%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP032^1 : 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 : n003.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 08:04:09 AM UTC 2026
% Result : Theorem 0.50s 0.47s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 2 equ; 0 cnn)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 284 ( 26 ~; 25 |; 10 &; 220 @)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
binary1439146945Tree_a: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_sort3,type,
set_a: $tType ).
thf(decl_sort4,type,
int: $tType ).
thf(decl_23,type,
binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(decl_30,type,
binary945792244etOf_a: binary1439146945Tree_a > set_a ).
thf(decl_31,type,
binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
thf(decl_46,type,
ord_less_int: int > int > $o ).
thf(decl_55,type,
member_a: a > set_a > $o ).
thf(decl_56,type,
e: a ).
thf(decl_57,type,
h: a > int ).
thf(decl_58,type,
t1: binary1439146945Tree_a ).
thf(decl_59,type,
t2: binary1439146945Tree_a ).
thf(decl_60,type,
w: a ).
thf(decl_61,type,
x: a ).
thf(decl_137,type,
esk68_4: ( a > int ) > binary1439146945Tree_a > a > binary1439146945Tree_a > a ).
thf(decl_138,type,
esk69_4: ( a > int ) > binary1439146945Tree_a > a > binary1439146945Tree_a > a ).
thf(conj_0,conjecture,
ord_less_int @ ( h @ w ) @ ( h @ x ),
file('/export/starexec/sandbox/tmp/tmp.HxfTqrLz7r/E---3.1_2968632.p',conj_0) ).
thf(fact_19_sortedTree_Osimps_I2_J,axiom,
! [X16: a > int,X17: binary1439146945Tree_a,X18: a,X19: binary1439146945Tree_a] :
( ( binary1721989714Tree_a @ X16 @ ( binary717961607le_T_a @ X17 @ X18 @ X19 ) )
<=> ( ( binary1721989714Tree_a @ X16 @ X17 )
& ! [X20: a] :
( ( member_a @ X20 @ ( binary945792244etOf_a @ X17 ) )
=> ( ord_less_int @ ( X16 @ X20 ) @ ( X16 @ X18 ) ) )
& ! [X20: a] :
( ( member_a @ X20 @ ( binary945792244etOf_a @ X19 ) )
=> ( ord_less_int @ ( X16 @ X18 ) @ ( X16 @ X20 ) ) )
& ( binary1721989714Tree_a @ X16 @ X19 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HxfTqrLz7r/E---3.1_2968632.p',fact_19_sortedTree_Osimps_I2_J) ).
thf(fact_7_xeqe,axiom,
( ( h @ x )
= ( h @ e ) ),
file('/export/starexec/sandbox/tmp/tmp.HxfTqrLz7r/E---3.1_2968632.p',fact_7_xeqe) ).
thf(fact_1_s,axiom,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
file('/export/starexec/sandbox/tmp/tmp.HxfTqrLz7r/E---3.1_2968632.p',fact_1_s) ).
thf(fact_0_whSet,axiom,
member_a @ w @ ( binary945792244etOf_a @ t1 ),
file('/export/starexec/sandbox/tmp/tmp.HxfTqrLz7r/E---3.1_2968632.p',fact_0_whSet) ).
thf(c_0_5,negated_conjecture,
~ ( ord_less_int @ ( h @ w ) @ ( h @ x ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_6,negated_conjecture,
~ ( ord_less_int @ ( h @ w ) @ ( h @ x ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
~ ( ord_less_int @ ( h @ w ) @ ( h @ x ) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_8,plain,
! [X1642: a > int,X1643: binary1439146945Tree_a,X1644: a,X1645: binary1439146945Tree_a,X1646: a,X1647: a,X1648: a > int,X1649: binary1439146945Tree_a,X1650: a,X1651: binary1439146945Tree_a] :
( ( ( binary1721989714Tree_a @ X1642 @ X1643 )
| ~ ( binary1721989714Tree_a @ X1642 @ ( binary717961607le_T_a @ X1643 @ X1644 @ X1645 ) ) )
& ( ~ ( member_a @ X1646 @ ( binary945792244etOf_a @ X1643 ) )
| ( ord_less_int @ ( X1642 @ X1646 ) @ ( X1642 @ X1644 ) )
| ~ ( binary1721989714Tree_a @ X1642 @ ( binary717961607le_T_a @ X1643 @ X1644 @ X1645 ) ) )
& ( ~ ( member_a @ X1647 @ ( binary945792244etOf_a @ X1645 ) )
| ( ord_less_int @ ( X1642 @ X1644 ) @ ( X1642 @ X1647 ) )
| ~ ( binary1721989714Tree_a @ X1642 @ ( binary717961607le_T_a @ X1643 @ X1644 @ X1645 ) ) )
& ( ( binary1721989714Tree_a @ X1642 @ X1645 )
| ~ ( binary1721989714Tree_a @ X1642 @ ( binary717961607le_T_a @ X1643 @ X1644 @ X1645 ) ) )
& ( ( member_a @ ( esk69_4 @ X1648 @ X1649 @ X1650 @ X1651 ) @ ( binary945792244etOf_a @ X1651 ) )
| ( member_a @ ( esk68_4 @ X1648 @ X1649 @ X1650 @ X1651 ) @ ( binary945792244etOf_a @ X1649 ) )
| ~ ( binary1721989714Tree_a @ X1648 @ X1649 )
