%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP031^1 : 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 : n018.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 0.33s 0.46s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 5 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 80 ( 11 ~; 2 |; 1 &; 62 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 0 ^; 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_sort2,type,
set_a: $tType ).
thf(decl_sort3,type,
int: $tType ).
thf(decl_27,type,
binary504661350_eqs_a: ( a > int ) > a > set_a ).
thf(decl_46,type,
ord_less_int: int > int > $o ).
thf(decl_58,type,
member_a: a > set_a > $o ).
thf(decl_59,type,
e: a ).
thf(decl_60,type,
h: a > int ).
thf(decl_63,type,
x: a ).
thf(decl_64,type,
esk1_0: a ).
thf(conj_0,conjecture,
! [X42: a] :
( ( member_a @ X42 @ ( binary504661350_eqs_a @ h @ e ) )
=> ( ( h @ X42 )
!= ( h @ x ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TDxeIiGdsA/E---3.1_548106.p',conj_0) ).
thf(fact_224_dual__order_Oirrefl,axiom,
! [X304: int] :
~ ( ord_less_int @ X304 @ X304 ),
file('/export/starexec/sandbox2/tmp/tmp.TDxeIiGdsA/E---3.1_548106.p',fact_224_dual__order_Oirrefl) ).
thf(fact_0_eqsLessX,axiom,
! [X1: a] :
( ( member_a @ X1 @ ( binary504661350_eqs_a @ h @ e ) )
=> ( ord_less_int @ ( h @ X1 ) @ ( h @ x ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TDxeIiGdsA/E---3.1_548106.p',fact_0_eqsLessX) ).
thf(c_0_3,negated_conjecture,
~ ! [X42: a] :
( ( member_a @ X42 @ ( binary504661350_eqs_a @ h @ e ) )
=> ( ( h @ X42 )
!= ( h @ x ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_4,negated_conjecture,
~ ! [X42: a] :
( ( member_a @ X42 @ ( binary504661350_eqs_a @ h @ e ) )
=> ( ( h @ X42 )
!= ( h @ x ) ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
thf(c_0_5,plain,
! [X304: int] :
~ ( ord_less_int @ X304 @ X304 ),
inference(fof_simplification,[status(thm)],[fact_224_dual__order_Oirrefl]) ).
thf(c_0_6,plain,
! [X1012: a] :
( ~ ( member_a @ X1012 @ ( binary504661350_eqs_a @ h @ e ) )
| ( ord_less_int @ ( h @ X1012 ) @ ( h @ x ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_eqsLessX])])]) ).
thf(c_0_7,negated_conjecture,
( ( member_a @ esk1_0 @ ( binary504661350_eqs_a @ h @ e ) )
& ( ( h @ esk1_0 )
= ( h @ x ) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
thf(c_0_8,plain,
! [X1090: int] :
~ ( ord_less_int @ X1090 @ X1090 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_5])]) ).
thf(c_0_9,plain,
! [X1: a] :
( ( ord_less_int @ ( h @ X1 ) @ ( h @ x ) )
| ~ ( member_a @ X1 @ ( binary504661350_eqs_a @ h @ e ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
member_a @ esk1_0 @ ( binary504661350_eqs_a @ h @ e ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
( ( h @ esk1_0 )
= ( h @ x ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X86: int] :
~ ( ord_less_int @ X86 @ X86 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP031^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n018.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 19:40:56 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.29 Running higher-order theorem proving
% 0.25/0.37 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.TDxeIiGdsA/E---3.1_548106.p
% 0.33/0.46 % Version: 3.5.1-ho
% 0.33/0.46 % Preprocessing class: HSLSSMSSSSLCHSA.
% 0.33/0.46 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.46 % Starting sh2 with 1200s (4) cores
% 0.33/0.46 % Starting full_lambda_3 with 300s (1) cores
% 0.33/0.46 % Starting ehoh_best7_lambda with 300s (1) cores
% 0.33/0.46 % Starting post_as_ho9 with 300s (1) cores
% 0.33/0.46 % Starting almost_fo_4 with 300s (1) cores
% 0.33/0.46 % post_as_ho9 with pid 548123 completed with status 0
% 0.33/0.46 % Result found by post_as_ho9
% 0.33/0.46 % Preprocessing class: HSLSSMSSSSLCHSA.
% 0.33/0.46 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.46 % Starting sh2 with 1200s (4) cores
% 0.33/0.46 % Starting full_lambda_3 with 300s (1) cores
% 0.33/0.46 % Starting ehoh_best7_lambda with 300s (1) cores
% 0.33/0.46 % Starting post_as_ho9 with 300s (1) cores
% 0.33/0.46 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 0.33/0.46 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.33/0.46 % Search class: HGHSM-FSLM32-MHSFFSBN
% 0.33/0.46 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.33/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.33/0.46 % SubtermCWHack with pid 548125 completed with status 0
% 0.33/0.46 % Result found by SubtermCWHack
% 0.33/0.46 % Preprocessing class: HSLSSMSSSSLCHSA.
