%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP125^1 : 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 : n007.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 08:04:26 AM UTC 2026
% Result : Theorem 1.64s 0.67s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 148 ( 21 ~; 11 |; 1 &; 109 @)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
formula_a: $tType ).
thf(decl_sort3,type,
trace_1367752404list_a: $tType ).
thf(decl_sort4,type,
prefix1027212443list_a: $tType ).
thf(decl_27,type,
monito1457594016ress_a: trace_1367752404list_a > formula_a > nat > nat ).
thf(decl_28,type,
ord_less_nat: nat > nat > $o ).
thf(decl_30,type,
ord_less_eq_nat: nat > nat > $o ).
thf(decl_33,type,
plen_P694648887list_a: prefix1027212443list_a > nat ).
thf(decl_37,type,
phi_1: formula_a ).
thf(decl_39,type,
pi: prefix1027212443list_a ).
thf(decl_40,type,
sigma: trace_1367752404list_a ).
thf(decl_47,type,
k: nat ).
thf(conj_0,conjecture,
ord_less_nat @ k @ ( plen_P694648887list_a @ pi ),
file('/export/starexec/sandbox2/tmp/tmp.u1d29bC5j3/E---3.1_3850990.p',conj_0) ).
thf(fact_163_not__le,axiom,
! [X8: nat,X9: nat] :
( ~ ( ord_less_eq_nat @ X8 @ X9 )
<=> ( ord_less_nat @ X9 @ X8 ) ),
file('/export/starexec/sandbox2/tmp/tmp.u1d29bC5j3/E---3.1_3850990.p',fact_163_not__le) ).
thf(fact_145_leD,axiom,
! [X9: nat,X8: nat] :
( ( ord_less_eq_nat @ X9 @ X8 )
=> ~ ( ord_less_nat @ X8 @ X9 ) ),
file('/export/starexec/sandbox2/tmp/tmp.u1d29bC5j3/E---3.1_3850990.p',fact_145_leD) ).
thf(fact_194_dual__order_Ostrict__trans2,axiom,
! [X13: nat,X37: nat,X238: nat] :
( ( ord_less_nat @ X13 @ X37 )
=> ( ( ord_less_eq_nat @ X238 @ X13 )
=> ( ord_less_nat @ X238 @ X37 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.u1d29bC5j3/E---3.1_3850990.p',fact_194_dual__order_Ostrict__trans2) ).
thf(fact_20_progress__le,axiom,
! [X17: trace_1367752404list_a,X18: formula_a,X11: nat] : ( ord_less_eq_nat @ ( monito1457594016ress_a @ X17 @ X18 @ X11 ) @ X11 ),
file('/export/starexec/sandbox2/tmp/tmp.u1d29bC5j3/E---3.1_3850990.p',fact_20_progress__le) ).
thf(fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
ord_less_nat @ k @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ),
file('/export/starexec/sandbox2/tmp/tmp.u1d29bC5j3/E---3.1_3850990.p',fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062) ).
thf(c_0_6,negated_conjecture,
~ ( ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_7,negated_conjecture,
~ ( ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
thf(c_0_8,plain,
! [X8: nat,X9: nat] :
( ~ ( ord_less_eq_nat @ X8 @ X9 )
<=> ( ord_less_nat @ X9 @ X8 ) ),
inference(fof_simplification,[status(thm)],[fact_163_not__le]) ).
thf(c_0_9,negated_conjecture,
~ ( ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) ),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X1673: nat,X1674: nat] :
( ( ( ord_less_eq_nat @ X1673 @ X1674 )
| ( ord_less_nat @ X1674 @ X1673 ) )
& ( ~ ( ord_less_nat @ X1674 @ X1673 )
| ~ ( ord_less_eq_nat @ X1673 @ X1674 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
thf(c_0_11,plain,
! [X9: nat,X8: nat] :
( ( ord_less_eq_nat @ X9 @ X8 )
=> ~ ( ord_less_nat @ X8 @ X9 ) ),
inference(fof_simplification,[status(thm)],[fact_145_leD]) ).
thf(c_0_12,plain,
! [X1746: nat,X1747: nat,X1748: nat] :
( ~ ( ord_less_nat @ X1746 @ X1747 )
| ~ ( ord_less_eq_nat @ X1748 @ X1746 )
| ( ord_less_nat @ X1748 @ X1747 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_194_dual__order_Ostrict__trans2])])]) ).
