%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP155^1 : 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 : n004.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 08:05:41 AM UTC 2026
% Result : Theorem 0.46s 0.46s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 6 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 224 ( 15 ~; 14 |; 0 &; 191 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
set_Product_prod_a_a: $tType ).
thf(decl_sort3,type,
set_a: $tType ).
thf(decl_sort4,type,
a: $tType ).
thf(decl_25,type,
finite_card_a: set_a > nat ).
thf(decl_31,type,
finite_finite_a: set_a > $o ).
thf(decl_46,type,
ord_less_eq_nat: nat > nat > $o ).
thf(decl_53,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(decl_62,type,
prefer1676310729than_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(decl_92,type,
member_a: a > set_a > $o ).
thf(decl_93,type,
carrier: set_a ).
thf(decl_94,type,
relation: set_Product_prod_a_a ).
thf(decl_95,type,
x: a ).
thf(decl_96,type,
y: a ).
thf(conj_0,conjecture,
ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ),
file('/export/starexec/sandbox2/tmp/tmp.7ZoXeW07rM/E---3.1_1773230.p',conj_0) ).
thf(fact_211_card__seteq,axiom,
! [X372: set_a,X82: set_a] :
( ( finite_finite_a @ X372 )
=> ( ( ord_less_eq_set_a @ X82 @ X372 )
=> ( ( ord_less_eq_nat @ ( finite_card_a @ X372 ) @ ( finite_card_a @ X82 ) )
=> ( X82 = X372 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7ZoXeW07rM/E---3.1_1773230.p',fact_211_card__seteq) ).
thf(fact_3__092_060open_062card_A_Ino__better__than_Ax_Acarrier_Arelation_J_A_092_060le_062_Acard_A_Ino__better__than_Ay_Acarrier_Arelation_J_092_060close_062,axiom,
ord_less_eq_nat @ ( finite_card_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) @ ( finite_card_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
file('/export/starexec/sandbox2/tmp/tmp.7ZoXeW07rM/E---3.1_1773230.p',fact_3__092_060open_062card_A_Ino__better__than_Ax_Acarrier_Arelation_J_A_092_060le_062_Acard_A_Ino__better__than_Ay_Acarrier_Arelation_J_092_060close_062) ).
thf(fact_4_nbt__nest,axiom,
! [X2: a,X1: a] :
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X2 @ carrier @ relation ) @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) @ ( prefer1676310729than_a @ X2 @ carrier @ relation ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7ZoXeW07rM/E---3.1_1773230.p',fact_4_nbt__nest) ).
thf(fact_15_fnt__carrier__fnt__nbt,axiom,
! [X3: a] :
( ( member_a @ X3 @ carrier )
=> ( finite_finite_a @ ( prefer1676310729than_a @ X3 @ carrier @ relation ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7ZoXeW07rM/E---3.1_1773230.p',fact_15_fnt__carrier__fnt__nbt) ).
thf(fact_1_assms_I1_J,axiom,
member_a @ x @ carrier,
file('/export/starexec/sandbox2/tmp/tmp.7ZoXeW07rM/E---3.1_1773230.p',fact_1_assms_I1_J) ).
thf(fact_154_subset__refl,axiom,
! [X82: set_a] : ( ord_less_eq_set_a @ X82 @ X82 ),
file('/export/starexec/sandbox2/tmp/tmp.7ZoXeW07rM/E---3.1_1773230.p',fact_154_subset__refl) ).
thf(c_0_7,negated_conjecture,
~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_8,plain,
! [X1933: set_a,X1934: set_a] :
( ~ ( finite_finite_a @ X1933 )
| ~ ( ord_less_eq_set_a @ X1934 @ X1933 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ X1933 ) @ ( finite_card_a @ X1934 ) )
| ( X1934 = X1933 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_211_card__seteq])])]) ).
thf(c_0_9,negated_conjecture,
~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X6: set_a,X18: set_a] :
( ( X18 = X6 )
| ~ ( finite_finite_a @ X6 )
| ~ ( ord_less_eq_set_a @ X18 @ X6 )
| ~ ( ord_less_eq_nat @ ( finite_card_a @ X6 ) @ ( finite_card_a @ X18 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,plain,
ord_less_eq_nat @ ( finite_card_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) @ ( finite_card_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
inference(split_conjunct,[status(thm)],[fact_3__092_060open_062card_A_Ino__better__than_Ax_Acarrier_Arelation_J_A_092_060le_062_Acard_A_Ino__better__than_Ay_Acarrier_Arelation_J_092_060close_062]) ).
thf(c_0_12,plain,
! [X1624: a,X1625: a] :
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X1624 @ carrier @ relation ) @ ( prefer1676310729than_a @ X1625 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X1625 @ carrier @ relation ) @ ( prefer1676310729than_a @ X1624 @ carrier @ relation ) ) ),
inference(variable_rename,[status(thm)],[fact_4_nbt__nest]) ).
thf(c_0_13,negated_conjecture,
~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
( ( ( prefer1676310729than_a @ y @ carrier @ relation )
= ( prefer1676310729than_a @ x @ carrier @ relation ) )
| ~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ y @ carrier @ relation ) @ ( prefer1676310729than_a @ x @ carrier @ relation ) )
| ~ ( finite_finite_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,plain,
! [X2: a,X1: a] :
( ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) @ ( prefer1676310729than_a @ X2 @ carrier @ relation ) )
| ( ord_less_eq_set_a @ ( prefer1676310729than_a @ X2 @ carrier @ relation ) @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
~ ( ord_less_eq_set_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) @ ( prefer1676310729than_a @ y @ carrier @ relation ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,plain,
! [X1808: a] :
( ~ ( member_a @ X1808 @ carrier )
| ( finite_finite_a @ ( prefer1676310729than_a @ X1808 @ carrier @ relation ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_15_fnt__carrier__fnt__nbt])])]) ).
