%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP097^1 : 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 : n009.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 08:04:21 AM UTC 2026
% Result : Theorem 0.20s 0.36s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 230 ( 7 ~; 3 |; 1 &; 218 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
real: $tType ).
thf(decl_sort2,type,
int: $tType ).
thf(decl_sort3,type,
nat: $tType ).
thf(decl_sort4,type,
num: $tType ).
thf(decl_23,type,
archim1371465213g_real: real > int ).
thf(decl_31,type,
nat2: int > nat ).
thf(decl_33,type,
ring_1_of_int_real: int > real ).
thf(decl_37,type,
semiri2110766477t_real: nat > real ).
thf(decl_40,type,
bit0: num > num ).
thf(decl_41,type,
one: num ).
thf(decl_42,type,
numeral_numeral_int: num > int ).
thf(decl_44,type,
numeral_numeral_real: num > real ).
thf(decl_47,type,
ord_less_eq_int: int > int > $o ).
thf(decl_50,type,
ord_less_eq_real: real > real > $o ).
thf(decl_51,type,
power_power_int: int > nat > int ).
thf(decl_55,type,
log: real > real > real ).
thf(decl_56,type,
powr_real: real > real > real ).
thf(decl_58,type,
d: int ).
thf(conj_0,conjecture,
ord_less_eq_int @ d @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OrZYBoSySI/E---3.1_272955.p',conj_0) ).
thf(fact_28_of__int__le__iff,axiom,
! [X26: int,X13: int] :
( ( ord_less_eq_real @ ( ring_1_of_int_real @ X26 ) @ ( ring_1_of_int_real @ X13 ) )
<=> ( ord_less_eq_int @ X26 @ X13 ) ),
file('/export/starexec/sandbox/tmp/tmp.OrZYBoSySI/E---3.1_272955.p',fact_28_of__int__le__iff) ).
thf(fact_103__092_060open_0622_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_A_092_060le_062_A2_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062,axiom,
ord_less_eq_real @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OrZYBoSySI/E---3.1_272955.p',fact_103__092_060open_0622_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_A_092_060le_062_A2_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062) ).
thf(fact_53__092_060open_062real__of__int_Ad_A_061_A2_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062,axiom,
( ( ring_1_of_int_real @ d )
= ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OrZYBoSySI/E---3.1_272955.p',fact_53__092_060open_062real__of__int_Ad_A_061_A2_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062) ).
thf(fact_102__092_060open_0622_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_A_061_Areal__of__int_A_I2_A_094_Anat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062,axiom,
( ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) )
= ( ring_1_of_int_real @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OrZYBoSySI/E---3.1_272955.p',fact_102__092_060open_0622_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_A_061_Areal__of__int_A_I2_A_094_Anat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062) ).
thf(c_0_5,negated_conjecture,
~ ( ord_less_eq_int @ d @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_6,negated_conjecture,
~ ( ord_less_eq_int @ d @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_7,plain,
! [X959: int,X960: int] :
( ( ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ X959 ) @ ( ring_1_of_int_real @ X960 ) )
| ( ord_less_eq_int @ X959 @ X960 ) )
& ( ~ ( ord_less_eq_int @ X959 @ X960 )
| ( ord_less_eq_real @ ( ring_1_of_int_real @ X959 ) @ ( ring_1_of_int_real @ X960 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_28_of__int__le__iff])])]) ).
thf(c_0_8,plain,
ord_less_eq_real @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[fact_103__092_060open_0622_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_A_092_060le_062_A2_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062]) ).
thf(c_0_9,plain,
( ( ring_1_of_int_real @ d )
= ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ),
inference(split_conjunct,[status(thm)],[fact_53__092_060open_062real__of__int_Ad_A_061_A2_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062]) ).
thf(c_0_10,plain,
( ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) )
= ( ring_1_of_int_real @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[fact_102__092_060open_0622_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_A_061_Areal__of__int_A_I2_A_094_Anat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062]) ).
thf(c_0_11,negated_conjecture,
~ ( ord_less_eq_int @ d @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_12,plain,
! [X3: int,X4: int] :
( ( ord_less_eq_int @ X3 @ X4 )
| ~ ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ ( ring_1_of_int_real @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_13,plain,
ord_less_eq_real @ ( ring_1_of_int_real @ d ) @ ( ring_1_of_int_real @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
thf(c_0_14,negated_conjecture,
~ ( ord_less_eq_int @ d @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP097^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n009.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 19:53:15 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.20/0.26 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.OrZYBoSySI/E---3.1_272955.p
% 0.20/0.36 % Version: 3.5.1-ho
% 0.20/0.36 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.20/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.36 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.36 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.20/0.36 % Starting full_lambda_6 with 300s (1) cores
% 0.20/0.36 % Starting full_lambda_9 with 300s (1) cores
% 0.20/0.36 % new_ho_10 with pid 272968 completed with status 0
% 0.20/0.36 % Result found by new_ho_10
% 0.20/0.36 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.20/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.36 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.36 % No SInE strategy applied
% 0.20/0.36 % Search class: HGHSM-FSLM31-DHFFFFBN
% 0.20/0.36 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.36 % Starting SubtermCWHack with 151s (1) cores
% 0.20/0.36 % Starting new_ho_10 with 301s (1) cores
% 0.20/0.36 % Starting sh3 with 301s (1) cores
% 0.20/0.36 % Starting ho_unfolding_3 with 301s (1) cores
% 0.20/0.36 % Starting new_ho_10_cnf2 with 301s (1) cores
% 0.20/0.36 % new_ho_10 with pid 272976 completed with status 0
% 0.20/0.36 % Result found by new_ho_10
% 0.20/0.36 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.20/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.36 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.36 % No SInE strategy applied
% 0.20/0.36 % Search class: HGHSM-FSLM31-DHFFFFBN
% 0.20/0.36 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.36 % Starting SubtermCWHack with 151s (1) cores
% 0.20/0.36 % Starting new_ho_10 with 301s (1) cores
% 0.20/0.36 % Preprocessing time : 0.008 s
% 0.20/0.36 % Presaturation interreduction done
% 0.20/0.36
% 0.20/0.36 % Proof found!
