%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP194^1 : 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 : n012.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 08:04:38 AM UTC 2026
% Result : Theorem 0.08s 0.20s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 17 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 171 ( 25 ~; 12 |; 1 &; 128 @)
% ( 0 <=>; 5 =>; 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 : 12 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 51 ( 6 ^; 45 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
poly_real: $tType ).
thf(decl_sort2,type,
real: $tType ).
thf(decl_32,type,
zero_zero_real: real ).
thf(decl_38,type,
ord_less_real: real > real > $o ).
thf(decl_42,type,
ord_less_eq_real: real > real > $o ).
thf(decl_44,type,
ord_min_real: real > real > real ).
thf(decl_58,type,
poly_real2: poly_real > real > real ).
thf(decl_74,type,
lb1: real ).
thf(decl_75,type,
lb2: real ).
thf(decl_76,type,
lb: real ).
thf(decl_77,type,
p: poly_real ).
thf(decl_79,type,
esk1_0: real ).
thf(fact_288_less__irrefl,axiom,
! [X397: real] :
~ ( ord_less_real @ X397 @ X397 ),
file('/export/starexec/sandbox2/tmp/tmp.anbYIveL7w/E---3.1_623178.p',fact_288_less__irrefl) ).
thf(fact_39_min_Ostrict__coboundedI2,axiom,
! [X10: real,X40: real,X9: real] :
( ( ord_less_real @ X10 @ X40 )
=> ( ord_less_real @ ( ord_min_real @ X9 @ X10 ) @ X40 ) ),
file('/export/starexec/sandbox2/tmp/tmp.anbYIveL7w/E---3.1_623178.p',fact_39_min_Ostrict__coboundedI2) ).
thf(fact_54_min_Ocommute,axiom,
( ord_min_real
= ( ^ [X47: real,X48: real] : ( ord_min_real @ X48 @ X47 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.anbYIveL7w/E---3.1_623178.p',fact_54_min_Ocommute) ).
thf(conj_0,conjecture,
! [X12: real] :
( ( ( poly_real2 @ p @ X12 )
!= zero_zero_real )
| ( ord_less_real @ lb @ X12 ) ),
file('/export/starexec/sandbox2/tmp/tmp.anbYIveL7w/E---3.1_623178.p',conj_0) ).
thf(fact_328_leI,axiom,
! [X462: real,X31: real] :
( ~ ( ord_less_real @ X462 @ X31 )
=> ( ord_less_eq_real @ X31 @ X462 ) ),
file('/export/starexec/sandbox2/tmp/tmp.anbYIveL7w/E---3.1_623178.p',fact_328_leI) ).
thf(fact_1_lb__def,axiom,
( lb
= ( ord_min_real @ lb1 @ lb2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.anbYIveL7w/E---3.1_623178.p',fact_1_lb__def) ).
thf(fact_98_min_OorderE,axiom,
! [X9: real,X10: real] :
( ( ord_less_eq_real @ X9 @ X10 )
=> ( X9
= ( ord_min_real @ X9 @ X10 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.anbYIveL7w/E---3.1_623178.p',fact_98_min_OorderE) ).
thf(fact_0_lb1,axiom,
! [X1: real] :
( ( ( poly_real2 @ p @ X1 )
= zero_zero_real )
=> ( ord_less_real @ lb1 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.anbYIveL7w/E---3.1_623178.p',fact_0_lb1) ).
thf(c_0_8,plain,
! [X397: real] :
~ ( ord_less_real @ X397 @ X397 ),
inference(fof_simplification,[status(thm)],[fact_288_less__irrefl]) ).
thf(c_0_9,plain,
! [X1430: real] :
~ ( ord_less_real @ X1430 @ X1430 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_8])]) ).
thf(c_0_10,plain,
! [X1288: real,X1289: real,X1290: real] :
( ~ ( ord_less_real @ X1288 @ X1289 )
| ( ord_less_real @ ( ord_min_real @ X1290 @ X1288 ) @ X1289 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_39_min_Ostrict__coboundedI2])])]) ).
thf(c_0_11,plain,
! [X1: real] :
~ ( ord_less_real @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,plain,
! [X1: real,X7: real,X2: real] :
( ( ord_less_real @ ( ord_min_real @ X7 @ X1 ) @ X2 )
| ~ ( ord_less_real @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,plain,
( ord_min_real
= ( ^ [Z0: real,Z1: real] : ( ord_min_real @ Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[fact_54_min_Ocommute]) ).