thf(c_0_13,negated_conjecture,
~ ( ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X2: nat,X1: nat] :
( ( ord_less_eq_nat @ X1 @ X2 )
| ( ord_less_nat @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
! [X1589: nat,X1590: nat] :
( ~ ( ord_less_eq_nat @ X1589 @ X1590 )
| ~ ( ord_less_nat @ X1590 @ X1589 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
thf(c_0_16,plain,
! [X3: nat,X2: nat,X1: nat] :
( ( ord_less_nat @ X3 @ X2 )
| ~ ( ord_less_nat @ X1 @ X2 )
| ~ ( ord_less_eq_nat @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,negated_conjecture,
ord_less_eq_nat @ ( plen_P694648887list_a @ pi ) @ k,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,plain,
! [X2: nat,X1: nat] :
( ~ ( ord_less_eq_nat @ X1 @ X2 )
| ~ ( ord_less_nat @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_19,negated_conjecture,
! [X1: nat] :
( ( ord_less_nat @ ( plen_P694648887list_a @ pi ) @ X1 )
| ~ ( ord_less_nat @ k @ X1 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_20,plain,
! [X1172: trace_1367752404list_a,X1173: formula_a,X1174: nat] : ( ord_less_eq_nat @ ( monito1457594016ress_a @ X1172 @ X1173 @ X1174 ) @ X1174 ),
inference(variable_rename,[status(thm)],[fact_20_progress__le]) ).
thf(c_0_21,negated_conjecture,
! [X1: nat] :
( ~ ( ord_less_eq_nat @ X1 @ ( plen_P694648887list_a @ pi ) )
| ~ ( ord_less_nat @ k @ X1 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_22,plain,
ord_less_nat @ k @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ),
inference(split_conjunct,[status(thm)],[fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062]) ).
thf(c_0_23,plain,
! [X18: formula_a,X17: trace_1367752404list_a,X1: nat] : ( ord_less_eq_nat @ ( monito1457594016ress_a @ X17 @ X18 @ X1 ) @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP125^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 % Computer : n007.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.25 % CPULimit : 300
% 0.09/0.25 % WCLimit : 300
% 0.09/0.25 % DateTime : Tue Sep 29 19:55:11 UTC 2026
% 0.09/0.25 % CPUTime :
% 0.09/0.25 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.31 Running higher-order theorem proving
% 0.23/0.38 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.u1d29bC5j3/E---3.1_3850990.p
% 1.64/0.67 % Version: 3.5.1-ho
% 1.64/0.67 % Preprocessing class: HSLSSMSMSSSNHFA.
% 1.64/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.64/0.67 % Starting new_ho_10 with 1500s (5) cores
% 1.64/0.67 % Starting new_ho_10_cnf2 with 300s (1) cores
% 1.64/0.67 % Starting full_lambda_6 with 300s (1) cores
% 1.64/0.67 % Starting full_lambda_9 with 300s (1) cores
% 1.64/0.67 % new_ho_10 with pid 3851003 completed with status 0
% 1.64/0.67 % Result found by new_ho_10
% 1.64/0.67 % Preprocessing class: HSLSSMSMSSSNHFA.
% 1.64/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.64/0.67 % Starting new_ho_10 with 1500s (5) cores
% 1.64/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.64/0.67 % No SInE strategy applied
% 1.64/0.67 % Search class: HGHSM-FSLM32-MHFFFSBC
% 1.64/0.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.64/0.67 % Starting SubtermCWHack with 136s (1) cores
% 1.64/0.67 % Starting new_ho_10 with 151s (1) cores
% 1.64/0.67 % Starting lpo6_lambda_fix with 136s (1) cores
% 1.64/0.67 % Starting new_ho_3 with 136s (1) cores
% 1.64/0.67 % Starting sh3 with 136s (1) cores
% 1.64/0.67 % sh3 with pid 3851014 completed with status 0
% 1.64/0.67 % Result found by sh3
% 1.64/0.67 % Preprocessing class: HSLSSMSMSSSNHFA.
% 1.64/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.64/0.67 % Starting new_ho_10 with 1500s (5) cores
% 1.64/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.64/0.67 % No SInE strategy applied
% 1.64/0.67 % Search class: HGHSM-FSLM32-MHFFFSBC
% 1.64/0.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.64/0.67 % Starting SubtermCWHack with 136s (1) cores
% 1.64/0.67 % Starting new_ho_10 with 151s (1) cores
% 1.64/0.67 % Starting lpo6_lambda_fix with 136s (1) cores
% 1.64/0.67 % Starting new_ho_3 with 136s (1) cores
% 1.64/0.67 % Starting sh3 with 136s (1) cores
% 1.64/0.67 % Preprocessing time : 0.022 s
% 1.64/0.67 % Presaturation interreduction done
% 1.64/0.67
% 1.64/0.67 % Proof found!
