%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP061^1 : 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 : 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 08:04:14 AM UTC 2026
% Result : Theorem 0.86s 0.43s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 12 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 212 ( 26 ~; 15 |; 5 &; 160 @)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 2 ^; 34 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
list_c1059388851t_unit: $tType ).
thf(decl_27,type,
minus_minus_nat: nat > nat > nat ).
thf(decl_28,type,
one_one_nat: nat ).
thf(decl_34,type,
suc: nat > nat ).
thf(decl_35,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(decl_37,type,
ord_less_nat: nat > nat > $o ).
thf(decl_38,type,
ord_less_eq_nat: nat > nat > $o ).
thf(decl_42,type,
occM2: nat ).
thf(decl_44,type,
fe: nat > list_c1059388851t_unit ).
thf(decl_47,type,
index: nat ).
thf(conj_0,conjecture,
( occM2
= ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.zXCVtNcGDz/E---3.1_550719.p',conj_0) ).
thf(fact_47_le__antisym,axiom,
! [X19: nat,X4: nat] :
( ( ord_less_eq_nat @ X19 @ X4 )
=> ( ( ord_less_eq_nat @ X4 @ X19 )
=> ( X19 = X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zXCVtNcGDz/E---3.1_550719.p',fact_47_le__antisym) ).
thf(fact_104_diff__le__mono,axiom,
! [X19: nat,X4: nat,X64: nat] :
( ( ord_less_eq_nat @ X19 @ X4 )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ X19 @ X64 ) @ ( minus_minus_nat @ X4 @ X64 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zXCVtNcGDz/E---3.1_550719.p',fact_104_diff__le__mono) ).
thf(fact_24_diff__Suc__1,axiom,
! [X4: nat] :
( ( minus_minus_nat @ ( suc @ X4 ) @ one_one_nat )
= X4 ),
file('/export/starexec/sandbox2/tmp/tmp.zXCVtNcGDz/E---3.1_550719.p',fact_24_diff__Suc__1) ).
thf(fact_201_less__le__not__le,axiom,
( ord_less_nat
= ( ^ [X212: nat,X134: nat] :
( ( ord_less_eq_nat @ X212 @ X134 )
& ~ ( ord_less_eq_nat @ X134 @ X212 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zXCVtNcGDz/E---3.1_550719.p',fact_201_less__le__not__le) ).
thf(fact_1__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_AOccM_092_060close_062,axiom,
ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ occM2,
file('/export/starexec/sandbox2/tmp/tmp.zXCVtNcGDz/E---3.1_550719.p',fact_1__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_AOccM_092_060close_062) ).
thf(fact_68_not__less__eq__eq,axiom,
! [X19: nat,X4: nat] :
( ~ ( ord_less_eq_nat @ X19 @ X4 )
<=> ( ord_less_eq_nat @ ( suc @ X4 ) @ X19 ) ),
file('/export/starexec/sandbox2/tmp/tmp.zXCVtNcGDz/E---3.1_550719.p',fact_68_not__less__eq__eq) ).
thf(fact_0_AssumpOccMFirstOccurrence_I3_J,axiom,
ord_less_nat @ occM2 @ ( size_s1406904903t_unit @ ( fe @ index ) ),
file('/export/starexec/sandbox2/tmp/tmp.zXCVtNcGDz/E---3.1_550719.p',fact_0_AssumpOccMFirstOccurrence_I3_J) ).
thf(c_0_8,negated_conjecture,
( occM2
!= ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_9,negated_conjecture,
( occM2
!= ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
thf(c_0_10,plain,
! [X920: nat,X921: nat] :
( ~ ( ord_less_eq_nat @ X920 @ X921 )
| ~ ( ord_less_eq_nat @ X921 @ X920 )
| ( X920 = X921 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_47_le__antisym])])]) ).
thf(c_0_11,negated_conjecture,
( occM2
!= ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
thf(c_0_12,plain,
! [X1097: nat,X1098: nat,X1099: nat] :
( ~ ( ord_less_eq_nat @ X1097 @ X1098 )
| ( ord_less_eq_nat @ ( minus_minus_nat @ X1097 @ X1099 ) @ ( minus_minus_nat @ X1098 @ X1099 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_104_diff__le__mono])])]) ).
thf(c_0_13,plain,
! [X868: nat] :
( ( minus_minus_nat @ ( suc @ X868 ) @ one_one_nat )
= X868 ),
inference(variable_rename,[status(thm)],[fact_24_diff__Suc__1]) ).
thf(c_0_14,plain,
! [X829: nat,X830: nat] :
( ( ord_less_nat @ X829 @ X830 )
<=> ( ( ord_less_eq_nat @ X829 @ X830 )
& ~ ( ord_less_eq_nat @ X830 @ X829 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_201_less__le__not__le])])]) ).
