%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP105^1 : 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 08:04:22 AM UTC 2026
% Result : Theorem 0.21s 0.32s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 19 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 11 ~; 5 |; 1 &; 45 @)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
list_list_a: $tType ).
thf(decl_sort3,type,
list_a: $tType ).
thf(decl_25,type,
zero_zero_nat: nat ).
thf(decl_29,type,
listSl97544552lice_a: list_a > nat > list_list_a ).
thf(decl_52,type,
nil_list_a: list_list_a ).
thf(decl_53,type,
nil_a: list_a ).
thf(decl_86,type,
size_size_list_a: list_a > nat ).
thf(decl_88,type,
ord_less_nat: nat > nat > $o ).
thf(decl_103,type,
k: nat ).
thf(conj_0,conjecture,
( ( listSl97544552lice_a @ nil_a @ k )
= nil_list_a ),
file('/export/starexec/sandbox/tmp/tmp.1O51Q5Dgbr/E---3.1_561704.p',conj_0) ).
thf(fact_9_list__slice__less,axiom,
! [X7: list_a,X6: nat] :
( ( ord_less_nat @ ( size_size_list_a @ X7 ) @ X6 )
=> ( ( listSl97544552lice_a @ X7 @ X6 )
= nil_list_a ) ),
file('/export/starexec/sandbox/tmp/tmp.1O51Q5Dgbr/E---3.1_561704.p',fact_9_list__slice__less) ).
thf(fact_63_neq0__conv,axiom,
! [X20: nat] :
( ( X20 != zero_zero_nat )
<=> ( ord_less_nat @ zero_zero_nat @ X20 ) ),
file('/export/starexec/sandbox/tmp/tmp.1O51Q5Dgbr/E---3.1_561704.p',fact_63_neq0__conv) ).
thf(fact_57_list_Osize_I3_J,axiom,
( ( size_size_list_a @ nil_a )
= zero_zero_nat ),
file('/export/starexec/sandbox/tmp/tmp.1O51Q5Dgbr/E---3.1_561704.p',fact_57_list_Osize_I3_J) ).
thf(fact_1_list__slice__0,axiom,
! [X2: list_a] :
( ( listSl97544552lice_a @ X2 @ zero_zero_nat )
= nil_list_a ),
file('/export/starexec/sandbox/tmp/tmp.1O51Q5Dgbr/E---3.1_561704.p',fact_1_list__slice__0) ).
thf(c_0_5,negated_conjecture,
( ( listSl97544552lice_a @ nil_a @ k )
!= nil_list_a ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_6,negated_conjecture,
( ( listSl97544552lice_a @ nil_a @ k )
!= nil_list_a ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
( ( listSl97544552lice_a @ nil_a @ k )
!= nil_list_a ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_8,plain,
! [X498: list_a,X499: nat] :
( ~ ( ord_less_nat @ ( size_size_list_a @ X498 ) @ X499 )
| ( ( listSl97544552lice_a @ X498 @ X499 )
= nil_list_a ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_9_list__slice__less])])]) ).
thf(c_0_9,plain,
! [X20: nat] :
( ( X20 != zero_zero_nat )
<=> ( ord_less_nat @ zero_zero_nat @ X20 ) ),
inference(fof_simplification,[status(thm)],[fact_63_neq0__conv]) ).
thf(c_0_10,negated_conjecture,
( ( listSl97544552lice_a @ nil_a @ k )
!= nil_list_a ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X2: list_a,X6: nat] :
( ( ( listSl97544552lice_a @ X2 @ X6 )
= nil_list_a )
| ~ ( ord_less_nat @ ( size_size_list_a @ X2 ) @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
( ( size_size_list_a @ nil_a )
= zero_zero_nat ),
inference(split_conjunct,[status(thm)],[fact_57_list_Osize_I3_J]) ).
thf(c_0_13,plain,
! [X508: nat] :
( ( ( X508 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ X508 ) )
& ( ~ ( ord_less_nat @ zero_zero_nat @ X508 )
| ( X508 != zero_zero_nat ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
thf(c_0_14,negated_conjecture,
~ ( ord_less_nat @ zero_zero_nat @ k ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
thf(c_0_15,plain,
! [X6: nat] :
( ( X6 = zero_zero_nat )
| ( ord_less_nat @ zero_zero_nat @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,plain,
! [X497: list_a] :
( ( listSl97544552lice_a @ X497 @ zero_zero_nat )
= nil_list_a ),
inference(variable_rename,[status(thm)],[fact_1_list__slice__0]) ).
