 % User time : 0.081 s
% 0.23/0.32 % System time : 0.025 s
% 0.23/0.32 % Total time : 0.106 s
% 0.23/0.32 % Maximum resident set size: 5120 pages
% 0.23/0.32 % E exiting
%------------------------------------------------------------------------------