thf(c_0_15,plain,
! [X2: nat,X1: nat] :
( ( X1 = X2 )
| ~ ( ord_less_eq_nat @ X1 @ X2 )
| ~ ( ord_less_eq_nat @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,plain,
ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ occM2,
inference(split_conjunct,[status(thm)],[fact_1__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_AOccM_092_060close_062]) ).
thf(c_0_17,negated_conjecture,
( occM2
!= ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_18,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ X1 @ X3 ) @ ( minus_minus_nat @ X2 @ X3 ) )
| ~ ( ord_less_eq_nat @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_19,plain,
! [X1: nat] :
( ( minus_minus_nat @ ( suc @ X1 ) @ one_one_nat )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_20,plain,
! [X19: nat,X4: nat] :
( ~ ( ord_less_eq_nat @ X19 @ X4 )
<=> ( ord_less_eq_nat @ ( suc @ X4 ) @ X19 ) ),
inference(fof_simplification,[status(thm)],[fact_68_not__less__eq__eq]) ).
thf(c_0_21,plain,
! [X1388: nat,X1389: nat] :
( ( ( ord_less_eq_nat @ X1388 @ X1389 )
| ~ ( ord_less_nat @ X1388 @ X1389 ) )
& ( ~ ( ord_less_eq_nat @ X1389 @ X1388 )
| ~ ( ord_less_nat @ X1388 @ X1389 ) )
& ( ~ ( ord_less_eq_nat @ X1388 @ X1389 )
| ( ord_less_eq_nat @ X1389 @ X1388 )
| ( ord_less_nat @ X1388 @ X1389 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
thf(c_0_22,plain,
~ ( ord_less_eq_nat @ occM2 @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
thf(c_0_23,plain,
! [X1: nat,X2: nat] :
( ( ord_less_eq_nat @ X1 @ ( minus_minus_nat @ X2 @ one_one_nat ) )
| ~ ( ord_less_eq_nat @ ( suc @ X1 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_24,plain,
! [X975: nat,X976: nat] :
( ( ( ord_less_eq_nat @ X975 @ X976 )
| ( ord_less_eq_nat @ ( suc @ X976 ) @ X975 ) )
& ( ~ ( ord_less_eq_nat @ ( suc @ X976 ) @ X975 )
| ~ ( ord_less_eq_nat @ X975 @ X976 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
thf(c_0_25,plain,
! [X2: nat,X1: nat] :
( ~ ( ord_less_eq_nat @ X1 @ X2 )
| ~ ( ord_less_nat @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_26,plain,
ord_less_nat @ occM2 @ ( size_s1406904903t_unit @ ( fe @ index ) ),
inference(split_conjunct,[status(thm)],[fact_0_AssumpOccMFirstOccurrence_I3_J]) ).
thf(c_0_27,plain,
~ ( ord_less_eq_nat @ ( suc @ occM2 ) @ ( size_s1406904903t_unit @ ( fe @ index ) ) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_28,plain,
! [X2: nat,X1: nat] :
( ( ord_less_eq_nat @ X1 @ X2 )
| ( ord_less_eq_nat @ ( suc @ X2 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_29,plain,
~ ( ord_less_eq_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ occM2 ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_30,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP061^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % 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 19:45:01 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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.zXCVtNcGDz/E---3.1_550719.p
% 0.86/0.43 % Version: 3.5.1-ho
% 0.86/0.43 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.86/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.86/0.43 % Starting new_ho_10 with 1500s (5) cores
% 0.86/0.43 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.86/0.43 % Starting full_lambda_6 with 300s (1) cores
% 0.86/0.43 % Starting full_lambda_9 with 300s (1) cores
% 0.86/0.43 % new_ho_10 with pid 550732 completed with status 0
% 0.86/0.43 % Result found by new_ho_10
% 0.86/0.43 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.86/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.86/0.43 % Starting new_ho_10 with 1500s (5) cores
% 0.86/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.86/0.43 % No SInE strategy applied
% 0.86/0.43 % Search class: HGHSM-FSLM32-MHFFFSBC
% 0.86/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.86/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.86/0.43 % Starting new_ho_10 with 151s (1) cores
% 0.86/0.43 % Starting lpo6_lambda_fix with 136s (1) cores
% 0.86/0.43 % Starting new_ho_3 with 136s (1) cores
% 0.86/0.43 % Starting sh3 with 136s (1) cores
% 0.86/0.43 % new_ho_10 with pid 550740 completed with status 0
% 0.86/0.43 % Result found by new_ho_10
% 0.86/0.43 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.86/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.86/0.43 % Starting new_ho_10 with 1500s (5) cores
% 0.86/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.86/0.43 % No SInE strategy applied
% 0.86/0.43 % Search class: HGHSM-FSLM32-MHFFFSBC
% 0.86/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.86/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.86/0.43 % Starting new_ho_10 with 151s (1) cores
% 0.86/0.43 % Preprocessing time : 0.004 s
% 0.86/0.43 % Presaturation interreduction done
% 0.86/0.43
% 0.86/0.43 % Proof found!