% 0.20/0.36 % SZS status Theorem
% 0.20/0.36 % SZS output start CNFRefutation
% See solution above
% 0.20/0.37 % Parsed axioms : 396
% 0.20/0.37 % Removed by relevancy pruning/SinE : 0
% 0.20/0.37 % Initial clauses : 592
% 0.20/0.37 % Removed in clause preprocessing : 72
% 0.20/0.37 % Initial clauses in saturation : 520
% 0.20/0.37 % Processed clauses : 702
% 0.20/0.37 % ...of these trivial : 28
% 0.20/0.37 % ...subsumed : 103
% 0.20/0.37 % ...remaining for further processing : 571
% 0.20/0.37 % Other redundant clauses eliminated : 91
% 0.20/0.37 % Clauses deleted for lack of memory : 0
% 0.20/0.37 % Backward-subsumed : 0
% 0.20/0.37 % Backward-rewritten : 12
% 0.20/0.37 % Generated clauses : 272
% 0.20/0.37 % ...of the previous two non-redundant : 130
% 0.20/0.37 % ...aggressively subsumed : 0
% 0.20/0.37 % Contextual simplify-reflections : 0
% 0.20/0.37 % Paramodulations : 179
% 0.20/0.37 % Factorizations : 0
% 0.20/0.37 % NegExts : 0
% 0.20/0.37 % Equation resolutions : 95
% 0.20/0.37 % Disequality decompositions : 0
% 0.20/0.37 % Total rewrite steps : 281
% 0.20/0.37 % ...of those cached : 193
% 0.20/0.37 % Propositional unsat checks : 0
% 0.20/0.37 % Propositional check models : 0
% 0.20/0.37 % Propositional check unsatisfiable : 0
% 0.20/0.37 % Propositional clauses : 0
% 0.20/0.37 % Propositional clauses after purity: 0
% 0.20/0.37 % Propositional unsat core size : 0
% 0.20/0.37 % Propositional preprocessing time : 0.000
% 0.20/0.37 % Propositional encoding time : 0.000
% 0.20/0.37 % Propositional solver time : 0.000
% 0.20/0.37 % Success case prop preproc time : 0.000
% 0.20/0.37 % Success case prop encoding time : 0.000
% 0.20/0.37 % Success case prop solver time : 0.000
% 0.20/0.37 % Current number of processed clauses : 131
% 0.20/0.37 % Positive orientable unit clauses : 60
% 0.20/0.37 % Positive unorientable unit clauses: 0
% 0.20/0.37 % Negative unit clauses : 22
% 0.20/0.37 % Non-unit-clauses : 49
% 0.20/0.37 % Current number of unprocessed clauses: 283
% 0.20/0.37 % ...number of literals in the above : 604
% 0.20/0.37 % Current number of archived formulas : 0
% 0.20/0.37 % Current number of archived clauses : 357
% 0.20/0.37 % Clause-clause subsumption calls (NU) : 13529
% 0.20/0.37 % Rec. Clause-clause subsumption calls : 10315
% 0.20/0.37 % Non-unit clause-clause subsumptions : 77
% 0.20/0.37 % Unit Clause-clause subsumption calls : 708
% 0.20/0.37 % Rewrite failures with RHS unbound : 0
% 0.20/0.37 % BW rewrite match attempts : 21
% 0.20/0.37 % BW rewrite match successes : 8
% 0.20/0.37 % Condensation attempts : 702
% 0.20/0.37 % Condensation successes : 2
% 0.20/0.37 % Termbank termtop insertions : 40199
% 0.20/0.37 % Search garbage collected termcells : 8122
% 0.20/0.37
% 0.20/0.37 % -------------------------------------------------
% 0.20/0.37 % User time : 0.063 s
% 0.20/0.37 % System time : 0.012 s
% 0.20/0.37 % Total time : 0.075 s
% 0.20/0.37 % Maximum resident set size: 5744 pages
% 0.20/0.37
% 0.20/0.37 % -------------------------------------------------
% 0.20/0.37 % User time : 0.193 s
% 0.20/0.37 % System time : 0.037 s
% 0.20/0.37 % Total time : 0.230 s
% 0.20/0.37 % Maximum resident set size: 5120 pages
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------