| ~ ( binary1721989714Tree_a @ X1648 @ X1651 )
| ( binary1721989714Tree_a @ X1648 @ ( binary717961607le_T_a @ X1649 @ X1650 @ X1651 ) ) )
& ( ~ ( ord_less_int @ ( X1648 @ X1650 ) @ ( X1648 @ ( esk69_4 @ X1648 @ X1649 @ X1650 @ X1651 ) ) )
| ( member_a @ ( esk68_4 @ X1648 @ X1649 @ X1650 @ X1651 ) @ ( binary945792244etOf_a @ X1649 ) )
| ~ ( binary1721989714Tree_a @ X1648 @ X1649 )
| ~ ( binary1721989714Tree_a @ X1648 @ X1651 )
| ( binary1721989714Tree_a @ X1648 @ ( binary717961607le_T_a @ X1649 @ X1650 @ X1651 ) ) )
& ( ( member_a @ ( esk69_4 @ X1648 @ X1649 @ X1650 @ X1651 ) @ ( binary945792244etOf_a @ X1651 ) )
| ~ ( ord_less_int @ ( X1648 @ ( esk68_4 @ X1648 @ X1649 @ X1650 @ X1651 ) ) @ ( X1648 @ X1650 ) )
| ~ ( binary1721989714Tree_a @ X1648 @ X1649 )
| ~ ( binary1721989714Tree_a @ X1648 @ X1651 )
| ( binary1721989714Tree_a @ X1648 @ ( binary717961607le_T_a @ X1649 @ X1650 @ X1651 ) ) )
& ( ~ ( ord_less_int @ ( X1648 @ X1650 ) @ ( X1648 @ ( esk69_4 @ X1648 @ X1649 @ X1650 @ X1651 ) ) )
| ~ ( ord_less_int @ ( X1648 @ ( esk68_4 @ X1648 @ X1649 @ X1650 @ X1651 ) ) @ ( X1648 @ X1650 ) )
| ~ ( binary1721989714Tree_a @ X1648 @ X1649 )
| ~ ( binary1721989714Tree_a @ X1648 @ X1651 )
| ( binary1721989714Tree_a @ X1648 @ ( binary717961607le_T_a @ X1649 @ X1650 @ X1651 ) ) ) ),
inference(distribute,[status(thm)],[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)],[fact_19_sortedTree_Osimps_I2_J])])])])])])]) ).
thf(c_0_9,negated_conjecture,
~ ( ord_less_int @ ( h @ w ) @ ( h @ x ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
( ( h @ x )
= ( h @ e ) ),
inference(split_conjunct,[status(thm)],[fact_7_xeqe]) ).
thf(c_0_11,plain,
! [X1: binary1439146945Tree_a,X2: a,X16: a > int,X5: a,X3: binary1439146945Tree_a] :
( ( ord_less_int @ ( X16 @ X2 ) @ ( X16 @ X5 ) )
| ~ ( member_a @ X2 @ ( binary945792244etOf_a @ X1 ) )
| ~ ( binary1721989714Tree_a @ X16 @ ( binary717961607le_T_a @ X1 @ X5 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
inference(split_conjunct,[status(thm)],[fact_1_s]) ).
thf(c_0_13,negated_conjecture,
~ ( ord_less_int @ ( h @ w ) @ ( h @ e ) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,plain,
! [X2: a] :
( ( ord_less_int @ ( h @ X2 ) @ ( h @ e ) )
| ~ ( member_a @ X2 @ ( binary945792244etOf_a @ t1 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_10]) ).
thf(c_0_15,plain,
member_a @ w @ ( binary945792244etOf_a @ t1 ),
inference(split_conjunct,[status(thm)],[fact_0_whSet]) ).
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
% 0.00/0.03 % Problem : ITP032^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n003.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 19:40:51 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.27 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.HxfTqrLz7r/E---3.1_2968632.p
% 0.50/0.47 % Version: 3.5.1-ho
% 0.50/0.47 % Preprocessing class: HSLSSMSSSSLCHFA.
% 0.50/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.50/0.47 % Starting ehoh_best4 with 1500s (5) cores
% 0.50/0.47 % Starting additional_ho_6 with 300s (1) cores
% 0.50/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.50/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.50/0.47 % new_bool_3 with pid 2968668 completed with status 0
% 0.50/0.47 % Result found by new_bool_3
% 0.50/0.47 % Preprocessing class: HSLSSMSSSSLCHFA.
% 0.50/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.50/0.47 % Starting ehoh_best4 with 1500s (5) cores
% 0.50/0.47 % Starting additional_ho_6 with 300s (1) cores
% 0.50/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.50/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.50/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.50/0.47 % Search class: HGHSM-FSLM32-DHFFFSBN
% 0.50/0.47 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.50/0.47 % Starting SubtermCWHack with 28s (1) cores
% 0.50/0.47 % SubtermCWHack with pid 2968680 completed with status 0
% 0.50/0.47 % Result found by SubtermCWHack
% 0.50/0.47 % Preprocessing class: HSLSSMSSSSLCHFA.