% 0.86/0.43 % SZS status Theorem
% 0.86/0.43 % SZS output start CNFRefutation
% See solution above
% 0.86/0.43 % Parsed axioms : 274
% 0.86/0.43 % Removed by relevancy pruning/SinE : 0
% 0.86/0.43 % Initial clauses : 491
% 0.86/0.43 % Removed in clause preprocessing : 58
% 0.86/0.43 % Initial clauses in saturation : 433
% 0.86/0.43 % Processed clauses : 1046
% 0.86/0.43 % ...of these trivial : 37
% 0.86/0.43 % ...subsumed : 303
% 0.86/0.43 % ...remaining for further processing : 706
% 0.86/0.43 % Other redundant clauses eliminated : 64
% 0.86/0.43 % Clauses deleted for lack of memory : 0
% 0.86/0.43 % Backward-subsumed : 9
% 0.86/0.43 % Backward-rewritten : 13
% 0.86/0.43 % Generated clauses : 6217
% 0.86/0.43 % ...of the previous two non-redundant : 5783
% 0.86/0.43 % ...aggressively subsumed : 0
% 0.86/0.43 % Contextual simplify-reflections : 3
% 0.86/0.43 % Paramodulations : 6132
% 0.86/0.43 % Factorizations : 10
% 0.86/0.43 % NegExts : 0
% 0.86/0.43 % Equation resolutions : 70
% 0.86/0.43 % Disequality decompositions : 0
% 0.86/0.43 % Total rewrite steps : 1167
% 0.86/0.43 % ...of those cached : 837
% 0.86/0.43 % Propositional unsat checks : 0
% 0.86/0.43 % Propositional check models : 0
% 0.86/0.43 % Propositional check unsatisfiable : 0
% 0.86/0.43 % Propositional clauses : 0
% 0.86/0.43 % Propositional clauses after purity: 0
% 0.86/0.43 % Propositional unsat core size : 0
% 0.86/0.43 % Propositional preprocessing time : 0.000
% 0.86/0.43 % Propositional encoding time : 0.000
% 0.86/0.43 % Propositional solver time : 0.000
% 0.86/0.43 % Success case prop preproc time : 0.000
% 0.86/0.43 % Success case prop encoding time : 0.000
% 0.86/0.43 % Success case prop solver time : 0.000
% 0.86/0.43 % Current number of processed clauses : 392
% 0.86/0.43 % Positive orientable unit clauses : 71
% 0.86/0.43 % Positive unorientable unit clauses: 1
% 0.86/0.43 % Negative unit clauses : 43
% 0.86/0.43 % Non-unit-clauses : 277
% 0.86/0.43 % Current number of unprocessed clauses: 5392
% 0.86/0.43 % ...number of literals in the above : 17589
% 0.86/0.43 % Current number of archived formulas : 0
% 0.86/0.43 % Current number of archived clauses : 266
% 0.86/0.43 % Clause-clause subsumption calls (NU) : 27975
% 0.86/0.43 % Rec. Clause-clause subsumption calls : 17791
% 0.86/0.43 % Non-unit clause-clause subsumptions : 211
% 0.86/0.43 % Unit Clause-clause subsumption calls : 375
% 0.86/0.43 % Rewrite failures with RHS unbound : 0
% 0.86/0.43 % BW rewrite match attempts : 45
% 0.86/0.43 % BW rewrite match successes : 21
% 0.86/0.43 % Condensation attempts : 1046
% 0.86/0.43 % Condensation successes : 14
% 0.86/0.43 % Termbank termtop insertions : 155001
% 0.86/0.43 % Search garbage collected termcells : 9910
% 0.86/0.43
% 0.86/0.43 % -------------------------------------------------
% 0.86/0.43 % User time : 0.137 s
% 0.86/0.43 % System time : 0.013 s
% 0.86/0.43 % Total time : 0.150 s
% 0.86/0.43 % Maximum resident set size: 5680 pages
% 0.86/0.43
% 0.86/0.43 % -------------------------------------------------
% 0.86/0.43 % User time : 0.501 s
% 0.86/0.43 % System time : 0.048 s
% 0.86/0.43 % Total time : 0.550 s
% 0.86/0.43 % Maximum resident set size: 5120 pages
% 0.86/0.43 % E exiting
%------------------------------------------------------------------------------