%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP093^1 : 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 : n009.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 08:04:20 AM UTC 2026
% Result : Theorem 0.24s 0.34s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 69 ( 7 ~; 4 |; 0 &; 56 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 6 ^; 6 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
set_Product_prod_a_a: $tType ).
thf(decl_sort2,type,
set_a: $tType ).
thf(decl_sort3,type,
a: $tType ).
thf(decl_sort4,type,
pair_p125712459t_unit: $tType ).
thf(decl_42,type,
finite179568208od_a_a: set_Product_prod_a_a > $o ).
thf(decl_66,type,
ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(decl_88,type,
pair_p133601421t_unit: pair_p125712459t_unit > set_Product_prod_a_a ).
thf(decl_93,type,
pair_p1047056820t_unit: pair_p125712459t_unit > set_a ).
thf(decl_108,type,
product_Sigma_a_a: set_a > ( a > set_a ) > set_Product_prod_a_a ).
thf(decl_128,type,
g: pair_p125712459t_unit ).
thf(conj_0,conjecture,
finite179568208od_a_a @ ( pair_p133601421t_unit @ g ),
file('/export/starexec/sandbox/tmp/tmp.Kr4mIWB1bd/E---3.1_272080.p',conj_0) ).
thf(fact_27_rev__finite__subset,axiom,
! [X37: set_Product_prod_a_a,X38: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ X37 )
=> ( ( ord_le1824328871od_a_a @ X38 @ X37 )
=> ( finite179568208od_a_a @ X38 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Kr4mIWB1bd/E---3.1_272080.p',fact_27_rev__finite__subset) ).
thf(fact_1__092_060open_062parcs_AG_A_092_060subseteq_062_Apverts_AG_A_092_060times_062_Apverts_AG_092_060close_062,axiom,
( ord_le1824328871od_a_a @ ( pair_p133601421t_unit @ g )
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [X1: a] : ( pair_p1047056820t_unit @ g ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Kr4mIWB1bd/E---3.1_272080.p',fact_1__092_060open_062parcs_AG_A_092_060subseteq_062_Apverts_AG_A_092_060times_062_Apverts_AG_092_060close_062) ).
thf(fact_0__092_060open_062finite_A_Ipverts_AG_A_092_060times_062_Apverts_AG_J_092_060close_062,axiom,
( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [X1: a] : ( pair_p1047056820t_unit @ g ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Kr4mIWB1bd/E---3.1_272080.p',fact_0__092_060open_062finite_A_Ipverts_AG_A_092_060times_062_Apverts_AG_J_092_060close_062) ).
thf(c_0_4,negated_conjecture,
~ ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_5,plain,
! [X1410: set_Product_prod_a_a,X1411: set_Product_prod_a_a] :
( ~ ( finite179568208od_a_a @ X1410 )
| ~ ( ord_le1824328871od_a_a @ X1411 @ X1410 )
| ( finite179568208od_a_a @ X1411 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_27_rev__finite__subset])]) ).
thf(c_0_6,plain,
( ord_le1824328871od_a_a @ ( pair_p133601421t_unit @ g )
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Z0: a] : ( pair_p1047056820t_unit @ g ) ) ),
inference(fof_simplification,[status(thm)],[fact_1__092_060open_062parcs_AG_A_092_060subseteq_062_Apverts_AG_A_092_060times_062_Apverts_AG_092_060close_062]) ).
thf(c_0_7,plain,
( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Z0: a] : ( pair_p1047056820t_unit @ g ) ) ),
inference(fof_simplification,[status(thm)],[fact_0__092_060open_062finite_A_Ipverts_AG_A_092_060times_062_Apverts_AG_J_092_060close_062]) ).
thf(c_0_8,negated_conjecture,
~ ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_9,plain,
! [X24: set_Product_prod_a_a,X23: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ X24 )
| ~ ( finite179568208od_a_a @ X23 )
| ~ ( ord_le1824328871od_a_a @ X24 @ X23 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,plain,
( ord_le1824328871od_a_a @ ( pair_p133601421t_unit @ g )
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Z0: a] : ( pair_p1047056820t_unit @ g ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,plain,
( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [Z0: a] : ( pair_p1047056820t_unit @ g ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,negated_conjecture,
~ ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[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 : ITP093^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n009.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:52:45 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.24/0.29 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.Kr4mIWB1bd/E---3.1_272080.p
% 0.24/0.34 % Version: 3.5.1-ho
% 0.24/0.34 % Preprocessing class: HSLMSMSSSSLNSFA.
% 0.24/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.34 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.34 % Starting sh5l with 300s (1) cores
% 0.24/0.34 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.34 % Starting new_bool_2 with 300s (1) cores
% 0.24/0.34 % new_bool_2 with pid 272096 completed with status 0
% 0.24/0.34 % Result found by new_bool_2
% 0.24/0.34 % Preprocessing class: HSLMSMSSSSLNSFA.
