TSTP Solution File: ITP095^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ITP095^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:16:17 EDT 2024
% Result : Theorem 0.80s 0.88s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 32
% Syntax : Number of formulae : 52 ( 21 unt; 25 typ; 0 def)
% Number of atoms : 44 ( 15 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 343 ( 18 ~; 11 |; 0 &; 308 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 9 con; 0-2 aty)
% Number of variables : 28 ( 0 ^ 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
set_real: $tType ).
thf(decl_sort2,type,
int: $tType ).
thf(decl_sort3,type,
poly_real: $tType ).
thf(decl_sort4,type,
real: $tType ).
thf(decl_sort5,type,
nat: $tType ).
thf(decl_24,type,
abs_abs_real: real > real ).
thf(decl_31,type,
one_one_real: real ).
thf(decl_32,type,
zero_zero_int: int ).
thf(decl_38,type,
zero_zero_real: real ).
thf(decl_41,type,
ring_1_Ints_real: set_real ).
thf(decl_45,type,
ring_1_of_int_real: int > real ).
thf(decl_46,type,
ord_less_int: int > int > $o ).
thf(decl_53,type,
ord_less_eq_real: real > real > $o ).
thf(decl_58,type,
degree_real: poly_real > nat ).
thf(decl_62,type,
poly_real2: poly_real > real > real ).
thf(decl_66,type,
coeff_real: poly_real > nat > real ).
thf(decl_67,type,
power_power_int: int > nat > int ).
thf(decl_72,type,
power_power_real: real > nat > real ).
thf(decl_77,type,
divide_divide_real: real > real > real ).
thf(decl_81,type,
member_real: real > set_real > $o ).
thf(decl_84,type,
a2: int ).
thf(decl_85,type,
b: int ).
thf(decl_86,type,
n: nat ).
thf(decl_87,type,
p: poly_real ).
thf(decl_105,type,
esk15_1: poly_real > nat ).
thf(conj_0,conjecture,
ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ ( degree_real @ p ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(fact_154_int__poly__rat__no__root__ge,axiom,
! [X6: poly_real,X2: int,X80: int] :
( ! [X30: nat] : ( member_real @ ( coeff_real @ X6 @ X30 ) @ ring_1_Ints_real )
=> ( ( ord_less_int @ zero_zero_int @ X2 )
=> ( ( ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X80 ) @ ( ring_1_of_int_real @ X2 ) ) )
!= zero_zero_real )
=> ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ X2 ) @ ( degree_real @ X6 ) ) ) @ ( abs_abs_real @ ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X80 ) @ ( ring_1_of_int_real @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_int__poly__rat__no__root__ge) ).
thf(fact_23_of__int__power,axiom,
! [X5: int,X7: nat] :
( ( ring_1_of_int_real @ ( power_power_int @ X5 @ X7 ) )
= ( power_power_real @ ( ring_1_of_int_real @ X5 ) @ X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_of__int__power) ).
thf(fact_6_n__def,axiom,
( n
= ( degree_real @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_n__def) ).
thf(fact_2_p_I1_J,axiom,
! [X1: nat] : ( member_real @ ( coeff_real @ p @ X1 ) @ ring_1_Ints_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_p_I1_J) ).
thf(fact_5_no__root,axiom,
( ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) )
!= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_no__root) ).
thf(fact_3_b,axiom,
ord_less_int @ zero_zero_int @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_b) ).
thf(c_0_7,negated_conjecture,
~ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ ( degree_real @ p ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
thf(c_0_8,plain,
! [X6: poly_real,X2: int,X80: int] :
( ! [X30: nat] : ( member_real @ ( coeff_real @ X6 @ X30 ) @ ring_1_Ints_real )
=> ( ( ord_less_int @ zero_zero_int @ X2 )
=> ( ( ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X80 ) @ ( ring_1_of_int_real @ X2 ) ) )
!= zero_zero_real )
=> ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ X2 ) @ ( degree_real @ X6 ) ) ) @ ( abs_abs_real @ ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X80 ) @ ( ring_1_of_int_real @ X2 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_154_int__poly__rat__no__root__ge]) ).
thf(c_0_9,negated_conjecture,
~ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ ( degree_real @ p ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) ),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X1106: poly_real,X1108: int,X1109: int] :
( ~ ( member_real @ ( coeff_real @ X1106 @ ( esk15_1 @ X1106 ) ) @ ring_1_Ints_real )
| ~ ( ord_less_int @ zero_zero_int @ X1108 )
| ( ( poly_real2 @ X1106 @ ( divide_divide_real @ ( ring_1_of_int_real @ X1109 ) @ ( ring_1_of_int_real @ X1108 ) ) )
= zero_zero_real )
| ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ X1108 ) @ ( degree_real @ X1106 ) ) ) @ ( abs_abs_real @ ( poly_real2 @ X1106 @ ( divide_divide_real @ ( ring_1_of_int_real @ X1109 ) @ ( ring_1_of_int_real @ X1108 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])])]) ).