% 0.50/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.50/0.47 % Starting ehoh_best4 with 1500s (5) cores
% 0.50/0.47 % Starting additional_ho_6 with 300s (1) cores
% 0.50/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.50/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.50/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.50/0.47 % Search class: HGHSM-FSLM32-DHFFFSBN
% 0.50/0.47 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.50/0.47 % Starting SubtermCWHack with 28s (1) cores
% 0.50/0.47 % Preprocessing time : 0.005 s
% 0.50/0.47
% 0.50/0.47 % Proof found!
% 0.50/0.47 % SZS status Theorem
% 0.50/0.47 % SZS output start CNFRefutation
% See solution above
% 0.50/0.47 % Parsed axioms : 394
% 0.50/0.47 % Removed by relevancy pruning/SinE : 125
% 0.50/0.47 % Initial clauses : 549
% 0.50/0.47 % Removed in clause preprocessing : 12
% 0.50/0.47 % Initial clauses in saturation : 537
% 0.50/0.47 % Processed clauses : 2489
% 0.50/0.47 % ...of these trivial : 168
% 0.50/0.47 % ...subsumed : 1337
% 0.50/0.47 % ...remaining for further processing : 984
% 0.50/0.47 % Other redundant clauses eliminated : 159
% 0.50/0.47 % Clauses deleted for lack of memory : 0
% 0.50/0.47 % Backward-subsumed : 2
% 0.50/0.47 % Backward-rewritten : 21
% 0.50/0.47 % Generated clauses : 8673
% 0.50/0.47 % ...of the previous two non-redundant : 7357
% 0.50/0.47 % ...aggressively subsumed : 0
% 0.50/0.47 % Contextual simplify-reflections : 1
% 0.50/0.47 % Paramodulations : 8468
% 0.50/0.47 % Factorizations : 8
% 0.50/0.47 % NegExts : 0
% 0.50/0.47 % Equation resolutions : 166
% 0.50/0.47 % Disequality decompositions : 0
% 0.50/0.47 % Total rewrite steps : 2672
% 0.50/0.47 % ...of those cached : 1974
% 0.50/0.47 % Propositional unsat checks : 0
% 0.50/0.47 % Propositional check models : 0
% 0.50/0.47 % Propositional check unsatisfiable : 0
% 0.50/0.47 % Propositional clauses : 0
% 0.50/0.47 % Propositional clauses after purity: 0
% 0.50/0.47 % Propositional unsat core size : 0
% 0.50/0.47 % Propositional preprocessing time : 0.000
% 0.50/0.47 % Propositional encoding time : 0.000
% 0.50/0.47 % Propositional solver time : 0.000
% 0.50/0.47 % Success case prop preproc time : 0.000
% 0.50/0.47 % Success case prop encoding time : 0.000
% 0.50/0.47 % Success case prop solver time : 0.000
% 0.50/0.47 % Current number of processed clauses : 863
% 0.50/0.47 % Positive orientable unit clauses : 212
% 0.50/0.47 % Positive unorientable unit clauses: 3
% 0.50/0.47 % Negative unit clauses : 409
% 0.50/0.47 % Non-unit-clauses : 239
% 0.50/0.47 % Current number of unprocessed clauses: 5293
% 0.50/0.47 % ...number of literals in the above : 10335
% 0.50/0.47 % Current number of archived formulas : 0
% 0.50/0.47 % Current number of archived clauses : 38
% 0.50/0.47 % Clause-clause subsumption calls (NU) : 15754
% 0.50/0.47 % Rec. Clause-clause subsumption calls : 9053
% 0.50/0.47 % Non-unit clause-clause subsumptions : 384
% 0.50/0.47 % Unit Clause-clause subsumption calls : 17328
% 0.50/0.47 % Rewrite failures with RHS unbound : 0
% 0.50/0.47 % BW rewrite match attempts : 1063
% 0.50/0.47 % BW rewrite match successes : 36
% 0.50/0.47 % Condensation attempts : 0
% 0.50/0.47 % Condensation successes : 0
% 0.50/0.47 % Termbank termtop insertions : 135254
% 0.50/0.47 % Search garbage collected termcells : 11361
% 0.50/0.47
% 0.50/0.47 % -------------------------------------------------
% 0.50/0.47 % User time : 0.144 s
% 0.50/0.47 % System time : 0.015 s
% 0.50/0.47 % Total time : 0.159 s
% 0.50/0.47 % Maximum resident set size: 6240 pages
% 0.50/0.47
% 0.50/0.47 % -------------------------------------------------
% 0.50/0.47 % User time : 0.156 s
% 0.50/0.47 % System time : 0.021 s
% 0.50/0.47 % Total time : 0.176 s
% 0.50/0.47 % Maximum resident set size: 5632 pages
% 0.50/0.47 % E exiting
%------------------------------------------------------------------------------