% 0.24/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.34 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.34 % Starting sh5l with 300s (1) cores
% 0.24/0.34 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.34 % Starting new_bool_2 with 300s (1) cores
% 0.24/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.34 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.34 % Search class: HGHSM-FSLM33-DSFFFSBN
% 0.24/0.34 % partial match(1): HGHSM-FSLM33-MSFFFSBN
% 0.24/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.34 % SubtermCWHack with pid 272097 completed with status 0
% 0.24/0.34 % Result found by SubtermCWHack
% 0.24/0.34 % Preprocessing class: HSLMSMSSSSLNSFA.
% 0.24/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.34 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.34 % Starting sh5l with 300s (1) cores
% 0.24/0.34 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.34 % Starting new_bool_2 with 300s (1) cores
% 0.24/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.34 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.34 % Search class: HGHSM-FSLM33-DSFFFSBN
% 0.24/0.34 % partial match(1): HGHSM-FSLM33-MSFFFSBN
% 0.24/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.34 % Preprocessing time : 0.006 s
% 0.24/0.34
% 0.24/0.34 % Proof found!
% 0.24/0.34 % SZS status Theorem
% 0.24/0.34 % SZS output start CNFRefutation
% See solution above
% 0.24/0.34 % Parsed axioms : 493
% 0.24/0.34 % Removed by relevancy pruning/SinE : 360
% 0.24/0.34 % Initial clauses : 261
% 0.24/0.34 % Removed in clause preprocessing : 11
% 0.24/0.34 % Initial clauses in saturation : 250
% 0.24/0.34 % Processed clauses : 41
% 0.24/0.34 % ...of these trivial : 5
% 0.24/0.34 % ...subsumed : 6
% 0.24/0.34 % ...remaining for further processing : 30
% 0.24/0.34 % Other redundant clauses eliminated : 11
% 0.24/0.34 % Clauses deleted for lack of memory : 0
% 0.24/0.34 % Backward-subsumed : 0
% 0.24/0.34 % Backward-rewritten : 0
% 0.24/0.34 % Generated clauses : 19
% 0.24/0.34 % ...of the previous two non-redundant : 2
% 0.24/0.34 % ...aggressively subsumed : 0
% 0.24/0.34 % Contextual simplify-reflections : 0
% 0.24/0.34 % Paramodulations : 6
% 0.24/0.34 % Factorizations : 2
% 0.24/0.34 % NegExts : 0
% 0.24/0.34 % Equation resolutions : 11
% 0.24/0.34 % Disequality decompositions : 0
% 0.24/0.34 % Total rewrite steps : 20
% 0.24/0.34 % ...of those cached : 14
% 0.24/0.34 % Propositional unsat checks : 0
% 0.24/0.34 % Propositional check models : 0
% 0.24/0.34 % Propositional check unsatisfiable : 0
% 0.24/0.34 % Propositional clauses : 0
% 0.24/0.34 % Propositional clauses after purity: 0
% 0.24/0.34 % Propositional unsat core size : 0
% 0.24/0.34 % Propositional preprocessing time : 0.000
% 0.24/0.34 % Propositional encoding time : 0.000
% 0.24/0.34 % Propositional solver time : 0.000
% 0.24/0.34 % Success case prop preproc time : 0.000
% 0.24/0.34 % Success case prop encoding time : 0.000
% 0.24/0.34 % Success case prop solver time : 0.000
% 0.24/0.34 % Current number of processed clauses : 19
% 0.24/0.34 % Positive orientable unit clauses : 5
% 0.24/0.34 % Positive unorientable unit clauses: 0
% 0.24/0.34 % Negative unit clauses : 2
% 0.24/0.34 % Non-unit-clauses : 12
% 0.24/0.34 % Current number of unprocessed clauses: 211
% 0.24/0.34 % ...number of literals in the above : 789
% 0.24/0.34 % Current number of archived formulas : 0
% 0.24/0.34 % Current number of archived clauses : 0
% 0.24/0.34 % Clause-clause subsumption calls (NU) : 37
% 0.24/0.34 % Rec. Clause-clause subsumption calls : 36
% 0.24/0.34 % Non-unit clause-clause subsumptions : 6
% 0.24/0.34 % Unit Clause-clause subsumption calls : 3
% 0.24/0.34 % Rewrite failures with RHS unbound : 0
% 0.24/0.34 % BW rewrite match attempts : 0
% 0.24/0.34 % BW rewrite match successes : 0
% 0.24/0.34 % Condensation attempts : 0
% 0.24/0.34 % Condensation successes : 0
% 0.24/0.34 % Termbank termtop insertions : 23665
% 0.24/0.34 % Search garbage collected termcells : 9105
% 0.24/0.34
% 0.24/0.34 % -------------------------------------------------
% 0.24/0.34 % User time : 0.013 s
% 0.24/0.34 % System time : 0.009 s
% 0.24/0.34 % Total time : 0.022 s
% 0.24/0.34 % Maximum resident set size: 6200 pages
% 0.24/0.34
% 0.24/0.34 % -------------------------------------------------
% 0.24/0.34 % User time : 0.030 s
% 0.24/0.34 % System time : 0.014 s
% 0.24/0.34 % Total time : 0.045 s
% 0.24/0.34 % Maximum resident set size: 6144 pages
% 0.24/0.34 % E exiting
%------------------------------------------------------------------------------