% 0.33/0.46 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.33/0.46 % Starting sh2 with 1200s (4) cores
% 0.33/0.46 % Starting full_lambda_3 with 300s (1) cores
% 0.33/0.46 % Starting ehoh_best7_lambda with 300s (1) cores
% 0.33/0.46 % Starting post_as_ho9 with 300s (1) cores
% 0.33/0.46 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 0.33/0.46 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.33/0.46 % Search class: HGHSM-FSLM32-MHSFFSBN
% 0.33/0.46 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.33/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.33/0.46 % Preprocessing time : 0.004 s
% 0.33/0.46
% 0.33/0.46 % Proof found!
% 0.33/0.46 % SZS status Theorem
% 0.33/0.46 % SZS output start CNFRefutation
% See solution above
% 0.33/0.46 % Parsed axioms : 404
% 0.33/0.46 % Removed by relevancy pruning/SinE : 240
% 0.33/0.46 % Initial clauses : 270
% 0.33/0.46 % Removed in clause preprocessing : 8
% 0.33/0.46 % Initial clauses in saturation : 262
% 0.33/0.46 % Processed clauses : 277
% 0.33/0.46 % ...of these trivial : 18
% 0.33/0.46 % ...subsumed : 115
% 0.33/0.46 % ...remaining for further processing : 144
% 0.33/0.46 % Other redundant clauses eliminated : 41
% 0.33/0.46 % Clauses deleted for lack of memory : 0
% 0.33/0.46 % Backward-subsumed : 2
% 0.33/0.46 % Backward-rewritten : 1
% 0.33/0.46 % Generated clauses : 372
% 0.33/0.46 % ...of the previous two non-redundant : 216
% 0.33/0.46 % ...aggressively subsumed : 0
% 0.33/0.46 % Contextual simplify-reflections : 0
% 0.33/0.46 % Paramodulations : 332
% 0.33/0.46 % Factorizations : 6
% 0.33/0.46 % NegExts : 0
% 0.33/0.46 % Equation resolutions : 42
% 0.33/0.46 % Disequality decompositions : 0
% 0.33/0.46 % Total rewrite steps : 134
% 0.33/0.46 % ...of those cached : 85
% 0.33/0.46 % Propositional unsat checks : 0
% 0.33/0.46 % Propositional check models : 0
% 0.33/0.46 % Propositional check unsatisfiable : 0
% 0.33/0.46 % Propositional clauses : 0
% 0.33/0.46 % Propositional clauses after purity: 0
% 0.33/0.46 % Propositional unsat core size : 0
% 0.33/0.46 % Propositional preprocessing time : 0.000
% 0.33/0.46 % Propositional encoding time : 0.000
% 0.33/0.46 % Propositional solver time : 0.000
% 0.33/0.46 % Success case prop preproc time : 0.000
% 0.33/0.46 % Success case prop encoding time : 0.000
% 0.33/0.46 % Success case prop solver time : 0.000
% 0.33/0.46 % Current number of processed clauses : 118
% 0.33/0.46 % Positive orientable unit clauses : 47
% 0.33/0.46 % Positive unorientable unit clauses: 1
% 0.33/0.46 % Negative unit clauses : 22
% 0.33/0.46 % Non-unit-clauses : 48
% 0.33/0.46 % Current number of unprocessed clauses: 196
% 0.33/0.46 % ...number of literals in the above : 509
% 0.33/0.46 % Current number of archived formulas : 0
% 0.33/0.46 % Current number of archived clauses : 3
% 0.33/0.46 % Clause-clause subsumption calls (NU) : 430
% 0.33/0.46 % Rec. Clause-clause subsumption calls : 390
% 0.33/0.46 % Non-unit clause-clause subsumptions : 75
% 0.33/0.46 % Unit Clause-clause subsumption calls : 223
% 0.33/0.46 % Rewrite failures with RHS unbound : 0
% 0.33/0.46 % BW rewrite match attempts : 36
% 0.33/0.46 % BW rewrite match successes : 9
% 0.33/0.46 % Condensation attempts : 0
% 0.33/0.46 % Condensation successes : 0
% 0.33/0.46 % Termbank termtop insertions : 24303
% 0.33/0.46 % Search garbage collected termcells : 6614
% 0.33/0.46
% 0.33/0.46 % -------------------------------------------------
% 0.33/0.46 % User time : 0.025 s
% 0.33/0.46 % System time : 0.008 s
% 0.33/0.46 % Total time : 0.034 s
% 0.33/0.46 % Maximum resident set size: 4968 pages
% 0.33/0.46
% 0.33/0.46 % -------------------------------------------------
% 0.33/0.46 % User time : 0.048 s
% 0.33/0.46 % System time : 0.015 s
% 0.33/0.46 % Total time : 0.063 s
% 0.33/0.46 % Maximum resident set size: 5376 pages
% 0.33/0.46 % E exiting
%------------------------------------------------------------------------------