%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP054^1 : 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 : n001.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 08:05:23 AM UTC 2026
% Result : Theorem 29.22s 4.69s
% Output : CNFRefutation 29.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 7 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 153 ( 23 ~; 16 |; 2 &; 107 @)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 ^; 25 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
list_c1059388851t_unit: $tType ).
thf(decl_47,type,
suc: nat > nat ).
thf(decl_48,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(decl_50,type,
ord_less_nat: nat > nat > $o ).
thf(decl_55,type,
fe: nat > list_c1059388851t_unit ).
thf(decl_58,type,
index: nat ).
thf(decl_61,type,
n1: nat ).
thf(decl_62,type,
nMsg: nat ).
thf(conj_0,conjecture,
ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ),
file('/export/starexec/sandbox2/tmp/tmp.X7eNrgaO6O/E---3.1_1729037.p',conj_0) ).
thf(fact_29_less__trans__Suc,axiom,
! [X28: nat,X29: nat,X35: nat] :
( ( ord_less_nat @ X28 @ X29 )
=> ( ( ord_less_nat @ X29 @ X35 )
=> ( ord_less_nat @ ( suc @ X28 ) @ X35 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X7eNrgaO6O/E---3.1_1729037.p',fact_29_less__trans__Suc) ).
thf(fact_41_Suc__lessD,axiom,
! [X19: nat,X10: nat] :
( ( ord_less_nat @ ( suc @ X19 ) @ X10 )
=> ( ord_less_nat @ X19 @ X10 ) ),
file('/export/starexec/sandbox2/tmp/tmp.X7eNrgaO6O/E---3.1_1729037.p',fact_41_Suc__lessD) ).
thf(fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062,axiom,
ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ),
file('/export/starexec/sandbox2/tmp/tmp.X7eNrgaO6O/E---3.1_1729037.p',fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062) ).
thf(fact_13_nat__neq__iff,axiom,
! [X19: nat,X10: nat] :
( ( X19 != X10 )
<=> ( ( ord_less_nat @ X19 @ X10 )
| ( ord_less_nat @ X10 @ X19 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X7eNrgaO6O/E---3.1_1729037.p',fact_13_nat__neq__iff) ).
thf(fact_0_AssumpGreaterOccurrence_I1_J,axiom,
~ ( ord_less_nat @ nMsg @ n1 ),
file('/export/starexec/sandbox2/tmp/tmp.X7eNrgaO6O/E---3.1_1729037.p',fact_0_AssumpGreaterOccurrence_I1_J) ).
thf(c_0_6,negated_conjecture,
~ ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_7,plain,
! [X792: nat,X793: nat,X794: nat] :
( ~ ( ord_less_nat @ X792 @ X793 )
| ~ ( ord_less_nat @ X793 @ X794 )
| ( ord_less_nat @ ( suc @ X792 ) @ X794 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_29_less__trans__Suc])])]) ).
thf(c_0_8,negated_conjecture,
~ ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X834: nat,X835: nat] :
( ~ ( ord_less_nat @ ( suc @ X834 ) @ X835 )
| ( ord_less_nat @ X834 @ X835 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_41_Suc__lessD])])]) ).
thf(c_0_10,plain,
! [X9: nat,X10: nat,X19: nat] :
( ( ord_less_nat @ ( suc @ X9 ) @ X19 )
| ~ ( ord_less_nat @ X9 @ X10 )
| ~ ( ord_less_nat @ X10 @ X19 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ),
inference(split_conjunct,[status(thm)],[fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062]) ).
thf(c_0_12,negated_conjecture,
~ ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ),
inference(fof_nnf,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
! [X9: nat,X10: nat] :
( ( ord_less_nat @ X9 @ X10 )
| ~ ( ord_less_nat @ ( suc @ X9 ) @ X10 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X9: nat] :
( ( ord_less_nat @ ( suc @ X9 ) @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
| ~ ( ord_less_nat @ X9 @ nMsg ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,plain,
! [X19: nat,X10: nat] :
( ( X19 != X10 )
<=> ( ( ord_less_nat @ X19 @ X10 )
| ( ord_less_nat @ X10 @ X19 ) ) ),
inference(fof_simplification,[status(thm)],[fact_13_nat__neq__iff]) ).