% 1.64/0.67 % SZS status Theorem
% 1.64/0.67 % SZS output start CNFRefutation
% See solution above
% 1.64/0.67 % Parsed axioms : 315
% 1.64/0.67 % Removed by relevancy pruning/SinE : 0
% 1.64/0.67 % Initial clauses : 663
% 1.64/0.67 % Removed in clause preprocessing : 46
% 1.64/0.67 % Initial clauses in saturation : 617
% 1.64/0.67 % Processed clauses : 808
% 1.64/0.67 % ...of these trivial : 5
% 1.64/0.67 % ...subsumed : 234
% 1.64/0.67 % ...remaining for further processing : 569
% 1.64/0.67 % Other redundant clauses eliminated : 78
% 1.64/0.67 % Clauses deleted for lack of memory : 0
% 1.64/0.67 % Backward-subsumed : 4
% 1.64/0.67 % Backward-rewritten : 3
% 1.64/0.67 % Generated clauses : 568
% 1.64/0.67 % ...of the previous two non-redundant : 490
% 1.64/0.67 % ...aggressively subsumed : 0
% 1.64/0.67 % Contextual simplify-reflections : 3
% 1.64/0.67 % Paramodulations : 482
% 1.64/0.67 % Factorizations : 2
% 1.64/0.67 % NegExts : 0
% 1.64/0.67 % Equation resolutions : 83
% 1.64/0.67 % Disequality decompositions : 0
% 1.64/0.67 % Total rewrite steps : 100
% 1.64/0.67 % ...of those cached : 68
% 1.64/0.67 % Propositional unsat checks : 0
% 1.64/0.67 % Propositional check models : 0
% 1.64/0.67 % Propositional check unsatisfiable : 0
% 1.64/0.67 % Propositional clauses : 0
% 1.64/0.67 % Propositional clauses after purity: 0
% 1.64/0.67 % Propositional unsat core size : 0
% 1.64/0.67 % Propositional preprocessing time : 0.000
% 1.64/0.67 % Propositional encoding time : 0.000
% 1.64/0.67 % Propositional solver time : 0.000
% 1.64/0.67 % Success case prop preproc time : 0.000
% 1.64/0.67 % Success case prop encoding time : 0.000
% 1.64/0.67 % Success case prop solver time : 0.000
% 1.64/0.67 % Current number of processed clauses : 120
% 1.64/0.67 % Positive orientable unit clauses : 34
% 1.64/0.67 % Positive unorientable unit clauses: 1
% 1.64/0.67 % Negative unit clauses : 26
% 1.64/0.67 % Non-unit-clauses : 59
% 1.64/0.67 % Current number of unprocessed clauses: 653
% 1.64/0.67 % ...number of literals in the above : 2187
% 1.64/0.67 % Current number of archived formulas : 0
% 1.64/0.67 % Current number of archived clauses : 371
% 1.64/0.67 % Clause-clause subsumption calls (NU) : 28522
% 1.64/0.67 % Rec. Clause-clause subsumption calls : 7141
% 1.64/0.67 % Non-unit clause-clause subsumptions : 201
% 1.64/0.67 % Unit Clause-clause subsumption calls : 151
% 1.64/0.67 % Rewrite failures with RHS unbound : 0
% 1.64/0.67 % BW rewrite match attempts : 19
% 1.64/0.67 % BW rewrite match successes : 15
% 1.64/0.67 % Condensation attempts : 0
% 1.64/0.67 % Condensation successes : 0
% 1.64/0.67 % Termbank termtop insertions : 75135
% 1.64/0.67 % Search garbage collected termcells : 12295
% 1.64/0.67
% 1.64/0.67 % -------------------------------------------------
% 1.64/0.67 % User time : 0.215 s
% 1.64/0.67 % System time : 0.020 s
% 1.64/0.67 % Total time : 0.235 s
% 1.64/0.67 % Maximum resident set size: 6208 pages
% 1.64/0.67
% 1.64/0.67 % -------------------------------------------------
% 1.97/0.67 % User time : 0.831 s
% 1.97/0.67 % System time : 0.078 s
% 1.97/0.67 % Total time : 0.908 s
% 1.97/0.67 % Maximum resident set size: 5376 pages
% 1.97/0.67 % E exiting
%------------------------------------------------------------------------------