thf(c_0_14,plain,
! [X2: real,X1: real] :
~ ( ord_less_real @ X1 @ ( ord_min_real @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_15,plain,
( ord_min_real
= ( ^ [Z0: real,Z1: real] : ( ord_min_real @ Z1 @ Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
~ ! [X12: real] :
( ( ( poly_real2 @ p @ X12 )
!= zero_zero_real )
| ( ord_less_real @ lb @ X12 ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_17,plain,
! [X7: real,X2: real,X1: real] :
~ ( ord_less_real @ X1 @ ( ord_min_real @ X2 @ ( ord_min_real @ X7 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
thf(c_0_18,plain,
! [X2: real,X1: real] :
( ( ord_min_real @ X1 @ X2 )
= ( ord_min_real @ X2 @ X1 ) ),
inference(arg_cong,[status(thm)],[c_0_15]) ).
thf(c_0_19,negated_conjecture,
~ ! [X12: real] :
( ( ( poly_real2 @ p @ X12 )
!= zero_zero_real )
| ( ord_less_real @ lb @ X12 ) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
thf(c_0_20,plain,
! [X462: real,X31: real] :
( ~ ( ord_less_real @ X462 @ X31 )
=> ( ord_less_eq_real @ X31 @ X462 ) ),
inference(fof_simplification,[status(thm)],[fact_328_leI]) ).
thf(c_0_21,plain,
! [X1: real,X2: real,X7: real] :
~ ( ord_less_real @ X1 @ ( ord_min_real @ X2 @ ( ord_min_real @ X1 @ X7 ) ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_22,plain,
( lb
= ( ord_min_real @ lb1 @ lb2 ) ),
inference(split_conjunct,[status(thm)],[fact_1_lb__def]) ).
thf(c_0_23,plain,
! [X1554: real,X1555: real] :
( ~ ( ord_less_eq_real @ X1554 @ X1555 )
| ( X1554
= ( ord_min_real @ X1554 @ X1555 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_98_min_OorderE])])]) ).
thf(c_0_24,plain,
! [X1532: real] :
( ( ( poly_real2 @ p @ X1532 )
!= zero_zero_real )
| ( ord_less_real @ lb1 @ X1532 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_lb1])])]) ).
thf(c_0_25,negated_conjecture,
( ( ( poly_real2 @ p @ esk1_0 )
= zero_zero_real )
& ~ ( ord_less_real @ lb @ esk1_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
thf(c_0_26,plain,
! [X1477: real,X1478: real] :
( ( ord_less_real @ X1477 @ X1478 )
| ( ord_less_eq_real @ X1478 @ X1477 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])]) ).
thf(c_0_27,plain,
! [X1: real] :
~ ( ord_less_real @ lb1 @ ( ord_min_real @ X1 @ lb ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_28,plain,
! [X1: real,X2: real] :
( ( X1
= ( ord_min_real @ X1 @ X2 ) )
| ~ ( ord_less_eq_real @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_29,plain,
! [X1: real] :
( ( ord_less_real @ lb1 @ X1 )
| ( ( poly_real2 @ p @ X1 )
!= zero_zero_real ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_30,negated_conjecture,
( ( poly_real2 @ p @ esk1_0 )
= zero_zero_real ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_31,negated_conjecture,
~ ( ord_less_real @ lb @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_32,plain,
! [X2: real,X1: real] :
( ( ord_less_real @ X1 @ X2 )
| ( ord_less_eq_real @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_33,plain,
! [X1: real] :
( ~ ( ord_less_real @ lb1 @ X1 )
| ~ ( ord_less_eq_real @ X1 @ lb ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_34,negated_conjecture,
ord_less_real @ lb1 @ esk1_0,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_35,negated_conjecture,
ord_less_eq_real @ esk1_0 @ lb,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP194^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 20:09:48 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.14 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.anbYIveL7w/E---3.1_623178.p
% 0.08/0.20 % Version: 3.5.1-ho
% 0.08/0.20 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.08/0.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.20 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.08/0.20 % Starting full_lambda_6 with 300s (1) cores
% 0.08/0.20 % Starting full_lambda_9 with 300s (1) cores
% 0.08/0.20 % full_lambda_9 with pid 623194 completed with status 0
% 0.08/0.20 % Result found by full_lambda_9
% 0.08/0.20 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.08/0.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.20 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.08/0.20 % Starting full_lambda_6 with 300s (1) cores
% 0.08/0.20 % Starting full_lambda_9 with 300s (1) cores
% 0.08/0.20 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.08/0.20 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.08/0.20 % Search class: HGHSM-FSLM33-DHFFFSBN
% 0.08/0.20 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.20 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.20 % SubtermCWHack with pid 623196 completed with status 0
% 0.08/0.20 % Result found by SubtermCWHack
% 0.08/0.20 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.08/0.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.20 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.08/0.20 % Starting full_lambda_6 with 300s (1) cores
% 0.08/0.20 % Starting full_lambda_9 with 300s (1) cores
% 0.08/0.20 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.08/0.20 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.08/0.20 % Search class: HGHSM-FSLM33-DHFFFSBN
% 0.08/0.20 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.20 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.20 % Preprocessing time : 0.004 s
% 0.08/0.20
% 0.08/0.20 % Proof found!