thf(c_0_16,plain,
~ ( ord_less_nat @ nMsg @ n1 ),
inference(fof_simplification,[status(thm)],[fact_0_AssumpGreaterOccurrence_I1_J]) ).
thf(c_0_17,negated_conjecture,
~ ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,plain,
! [X9: nat] :
( ( ord_less_nat @ X9 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
| ~ ( ord_less_nat @ X9 @ nMsg ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_19,plain,
! [X758: nat,X759: nat] :
( ( ( X758 = X759 )
| ( ord_less_nat @ X758 @ X759 )
| ( ord_less_nat @ X759 @ X758 ) )
& ( ~ ( ord_less_nat @ X758 @ X759 )
| ( X758 != X759 ) )
& ( ~ ( ord_less_nat @ X759 @ X758 )
| ( X758 != X759 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
thf(c_0_20,plain,
~ ( ord_less_nat @ nMsg @ n1 ),
inference(fof_nnf,[status(thm)],[c_0_16]) ).
thf(c_0_21,negated_conjecture,
~ ( ord_less_nat @ n1 @ nMsg ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_22,plain,
! [X10: nat,X9: nat] :
( ( X9 = X10 )
| ( ord_less_nat @ X9 @ X10 )
| ( ord_less_nat @ X10 @ X9 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_23,plain,
~ ( ord_less_nat @ nMsg @ n1 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,negated_conjecture,
n1 = nMsg,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
thf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_24]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP054^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n001.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
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:49:51 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.26 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.X7eNrgaO6O/E---3.1_1729037.p
% 29.22/4.69 % Version: 3.5.1-ho
% 29.22/4.69 % Preprocessing class: HSLSSMSMSSSNHFA.
% 29.22/4.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.22/4.69 % Starting new_ho_10 with 1500s (5) cores
% 29.22/4.69 % Starting new_ho_10_cnf2 with 300s (1) cores
% 29.22/4.69 % Starting full_lambda_6 with 300s (1) cores
% 29.22/4.69 % Starting full_lambda_9 with 300s (1) cores
% 29.22/4.69 % new_ho_10 with pid 1729050 completed with status 0
% 29.22/4.69 % Result found by new_ho_10
% 29.22/4.69 % Preprocessing class: HSLSSMSMSSSNHFA.
% 29.22/4.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.22/4.69 % Starting new_ho_10 with 1500s (5) cores
% 29.22/4.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 29.22/4.69 % No SInE strategy applied
% 29.22/4.69 % Search class: HGHSM-FSLM31-MHFFFSBC
% 29.22/4.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 29.22/4.69 % Starting SubtermCWHack with 136s (1) cores
% 29.22/4.69 % Starting new_ho_10 with 151s (1) cores
% 29.22/4.69 % Starting almost_fo_4 with 136s (1) cores
% 29.22/4.69 % Starting new_ho_10_unif with 136s (1) cores
% 29.22/4.69 % Starting ehoh_best3_fo with 136s (1) cores
% 29.22/4.69 % ehoh_best3_fo with pid 1729061 completed with status 0
% 29.22/4.69 % Result found by ehoh_best3_fo
% 29.22/4.69 % Preprocessing class: HSLSSMSMSSSNHFA.
% 29.22/4.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.22/4.69 % Starting new_ho_10 with 1500s (5) cores
% 29.22/4.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 29.22/4.69 % No SInE strategy applied
% 29.22/4.69 % Search class: HGHSM-FSLM31-MHFFFSBC
% 29.22/4.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 29.22/4.69 % Starting SubtermCWHack with 136s (1) cores
% 29.22/4.69 % Starting new_ho_10 with 151s (1) cores
% 29.22/4.69 % Starting almost_fo_4 with 136s (1) cores
% 29.22/4.69 % Starting new_ho_10_unif with 136s (1) cores
% 29.22/4.69 % Starting ehoh_best3_fo with 136s (1) cores
% 29.22/4.69 % Preprocessing time : 0.010 s
% 29.22/4.69 % Presaturation interreduction done
% 29.22/4.69
% 29.22/4.69 % Proof found!
