%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP195^1 : 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 : 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 08:04:39 AM UTC 2026
% Result : Theorem 0.41s 0.38s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 18 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 220 ( 31 ~; 20 |; 8 &; 150 @)
% ( 1 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
poly_real: $tType ).
thf(decl_sort2,type,
real: $tType ).
thf(decl_33,type,
zero_zero_real: real ).
thf(decl_40,type,
ord_less_real: real > real > $o ).
thf(decl_59,type,
pderiv_real: poly_real > poly_real ).
thf(decl_66,type,
poly_real2: poly_real > real > real ).
thf(decl_85,type,
sturm_469514713_r_pos: poly_real > real > $o ).
thf(decl_88,type,
p: poly_real ).
thf(decl_89,type,
x: real ).
thf(conj_0,conjecture,
( ( sturm_469514713_r_pos @ p @ x )
<~> ~ ( ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
& ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QeaqnkrXhG/E---3.1_3869732.p',conj_0) ).
thf(fact_0_False,axiom,
( ( poly_real2 @ p @ x )
!= zero_zero_real ),
file('/export/starexec/sandbox/tmp/tmp.QeaqnkrXhG/E---3.1_3869732.p',fact_0_False) ).
thf(fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062,axiom,
( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
=> ( sturm_469514713_r_pos @ p @ x ) ),
file('/export/starexec/sandbox/tmp/tmp.QeaqnkrXhG/E---3.1_3869732.p',fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062) ).
thf(fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062,axiom,
( ( sturm_469514713_r_pos @ p @ x )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QeaqnkrXhG/E---3.1_3869732.p',fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062) ).
thf(c_0_4,negated_conjecture,
~ ( ( sturm_469514713_r_pos @ p @ x )
<~> ~ ( ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
& ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_5,negated_conjecture,
~ ~ ( ( sturm_469514713_r_pos @ p @ x )
<=> ~ ( ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
=> ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x ) )
& ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
=> ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_6,plain,
( ( poly_real2 @ p @ x )
!= zero_zero_real ),
inference(fof_simplification,[status(thm)],[fact_0_False]) ).
thf(c_0_7,negated_conjecture,
( ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
| ( ( poly_real2 @ p @ x )
= zero_zero_real )
| ~ ( sturm_469514713_r_pos @ p @ x ) )
& ( ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
| ( ( poly_real2 @ p @ x )
= zero_zero_real )
| ~ ( sturm_469514713_r_pos @ p @ x ) )
& ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
| ~ ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x )
| ~ ( sturm_469514713_r_pos @ p @ x ) )
& ( ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
| ~ ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x )
| ~ ( sturm_469514713_r_pos @ p @ x ) )
& ( ( ( poly_real2 @ p @ x )
!= zero_zero_real )
| ( sturm_469514713_r_pos @ ( pderiv_real @ p ) @ x )
| ( sturm_469514713_r_pos @ p @ x ) )
& ( ( ( poly_real2 @ p @ x )
= zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
| ( sturm_469514713_r_pos @ p @ x ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
thf(c_0_8,plain,
( ( poly_real2 @ p @ x )
!= zero_zero_real ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
( ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
| ( sturm_469514713_r_pos @ p @ x ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2__092_060open_0620_A_060_Apoly_Ap_Ax_A_092_060Longrightarrow_062_Asign__r__pos_Ap_Ax_092_060close_062])]) ).
thf(c_0_10,negated_conjecture,
( ( ( poly_real2 @ p @ x )
= zero_zero_real )
| ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
| ~ ( sturm_469514713_r_pos @ p @ x ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
( ( poly_real2 @ p @ x )
!= zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
( ( sturm_469514713_r_pos @ p @ x )
| ~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
( ~ ( sturm_469514713_r_pos @ p @ x )
| ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1__092_060open_062sign__r__pos_Ap_Ax_A_092_060Longrightarrow_062_A0_A_060_Apoly_Ap_Ax_092_060close_062])]) ).
thf(c_0_14,negated_conjecture,
( ( ( poly_real2 @ p @ x )
= zero_zero_real )
| ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
| ( sturm_469514713_r_pos @ p @ x ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_15,negated_conjecture,
~ ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
thf(c_0_16,plain,
( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ p @ x ) )
| ~ ( sturm_469514713_r_pos @ p @ x ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,negated_conjecture,
sturm_469514713_r_pos @ p @ x,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_14,c_0_11]),c_0_15]) ).
