%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP130^1 : 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 : n002.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 08:05:36 AM UTC 2026
% Result : Theorem 0.23s 0.36s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 5 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 106 ( 8 ~; 3 |; 1 &; 93 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
int: $tType ).
thf(decl_sort2,type,
nat: $tType ).
thf(decl_sort3,type,
real: $tType ).
thf(decl_27,type,
ring_1_of_int_real: int > real ).
thf(decl_28,type,
suc: nat > nat ).
thf(decl_30,type,
ord_less_int: int > int > $o ).
thf(decl_32,type,
ord_less_real: real > real > $o ).
thf(decl_36,type,
power_power_int: int > nat > int ).
thf(decl_38,type,
power_power_real: real > nat > real ).
thf(decl_43,type,
na: int ).
thf(decl_44,type,
p: nat ).
thf(decl_45,type,
pm: nat ).
thf(decl_48,type,
ya: int ).
thf(conj_0,conjecture,
ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ),
file('/export/starexec/sandbox/tmp/tmp.I4Fp33MMRl/E---3.1_1773006.p',conj_0) ).
thf(fact_5_of__int__power,axiom,
! [X4: int,X5: nat] :
( ( ring_1_of_int_real @ ( power_power_int @ X4 @ X5 ) )
= ( power_power_real @ ( ring_1_of_int_real @ X4 ) @ X5 ) ),
file('/export/starexec/sandbox/tmp/tmp.I4Fp33MMRl/E---3.1_1773006.p',fact_5_of__int__power) ).
thf(fact_86_p,axiom,
( p
= ( suc @ pm ) ),
file('/export/starexec/sandbox/tmp/tmp.I4Fp33MMRl/E---3.1_1773006.p',fact_86_p) ).
thf(fact_11_of__int__less__iff,axiom,
! [X6: int,X4: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ X6 ) @ ( ring_1_of_int_real @ X4 ) )
<=> ( ord_less_int @ X6 @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.I4Fp33MMRl/E---3.1_1773006.p',fact_11_of__int__less__iff) ).
thf(fact_81_yyn,axiom,
ord_less_int @ na @ ( power_power_int @ ya @ p ),
file('/export/starexec/sandbox/tmp/tmp.I4Fp33MMRl/E---3.1_1773006.p',fact_81_yyn) ).
thf(c_0_5,negated_conjecture,
~ ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_6,negated_conjecture,
~ ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
~ ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_8,plain,
! [X892: int,X893: nat] :
( ( ring_1_of_int_real @ ( power_power_int @ X892 @ X893 ) )
= ( power_power_real @ ( ring_1_of_int_real @ X892 ) @ X893 ) ),
inference(variable_rename,[status(thm)],[fact_5_of__int__power]) ).
thf(c_0_9,negated_conjecture,
~ ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X1: int,X2: nat] :
( ( ring_1_of_int_real @ ( power_power_int @ X1 @ X2 ) )
= ( power_power_real @ ( ring_1_of_int_real @ X1 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,plain,
( p
= ( suc @ pm ) ),
inference(split_conjunct,[status(thm)],[fact_86_p]) ).
thf(c_0_12,plain,
! [X908: int,X909: int] :
( ( ~ ( ord_less_real @ ( ring_1_of_int_real @ X908 ) @ ( ring_1_of_int_real @ X909 ) )
| ( ord_less_int @ X908 @ X909 ) )
& ( ~ ( ord_less_int @ X908 @ X909 )
| ( ord_less_real @ ( ring_1_of_int_real @ X908 ) @ ( ring_1_of_int_real @ X909 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_11_of__int__less__iff])])]) ).
thf(c_0_13,negated_conjecture,
~ ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( ring_1_of_int_real @ ( power_power_int @ ya @ p ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
thf(c_0_14,plain,
! [X1: int,X3: int] :
( ( ord_less_real @ ( ring_1_of_int_real @ X1 ) @ ( ring_1_of_int_real @ X3 ) )
| ~ ( ord_less_int @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,plain,
ord_less_int @ na @ ( power_power_int @ ya @ p ),
inference(split_conjunct,[status(thm)],[fact_81_yyn]) ).
thf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP130^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n002.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 20:00:37 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.25 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.I4Fp33MMRl/E---3.1_1773006.p
% 0.23/0.36 % Version: 3.5.1-ho
% 0.23/0.36 % Preprocessing class: HSLSSMSMSSSNSFA.
% 0.23/0.36 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.36 % Starting new_ho_10 with 900s (3) cores
% 0.23/0.36 % Starting sh2lt with 300s (1) cores
% 0.23/0.36 % Starting new_ho_5 with 300s (1) cores
% 0.23/0.36 % Starting full_lambda_5 with 300s (1) cores
% 0.23/0.36 % Starting sh9 with 300s (1) cores
% 0.23/0.36 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.23/0.36 % new_ho_10 with pid 1773019 completed with status 0
% 0.23/0.36 % Result found by new_ho_10
% 0.23/0.36 % Preprocessing class: HSLSSMSMSSSNSFA.