% 29.22/4.69 % SZS status Theorem
% 29.22/4.69 % SZS output start CNFRefutation
% See solution above
% 29.22/4.69 % Parsed axioms : 309
% 29.22/4.69 % Removed by relevancy pruning/SinE : 0
% 29.22/4.69 % Initial clauses : 491
% 29.22/4.69 % Removed in clause preprocessing : 67
% 29.22/4.69 % Initial clauses in saturation : 424
% 29.22/4.69 % Processed clauses : 12432
% 29.22/4.69 % ...of these trivial : 346
% 29.22/4.69 % ...subsumed : 9385
% 29.22/4.69 % ...remaining for further processing : 2701
% 29.22/4.69 % Other redundant clauses eliminated : 589
% 29.22/4.69 % Clauses deleted for lack of memory : 0
% 29.22/4.69 % Backward-subsumed : 54
% 29.22/4.69 % Backward-rewritten : 224
% 29.22/4.69 % Generated clauses : 194722
% 29.22/4.69 % ...of the previous two non-redundant : 165655
% 29.22/4.69 % ...aggressively subsumed : 0
% 29.22/4.69 % Contextual simplify-reflections : 33
% 29.22/4.69 % Paramodulations : 193461
% 29.22/4.69 % Factorizations : 31
% 29.22/4.69 % NegExts : 0
% 29.22/4.69 % Equation resolutions : 595
% 29.22/4.69 % Disequality decompositions : 0
% 29.22/4.69 % Total rewrite steps : 68877
% 29.22/4.69 % ...of those cached : 63726
% 29.22/4.69 % Propositional unsat checks : 0
% 29.22/4.69 % Propositional check models : 0
% 29.22/4.69 % Propositional check unsatisfiable : 0
% 29.22/4.69 % Propositional clauses : 0
% 29.22/4.69 % Propositional clauses after purity: 0
% 29.22/4.69 % Propositional unsat core size : 0
% 29.22/4.69 % Propositional preprocessing time : 0.000
% 29.22/4.69 % Propositional encoding time : 0.000
% 29.22/4.69 % Propositional solver time : 0.000
% 29.22/4.69 % Success case prop preproc time : 0.000
% 29.22/4.69 % Success case prop encoding time : 0.000
% 29.22/4.69 % Success case prop solver time : 0.000
% 29.22/4.69 % Current number of processed clauses : 2044
% 29.22/4.69 % Positive orientable unit clauses : 402
% 29.22/4.69 % Positive unorientable unit clauses: 10
% 29.22/4.69 % Negative unit clauses : 170
% 29.22/4.69 % Non-unit-clauses : 1462
% 29.22/4.69 % Current number of unprocessed clauses: 153074
% 29.22/4.69 % ...number of literals in the above : 441580
% 29.22/4.69 % Current number of archived formulas : 0
% 29.22/4.69 % Current number of archived clauses : 614
% 29.22/4.69 % Clause-clause subsumption calls (NU) : 312134
% 29.22/4.69 % Rec. Clause-clause subsumption calls : 219561
% 29.22/4.69 % Non-unit clause-clause subsumptions : 4063
% 29.22/4.69 % Unit Clause-clause subsumption calls : 32192
% 29.22/4.69 % Rewrite failures with RHS unbound : 0
% 29.22/4.69 % BW rewrite match attempts : 10011
% 29.22/4.69 % BW rewrite match successes : 2182
% 29.22/4.69 % Condensation attempts : 0
% 29.22/4.69 % Condensation successes : 0
% 29.22/4.69 % Termbank termtop insertions : 6411387
% 29.22/4.69 % Search garbage collected termcells : 9508
% 29.22/4.69
% 29.22/4.69 % -------------------------------------------------
% 29.22/4.69 % User time : 3.916 s
% 29.22/4.69 % System time : 0.145 s
% 29.22/4.69 % Total time : 4.062 s
% 29.22/4.69 % Maximum resident set size: 5652 pages
% 29.22/4.69
% 29.22/4.69 % -------------------------------------------------
% 29.22/4.69 % User time : 19.970 s
% 29.22/4.69 % System time : 0.700 s
% 29.22/4.69 % Total time : 20.671 s
% 29.22/4.69 % Maximum resident set size: 5376 pages
% 29.22/4.69 % E exiting
%------------------------------------------------------------------------------