thf(c_0_18,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP195^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n007.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 20:08:26 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.24 Running higher-order theorem proving
% 0.21/0.28 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.QeaqnkrXhG/E---3.1_3869732.p
% 0.41/0.38 % Version: 3.5.1-ho
% 0.41/0.38 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.41/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.41/0.38 % Starting new_ho_10 with 1500s (5) cores
% 0.41/0.38 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.41/0.38 % Starting full_lambda_6 with 300s (1) cores
% 0.41/0.38 % Starting full_lambda_9 with 300s (1) cores
% 0.41/0.38 % new_ho_10 with pid 3869773 completed with status 0
% 0.41/0.38 % Result found by new_ho_10
% 0.41/0.38 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.41/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.41/0.38 % Starting new_ho_10 with 1500s (5) cores
% 0.41/0.38 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.41/0.38 % No SInE strategy applied
% 0.41/0.38 % Search class: HGHSM-FSLM32-SHFFFSBC
% 0.41/0.38 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.41/0.38 % Starting SubtermCWHack with 151s (1) cores
% 0.41/0.38 % Starting new_ho_10 with 901s (1) cores
% 0.41/0.38 % Starting sh5l with 151s (1) cores
% 0.41/0.38 % Starting new_bool_1 with 151s (1) cores
% 0.41/0.38 % Starting new_bool_2 with 146s (1) cores
% 0.41/0.38 % new_ho_10 with pid 3869799 completed with status 0
% 0.41/0.38 % Result found by new_ho_10
% 0.41/0.38 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.41/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.41/0.38 % Starting new_ho_10 with 1500s (5) cores
% 0.41/0.38 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.41/0.38 % No SInE strategy applied
% 0.41/0.38 % Search class: HGHSM-FSLM32-SHFFFSBC
% 0.41/0.38 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.41/0.38 % Starting SubtermCWHack with 151s (1) cores
% 0.41/0.38 % Starting new_ho_10 with 901s (1) cores
% 0.41/0.38 % Preprocessing time : 0.013 s
% 0.41/0.38 % Presaturation interreduction done
% 0.41/0.38
% 0.41/0.38 % Proof found!
% 0.41/0.38 % SZS status Theorem
% 0.41/0.38 % SZS output start CNFRefutation
% See solution above
% 0.41/0.38 % Parsed axioms : 424
% 0.41/0.38 % Removed by relevancy pruning/SinE : 0
% 0.41/0.38 % Initial clauses : 859
% 0.41/0.38 % Removed in clause preprocessing : 137
% 0.41/0.38 % Initial clauses in saturation : 722
% 0.41/0.38 % Processed clauses : 16
% 0.41/0.38 % ...of these trivial : 0
% 0.41/0.38 % ...subsumed : 3
% 0.41/0.38 % ...remaining for further processing : 13
% 0.41/0.38 % Other redundant clauses eliminated : 0
% 0.41/0.38 % Clauses deleted for lack of memory : 0
% 0.41/0.38 % Backward-subsumed : 3
% 0.41/0.38 % Backward-rewritten : 1
% 0.41/0.38 % Generated clauses : 0
% 0.41/0.38 % ...of the previous two non-redundant : 0
% 0.41/0.38 % ...aggressively subsumed : 0
% 0.41/0.38 % Contextual simplify-reflections : 2
% 0.41/0.38 % Paramodulations : 0
% 0.41/0.38 % Factorizations : 0
% 0.41/0.38 % NegExts : 0
% 0.41/0.38 % Equation resolutions : 0
% 0.41/0.38 % Disequality decompositions : 0
% 0.41/0.38 % Total rewrite steps : 1
% 0.41/0.38 % ...of those cached : 0
% 0.41/0.38 % Propositional unsat checks : 0
% 0.41/0.38 % Propositional check models : 0
% 0.41/0.38 % Propositional check unsatisfiable : 0
% 0.41/0.38 % Propositional clauses : 0
% 0.41/0.38 % Propositional clauses after purity: 0
% 0.41/0.38 % Propositional unsat core size : 0
% 0.41/0.38 % Propositional preprocessing time : 0.000
% 0.41/0.38 % Propositional encoding time : 0.000
% 0.41/0.38 % Propositional solver time : 0.000
% 0.41/0.38 % Success case prop preproc time : 0.000
% 0.41/0.38 % Success case prop encoding time : 0.000
% 0.41/0.38 % Success case prop solver time : 0.000
% 0.41/0.38 % Current number of processed clauses : 9
% 0.41/0.38 % Positive orientable unit clauses : 5
% 0.41/0.38 % Positive unorientable unit clauses: 0
% 0.41/0.38 % Negative unit clauses : 4
% 0.41/0.38 % Non-unit-clauses : 0
% 0.41/0.38 % Current number of unprocessed clauses: 706
% 0.41/0.38 % ...number of literals in the above : 2258
% 0.41/0.38 % Current number of archived formulas : 0
% 0.41/0.38 % Current number of archived clauses : 4
% 0.41/0.38 % Clause-clause subsumption calls (NU) : 3
% 0.41/0.38 % Rec. Clause-clause subsumption calls : 3
% 0.41/0.38 % Non-unit clause-clause subsumptions : 2
% 0.41/0.38 % Unit Clause-clause subsumption calls : 6
% 0.41/0.38 % Rewrite failures with RHS unbound : 0
% 0.41/0.38 % BW rewrite match attempts : 1
% 0.41/0.38 % BW rewrite match successes : 1
% 0.41/0.38 % Condensation attempts : 16
% 0.41/0.38 % Condensation successes : 0
% 0.41/0.38 % Termbank termtop insertions : 53161
% 0.41/0.38 % Search garbage collected termcells : 15554
% 0.41/0.38
% 0.41/0.38 % -------------------------------------------------
% 0.41/0.38 % User time : 0.050 s
% 0.41/0.38 % System time : 0.016 s
% 0.41/0.38 % Total time : 0.066 s
% 0.41/0.38 % Maximum resident set size: 7076 pages
% 0.41/0.38
% 0.41/0.38 % -------------------------------------------------
% 0.41/0.38 % User time : 0.100 s
% 0.41/0.38 % System time : 0.041 s
% 0.41/0.38 % Total time : 0.142 s
% 0.41/0.38 % Maximum resident set size: 5376 pages
% 0.41/0.38 % E exiting
%------------------------------------------------------------------------------