thf(c_0_11,plain,
! [X920: int,X921: nat] :
( ( ring_1_of_int_real @ ( power_power_int @ X920 @ X921 ) )
= ( power_power_real @ ( ring_1_of_int_real @ X920 ) @ X921 ) ),
inference(variable_rename,[status(thm)],[fact_23_of__int__power]) ).
thf(c_0_12,negated_conjecture,
~ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ ( degree_real @ p ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
( n
= ( degree_real @ p ) ),
inference(split_conjunct,[status(thm)],[fact_6_n__def]) ).
thf(c_0_14,plain,
! [X6: poly_real,X4: int,X2: int] :
( ( ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X4 ) @ ( ring_1_of_int_real @ X2 ) ) )
= zero_zero_real )
| ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ X2 ) @ ( degree_real @ X6 ) ) ) @ ( abs_abs_real @ ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X4 ) @ ( ring_1_of_int_real @ X2 ) ) ) ) )
| ~ ( member_real @ ( coeff_real @ X6 @ ( esk15_1 @ X6 ) ) @ ring_1_Ints_real )
| ~ ( ord_less_int @ zero_zero_int @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
! [X2: int,X1: nat] :
( ( ring_1_of_int_real @ ( power_power_int @ X2 @ X1 ) )
= ( power_power_real @ ( ring_1_of_int_real @ X2 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
! [X889: nat] : ( member_real @ ( coeff_real @ p @ X889 ) @ ring_1_Ints_real ),
inference(variable_rename,[status(thm)],[fact_2_p_I1_J]) ).
thf(c_0_17,plain,
( ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) )
!= zero_zero_real ),
inference(fof_simplification,[status(thm)],[fact_5_no__root]) ).
thf(c_0_18,negated_conjecture,
~ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( ring_1_of_int_real @ b ) @ n ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_19,plain,
! [X2: int,X6: poly_real,X4: int] :
( ( ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ X4 ) ) )
= zero_zero_real )
| ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( ring_1_of_int_real @ ( power_power_int @ X4 @ ( degree_real @ X6 ) ) ) ) @ ( abs_abs_real @ ( poly_real2 @ X6 @ ( divide_divide_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ X4 ) ) ) ) )
| ~ ( member_real @ ( coeff_real @ X6 @ ( esk15_1 @ X6 ) ) @ ring_1_Ints_real )
| ~ ( ord_less_int @ zero_zero_int @ X4 ) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_20,plain,
! [X1: nat] : ( member_real @ ( coeff_real @ p @ X1 ) @ ring_1_Ints_real ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_21,plain,
( ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) )
!= zero_zero_real ),
inference(fof_nnf,[status(thm)],[c_0_17]) ).
thf(c_0_22,negated_conjecture,
~ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( ring_1_of_int_real @ ( power_power_int @ b @ n ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
thf(c_0_23,plain,
! [X2: int,X4: int] :
( ( ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ X4 ) ) )
= zero_zero_real )
| ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( ring_1_of_int_real @ ( power_power_int @ X4 @ n ) ) ) @ ( abs_abs_real @ ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ X4 ) ) ) ) )
| ~ ( ord_less_int @ zero_zero_int @ X4 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_13]),c_0_20])]) ).
thf(c_0_24,plain,
ord_less_int @ zero_zero_int @ b,
inference(split_conjunct,[status(thm)],[fact_3_b]) ).
thf(c_0_25,plain,
( ( poly_real2 @ p @ ( divide_divide_real @ ( ring_1_of_int_real @ a2 ) @ ( ring_1_of_int_real @ b ) ) )
!= zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : ITP095^1 : TPTP v8.2.0. Released v7.5.0.
% 0.14/0.15 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat May 18 16:11:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.22/0.50 Running higher-order theorem proving
% 0.22/0.50 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/benchmark/theBenchmark.p
% 0.80/0.88 # Version: 3.1.0-ho
% 0.80/0.88 # Preprocessing class: HSLSSMSMSSSNSFA.
% 0.80/0.88 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.88 # Starting new_ho_10 with 900s (3) cores
% 0.80/0.88 # Starting sh2lt with 300s (1) cores
% 0.80/0.88 # Starting new_ho_5 with 300s (1) cores
% 0.80/0.88 # Starting full_lambda_5 with 300s (1) cores
% 0.80/0.88 # Starting sh9 with 300s (1) cores
% 0.80/0.88 # Starting ehoh_best8_lambda with 300s (1) cores
% 0.80/0.88 # new_ho_10 with pid 8925 completed with status 0
% 0.80/0.88 # Result found by new_ho_10
% 0.80/0.88 # Preprocessing class: HSLSSMSMSSSNSFA.
% 0.80/0.88 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.88 # Starting new_ho_10 with 900s (3) cores
% 0.80/0.88 # No SInE strategy applied
% 0.80/0.88 # Search class: HGHSM-FSLM31-MSFFFFBN
% 0.80/0.88 # Scheduled 5 strats onto 3 cores with 900 seconds (900 total)
% 0.80/0.88 # Starting new_ho_10 with 541s (1) cores
% 0.80/0.88 # Starting almost_fo_4 with 91s (1) cores
% 0.80/0.88 # Starting pre_casc_8 with 91s (1) cores
% 0.80/0.88 # new_ho_10 with pid 8934 completed with status 0
% 0.80/0.88 # Result found by new_ho_10
% 0.80/0.88 # Preprocessing class: HSLSSMSMSSSNSFA.