% 0.23/0.36 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.36 % Starting new_ho_10 with 900s (3) cores
% 0.23/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.36 % No SInE strategy applied
% 0.23/0.36 % Search class: HGHSM-FSLM31-MSFFFSBN
% 0.23/0.36 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 0.23/0.36 % Starting SubtermCWHack with 82s (1) cores
% 0.23/0.36 % Starting new_ho_10 with 91s (1) cores
% 0.23/0.36 % Starting sh2lt with 82s (1) cores
% 0.23/0.36 % new_ho_10 with pid 1773028 completed with status 0
% 0.23/0.36 % Result found by new_ho_10
% 0.23/0.36 % Preprocessing class: HSLSSMSMSSSNSFA.
% 0.23/0.36 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.36 % Starting new_ho_10 with 900s (3) cores
% 0.23/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.36 % No SInE strategy applied
% 0.23/0.36 % Search class: HGHSM-FSLM31-MSFFFSBN
% 0.23/0.36 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 0.23/0.36 % Starting SubtermCWHack with 82s (1) cores
% 0.23/0.36 % Starting new_ho_10 with 91s (1) cores
% 0.23/0.36 % Preprocessing time : 0.008 s
% 0.23/0.36 % Presaturation interreduction done
% 0.23/0.36
% 0.23/0.36 % Proof found!
% 0.23/0.36 % SZS status Theorem
% 0.23/0.36 % SZS output start CNFRefutation
% See solution above
% 0.23/0.36 % Parsed axioms : 349
% 0.23/0.36 % Removed by relevancy pruning/SinE : 0
% 0.23/0.36 % Initial clauses : 555
% 0.23/0.36 % Removed in clause preprocessing : 44
% 0.23/0.36 % Initial clauses in saturation : 511
% 0.23/0.36 % Processed clauses : 627
% 0.23/0.36 % ...of these trivial : 12
% 0.23/0.36 % ...subsumed : 122
% 0.23/0.36 % ...remaining for further processing : 493
% 0.23/0.36 % Other redundant clauses eliminated : 50
% 0.23/0.36 % Clauses deleted for lack of memory : 0
% 0.23/0.36 % Backward-subsumed : 0
% 0.23/0.36 % Backward-rewritten : 2
% 0.23/0.36 % Generated clauses : 93
% 0.23/0.36 % ...of the previous two non-redundant : 57
% 0.23/0.36 % ...aggressively subsumed : 0
% 0.23/0.36 % Contextual simplify-reflections : 2
% 0.23/0.36 % Paramodulations : 39
% 0.23/0.36 % Factorizations : 0
% 0.23/0.36 % NegExts : 0
% 0.23/0.36 % Equation resolutions : 52
% 0.23/0.36 % Disequality decompositions : 0
% 0.23/0.36 % Total rewrite steps : 77
% 0.23/0.36 % ...of those cached : 45
% 0.23/0.36 % Propositional unsat checks : 0
% 0.23/0.36 % Propositional check models : 0
% 0.23/0.36 % Propositional check unsatisfiable : 0
% 0.23/0.36 % Propositional clauses : 0
% 0.23/0.36 % Propositional clauses after purity: 0
% 0.23/0.36 % Propositional unsat core size : 0
% 0.23/0.36 % Propositional preprocessing time : 0.000
% 0.23/0.36 % Propositional encoding time : 0.000
% 0.23/0.36 % Propositional solver time : 0.000
% 0.23/0.36 % Success case prop preproc time : 0.000
% 0.23/0.36 % Success case prop encoding time : 0.000
% 0.23/0.36 % Success case prop solver time : 0.000
% 0.23/0.36 % Current number of processed clauses : 78
% 0.23/0.36 % Positive orientable unit clauses : 43
% 0.23/0.36 % Positive unorientable unit clauses: 0
% 0.23/0.36 % Negative unit clauses : 17
% 0.23/0.36 % Non-unit-clauses : 18
% 0.23/0.36 % Current number of unprocessed clauses: 304
% 0.23/0.36 % ...number of literals in the above : 848
% 0.23/0.36 % Current number of archived formulas : 0
% 0.23/0.36 % Current number of archived clauses : 365
% 0.23/0.36 % Clause-clause subsumption calls (NU) : 19204
% 0.23/0.36 % Rec. Clause-clause subsumption calls : 12945
% 0.23/0.36 % Non-unit clause-clause subsumptions : 90
% 0.23/0.36 % Unit Clause-clause subsumption calls : 327
% 0.23/0.36 % Rewrite failures with RHS unbound : 0
% 0.23/0.36 % BW rewrite match attempts : 10
% 0.23/0.36 % BW rewrite match successes : 2
% 0.23/0.36 % Condensation attempts : 627
% 0.23/0.36 % Condensation successes : 0
% 0.23/0.36 % Termbank termtop insertions : 49228
% 0.23/0.36 % Search garbage collected termcells : 10777
% 0.23/0.36
% 0.23/0.36 % -------------------------------------------------
% 0.23/0.36 % User time : 0.074 s
% 0.23/0.36 % System time : 0.012 s
% 0.23/0.36 % Total time : 0.086 s
% 0.23/0.36 % Maximum resident set size: 5940 pages
% 0.23/0.36
% 0.23/0.36 % -------------------------------------------------
% 0.23/0.36 % User time : 0.177 s
% 0.23/0.36 % System time : 0.029 s
% 0.23/0.36 % Total time : 0.206 s
% 0.23/0.36 % Maximum resident set size: 5376 pages
% 0.23/0.36 % E exiting
%------------------------------------------------------------------------------