thf(c_0_17,negated_conjecture,
k = zero_zero_nat,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,plain,
! [X2: list_a] :
( ( listSl97544552lice_a @ X2 @ zero_zero_nat )
= nil_list_a ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_17]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP105^1 : 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 : n011.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 19:54:31 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
% 0.21/0.27 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.1O51Q5Dgbr/E---3.1_561704.p
% 0.21/0.32 % Version: 3.5.1-ho
% 0.21/0.32 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.21/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.32 % Starting new_ho_3 with 1500s (5) cores
% 0.21/0.32 % Starting pre_casc_2 with 300s (1) cores
% 0.21/0.32 % Starting additional_ho_7 with 300s (1) cores
% 0.21/0.32 % Starting lpo8_s with 300s (1) cores
% 0.21/0.32 % additional_ho_7 with pid 561719 completed with status 0
% 0.21/0.32 % Result found by additional_ho_7
% 0.21/0.32 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.21/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.32 % Starting new_ho_3 with 1500s (5) cores
% 0.21/0.32 % Starting pre_casc_2 with 300s (1) cores
% 0.21/0.32 % Starting additional_ho_7 with 300s (1) cores
% 0.21/0.32 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4.0,,2,20000,1.0))
% 0.21/0.32 % SinE strategy is GSinE(CountFormulas,hypos,4.0,,2,20000,1.0)
% 0.21/0.32 % Search class: HGHSM-FFMM31-MSFFFFBN
% 0.21/0.32 % partial match(1): HGHSM-FFMM31-DSFFFFBN
% 0.21/0.32 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.32 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.32 % SubtermCWHack with pid 561721 completed with status 0
% 0.21/0.32 % Result found by SubtermCWHack
% 0.21/0.32 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.21/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.32 % Starting new_ho_3 with 1500s (5) cores
% 0.21/0.32 % Starting pre_casc_2 with 300s (1) cores
% 0.21/0.32 % Starting additional_ho_7 with 300s (1) cores
% 0.21/0.32 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4.0,,2,20000,1.0))
% 0.21/0.32 % SinE strategy is GSinE(CountFormulas,hypos,4.0,,2,20000,1.0)
% 0.21/0.32 % Search class: HGHSM-FFMM31-MSFFFFBN
% 0.21/0.32 % partial match(1): HGHSM-FFMM31-DSFFFFBN
% 0.21/0.32 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.32 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.32 % Preprocessing time : 0.004 s
% 0.21/0.32
% 0.21/0.32 % Proof found!
% 0.21/0.32 % SZS status Theorem
% 0.21/0.32 % SZS output start CNFRefutation
% See solution above
% 0.21/0.32 % Parsed axioms : 444
% 0.21/0.32 % Removed by relevancy pruning/SinE : 334
% 0.21/0.32 % Initial clauses : 171
% 0.21/0.32 % Removed in clause preprocessing : 6
% 0.21/0.32 % Initial clauses in saturation : 165
% 0.21/0.32 % Processed clauses : 244
% 0.21/0.32 % ...of these trivial : 8
% 0.21/0.32 % ...subsumed : 102
% 0.21/0.32 % ...remaining for further processing : 134
% 0.21/0.32 % Other redundant clauses eliminated : 36
% 0.21/0.32 % Clauses deleted for lack of memory : 0
% 0.21/0.32 % Backward-subsumed : 2
% 0.21/0.32 % Backward-rewritten : 5
% 0.21/0.32 % Generated clauses : 274
% 0.21/0.32 % ...of the previous two non-redundant : 209
% 0.21/0.32 % ...aggressively subsumed : 0
% 0.21/0.32 % Contextual simplify-reflections : 0
% 0.21/0.32 % Paramodulations : 235
% 0.21/0.32 % Factorizations : 2
% 0.21/0.32 % NegExts : 0
% 0.21/0.32 % Equation resolutions : 36
% 0.21/0.32 % Disequality decompositions : 0
% 0.21/0.32 % Total rewrite steps : 70
% 0.21/0.32 % ...of those cached : 52
% 0.21/0.32 % Propositional unsat checks : 0
% 0.21/0.32 % Propositional check models : 0
% 0.21/0.32 % Propositional check unsatisfiable : 0
% 0.21/0.32 % Propositional clauses : 0
% 0.21/0.32 % Propositional clauses after purity: 0
% 0.21/0.32 % Propositional unsat core size : 0
% 0.21/0.32 % Propositional preprocessing time : 0.000
% 0.21/0.32 % Propositional encoding time : 0.000
% 0.21/0.32 % Propositional solver time : 0.000
% 0.21/0.32 % Success case prop preproc time : 0.000
% 0.21/0.32 % Success case prop encoding time : 0.000
% 0.21/0.32 % Success case prop solver time : 0.000
% 0.21/0.32 % Current number of processed clauses : 94
% 0.21/0.32 % Positive orientable unit clauses : 21
% 0.21/0.32 % Positive unorientable unit clauses: 0
% 0.21/0.32 % Negative unit clauses : 6
% 0.21/0.32 % Non-unit-clauses : 67
% 0.21/0.32 % Current number of unprocessed clauses: 119
% 0.21/0.32 % ...number of literals in the above : 366
% 0.21/0.32 % Current number of archived formulas : 0
% 0.21/0.32 % Current number of archived clauses : 7
% 0.21/0.32 % Clause-clause subsumption calls (NU) : 729
% 0.21/0.32 % Rec. Clause-clause subsumption calls : 669
% 0.21/0.32 % Non-unit clause-clause subsumptions : 66
% 0.21/0.32 % Unit Clause-clause subsumption calls : 83
% 0.21/0.32 % Rewrite failures with RHS unbound : 0
% 0.21/0.32 % BW rewrite match attempts : 7
% 0.21/0.32 % BW rewrite match successes : 4
% 0.21/0.32 % Condensation attempts : 0
% 0.21/0.32 % Condensation successes : 0
% 0.21/0.32 % Termbank termtop insertions : 17099
% 0.21/0.32 % Search garbage collected termcells : 4705
% 0.21/0.32
% 0.21/0.32 % -------------------------------------------------
% 0.21/0.32 % User time : 0.023 s
% 0.21/0.32 % System time : 0.004 s
% 0.21/0.32 % Total time : 0.027 s
% 0.21/0.32 % Maximum resident set size: 5080 pages
% 0.21/0.32
% 0.21/0.32 % -------------------------------------------------
% 0.21/0.32 % User time : 0.035 s
% 0.21/0.32 % System time : 0.008 s
% 0.21/0.32 % Total time : 0.043 s
% 0.21/0.32 % Maximum resident set size: 5632 pages
% 0.21/0.32 % E exiting
%------------------------------------------------------------------------------