% 0.08/0.20 % SZS status Theorem
% 0.08/0.20 % SZS output start CNFRefutation
% See solution above
% 0.08/0.20 % Parsed axioms : 415
% 0.08/0.20 % Removed by relevancy pruning/SinE : 124
% 0.08/0.20 % Initial clauses : 572
% 0.08/0.20 % Removed in clause preprocessing : 19
% 0.08/0.20 % Initial clauses in saturation : 553
% 0.08/0.20 % Processed clauses : 415
% 0.08/0.20 % ...of these trivial : 22
% 0.08/0.20 % ...subsumed : 184
% 0.08/0.20 % ...remaining for further processing : 209
% 0.08/0.20 % Other redundant clauses eliminated : 41
% 0.08/0.20 % Clauses deleted for lack of memory : 0
% 0.08/0.20 % Backward-subsumed : 2
% 0.08/0.20 % Backward-rewritten : 2
% 0.08/0.20 % Generated clauses : 623
% 0.08/0.20 % ...of the previous two non-redundant : 425
% 0.08/0.20 % ...aggressively subsumed : 0
% 0.08/0.20 % Contextual simplify-reflections : 0
% 0.08/0.20 % Paramodulations : 555
% 0.08/0.20 % Factorizations : 8
% 0.08/0.20 % NegExts : 0
% 0.08/0.20 % Equation resolutions : 42
% 0.08/0.20 % Disequality decompositions : 0
% 0.08/0.20 % Total rewrite steps : 185
% 0.08/0.20 % ...of those cached : 129
% 0.08/0.20 % Propositional unsat checks : 0
% 0.08/0.20 % Propositional check models : 0
% 0.08/0.20 % Propositional check unsatisfiable : 0
% 0.08/0.20 % Propositional clauses : 0
% 0.08/0.20 % Propositional clauses after purity: 0
% 0.08/0.20 % Propositional unsat core size : 0
% 0.08/0.20 % Propositional preprocessing time : 0.000
% 0.08/0.20 % Propositional encoding time : 0.000
% 0.08/0.20 % Propositional solver time : 0.000
% 0.08/0.20 % Success case prop preproc time : 0.000
% 0.08/0.20 % Success case prop encoding time : 0.000
% 0.08/0.20 % Success case prop solver time : 0.000
% 0.08/0.20 % Current number of processed clauses : 167
% 0.08/0.20 % Positive orientable unit clauses : 52
% 0.08/0.20 % Positive unorientable unit clauses: 2
% 0.08/0.20 % Negative unit clauses : 34
% 0.08/0.20 % Non-unit-clauses : 79
% 0.08/0.20 % Current number of unprocessed clauses: 557
% 0.08/0.20 % ...number of literals in the above : 1780
% 0.08/0.20 % Current number of archived formulas : 0
% 0.08/0.20 % Current number of archived clauses : 4
% 0.08/0.20 % Clause-clause subsumption calls (NU) : 968
% 0.08/0.20 % Rec. Clause-clause subsumption calls : 948
% 0.08/0.20 % Non-unit clause-clause subsumptions : 97
% 0.08/0.20 % Unit Clause-clause subsumption calls : 578
% 0.08/0.20 % Rewrite failures with RHS unbound : 0
% 0.08/0.20 % BW rewrite match attempts : 40
% 0.08/0.20 % BW rewrite match successes : 16
% 0.08/0.20 % Condensation attempts : 0
% 0.08/0.20 % Condensation successes : 0
% 0.08/0.20 % Termbank termtop insertions : 46119
% 0.08/0.20 % Search garbage collected termcells : 12318
% 0.08/0.20
% 0.08/0.20 % -------------------------------------------------
% 0.08/0.20 % User time : 0.027 s
% 0.08/0.20 % System time : 0.007 s
% 0.08/0.20 % Total time : 0.034 s
% 0.08/0.20 % Maximum resident set size: 6248 pages
% 0.08/0.20
% 0.08/0.20 % -------------------------------------------------
% 0.08/0.20 % User time : 0.032 s
% 0.08/0.20 % System time : 0.010 s
% 0.08/0.20 % Total time : 0.043 s
% 0.08/0.20 % Maximum resident set size: 5632 pages
% 0.08/0.20 % E exiting
%------------------------------------------------------------------------------