% 0.80/0.88 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.80/0.88 # Starting new_ho_10 with 900s (3) cores
% 0.80/0.88 # No SInE strategy applied
% 0.80/0.88 # Search class: HGHSM-FSLM31-MSFFFFBN
% 0.80/0.88 # Scheduled 5 strats onto 3 cores with 900 seconds (900 total)
% 0.80/0.88 # Starting new_ho_10 with 541s (1) cores
% 0.80/0.88 # Preprocessing time : 0.007 s
% 0.80/0.88 # Presaturation interreduction done
% 0.80/0.88
% 0.80/0.88 # Proof found!
% 0.80/0.88 # SZS status Theorem
% 0.80/0.88 # SZS output start CNFRefutation
% See solution above
% 0.80/0.88 # Parsed axioms : 433
% 0.80/0.88 # Removed by relevancy pruning/SinE : 0
% 0.80/0.88 # Initial clauses : 631
% 0.80/0.88 # Removed in clause preprocessing : 93
% 0.80/0.88 # Initial clauses in saturation : 538
% 0.80/0.88 # Processed clauses : 3259
% 0.80/0.88 # ...of these trivial : 60
% 0.80/0.88 # ...subsumed : 1387
% 0.80/0.88 # ...remaining for further processing : 1812
% 0.80/0.88 # Other redundant clauses eliminated : 81
% 0.80/0.88 # Clauses deleted for lack of memory : 0
% 0.80/0.88 # Backward-subsumed : 34
% 0.80/0.88 # Backward-rewritten : 35
% 0.80/0.88 # Generated clauses : 14761
% 0.80/0.88 # ...of the previous two non-redundant : 11734
% 0.80/0.88 # ...aggressively subsumed : 0
% 0.80/0.88 # Contextual simplify-reflections : 12
% 0.80/0.88 # Paramodulations : 14656
% 0.80/0.88 # Factorizations : 4
% 0.80/0.88 # NegExts : 2
% 0.80/0.88 # Equation resolutions : 99
% 0.80/0.88 # Disequality decompositions : 0
% 0.80/0.88 # Total rewrite steps : 11147
% 0.80/0.88 # ...of those cached : 10710
% 0.80/0.88 # Propositional unsat checks : 0
% 0.80/0.88 # Propositional check models : 0
% 0.80/0.88 # Propositional check unsatisfiable : 0
% 0.80/0.88 # Propositional clauses : 0
% 0.80/0.88 # Propositional clauses after purity: 0
% 0.80/0.88 # Propositional unsat core size : 0
% 0.80/0.88 # Propositional preprocessing time : 0.000
% 0.80/0.88 # Propositional encoding time : 0.000
% 0.80/0.88 # Propositional solver time : 0.000
% 0.80/0.88 # Success case prop preproc time : 0.000
% 0.80/0.88 # Success case prop encoding time : 0.000
% 0.80/0.88 # Success case prop solver time : 0.000
% 0.80/0.88 # Current number of processed clauses : 1257
% 0.80/0.88 # Positive orientable unit clauses : 160
% 0.80/0.88 # Positive unorientable unit clauses: 0
% 0.80/0.88 # Negative unit clauses : 53
% 0.80/0.88 # Non-unit-clauses : 1044
% 0.80/0.88 # Current number of unprocessed clauses: 9337
% 0.80/0.88 # ...number of literals in the above : 32218
% 0.80/0.88 # Current number of archived formulas : 0
% 0.80/0.88 # Current number of archived clauses : 501
% 0.80/0.88 # Clause-clause subsumption calls (NU) : 144678
% 0.80/0.88 # Rec. Clause-clause subsumption calls : 100539
% 0.80/0.88 # Non-unit clause-clause subsumptions : 602
% 0.80/0.88 # Unit Clause-clause subsumption calls : 8089
% 0.80/0.88 # Rewrite failures with RHS unbound : 0
% 0.80/0.88 # BW rewrite match attempts : 23
% 0.80/0.88 # BW rewrite match successes : 18
% 0.80/0.88 # Condensation attempts : 3263
% 0.80/0.88 # Condensation successes : 23
% 0.80/0.88 # Termbank termtop insertions : 270170
% 0.80/0.88 # Search garbage collected termcells : 9681
% 0.80/0.88
% 0.80/0.88 # -------------------------------------------------
% 0.80/0.88 # User time : 0.339 s
% 0.80/0.88 # System time : 0.017 s
% 0.80/0.88 # Total time : 0.356 s
% 0.80/0.88 # Maximum resident set size: 4184 pages
% 0.80/0.88
% 0.80/0.88 # -------------------------------------------------
% 0.80/0.88 # User time : 0.972 s
% 0.80/0.88 # System time : 0.050 s
% 0.80/0.88 # Total time : 1.022 s
% 0.80/0.88 # Maximum resident set size: 2324 pages
% 0.80/0.88 % E---3.1 exiting
% 0.80/0.89 % E exiting
%------------------------------------------------------------------------------