thf(c_0_18,plain,
( ( ( prefer1676310729than_a @ y @ carrier @ relation )
= ( prefer1676310729than_a @ x @ carrier @ relation ) )
| ~ ( finite_finite_a @ ( prefer1676310729than_a @ x @ carrier @ relation ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
thf(c_0_19,plain,
! [X1: a] :
( ( finite_finite_a @ ( prefer1676310729than_a @ X1 @ carrier @ relation ) )
| ~ ( member_a @ X1 @ carrier ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,plain,
member_a @ x @ carrier,
inference(split_conjunct,[status(thm)],[fact_1_assms_I1_J]) ).
thf(c_0_21,plain,
! [X1683: set_a] : ( ord_less_eq_set_a @ X1683 @ X1683 ),
inference(variable_rename,[status(thm)],[fact_154_subset__refl]) ).
thf(c_0_22,plain,
( ( prefer1676310729than_a @ y @ carrier @ relation )
= ( prefer1676310729than_a @ x @ carrier @ relation ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
thf(c_0_23,plain,
! [X6: set_a] : ( ord_less_eq_set_a @ X6 @ X6 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_22]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP155^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n004.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 20:02:37 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running higher-order theorem proving
% 0.22/0.27 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.7ZoXeW07rM/E---3.1_1773230.p
% 0.46/0.46 % Version: 3.5.1-ho
% 0.46/0.46 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.46/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.46/0.46 % Starting new_ho_3 with 1500s (5) cores
% 0.46/0.46 % Starting pre_casc_2 with 300s (1) cores
% 0.46/0.46 % Starting additional_ho_7 with 300s (1) cores
% 0.46/0.46 % Starting lpo8_s with 300s (1) cores
% 0.46/0.46 % new_ho_3 with pid 1773280 completed with status 0
% 0.46/0.46 % Result found by new_ho_3
% 0.46/0.46 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.46/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.46/0.46 % Starting new_ho_3 with 1500s (5) cores
% 0.46/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.46/0.46 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.46/0.46 % Search class: HGHSM-FSLM32-SSFFFSBN
% 0.46/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.46/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.46/0.46 % Starting new_ho_3 with 151s (1) cores
% 0.46/0.46 % Starting new_bool_9 with 136s (1) cores
% 0.46/0.46 % Starting lpo1_def_fix with 136s (1) cores
% 0.46/0.46 % Starting ehoh_best3_rw with 136s (1) cores
% 0.46/0.46 % new_ho_3 with pid 1773300 completed with status 0
% 0.46/0.46 % Result found by new_ho_3
% 0.46/0.46 % Preprocessing class: HSLSSMSMSSMNSFA.
% 0.46/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.46/0.46 % Starting new_ho_3 with 1500s (5) cores
% 0.46/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.46/0.46 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.46/0.46 % Search class: HGHSM-FSLM32-SSFFFSBN
% 0.46/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.46/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.46/0.46 % Starting new_ho_3 with 151s (1) cores
% 0.46/0.46 % Preprocessing time : 0.013 s
% 0.46/0.46 % Presaturation interreduction done
% 0.46/0.46
% 0.46/0.46 % Proof found!
% 0.46/0.46 % SZS status Theorem
% 0.46/0.46 % SZS output start CNFRefutation
% See solution above
% 0.46/0.46 % Parsed axioms : 443
% 0.46/0.46 % Removed by relevancy pruning/SinE : 140
% 0.46/0.46 % Initial clauses : 675
% 0.46/0.46 % Removed in clause preprocessing : 21
% 0.46/0.46 % Initial clauses in saturation : 654
% 0.46/0.46 % Processed clauses : 873
% 0.46/0.46 % ...of these trivial : 10
% 0.46/0.46 % ...subsumed : 196
% 0.46/0.46 % ...remaining for further processing : 667
% 0.46/0.46 % Other redundant clauses eliminated : 65
% 0.46/0.46 % Clauses deleted for lack of memory : 0
% 0.46/0.46 % Backward-subsumed : 2
% 0.46/0.46 % Backward-rewritten : 6
% 0.46/0.46 % Generated clauses : 293
% 0.46/0.46 % ...of the previous two non-redundant : 189
% 0.46/0.46 % ...aggressively subsumed : 0
% 0.46/0.46 % Contextual simplify-reflections : 8
% 0.46/0.46 % Paramodulations : 206
% 0.46/0.46 % Factorizations : 4
% 0.46/0.46 % NegExts : 0
% 0.46/0.46 % Equation resolutions : 67
% 0.46/0.46 % Disequality decompositions : 0
% 0.46/0.46 % Total rewrite steps : 120
% 0.46/0.46 % ...of those cached : 77
% 0.46/0.46 % Propositional unsat checks : 0
% 0.46/0.46 % Propositional check models : 0
% 0.46/0.46 % Propositional check unsatisfiable : 0
% 0.46/0.46 % Propositional clauses : 0
% 0.46/0.46 % Propositional clauses after purity: 0
% 0.46/0.46 % Propositional unsat core size : 0
% 0.46/0.46 % Propositional preprocessing time : 0.000
% 0.46/0.46 % Propositional encoding time : 0.000
% 0.46/0.46 % Propositional solver time : 0.000
% 0.46/0.46 % Success case prop preproc time : 0.000
% 0.46/0.46 % Success case prop encoding time : 0.000
% 0.46/0.46 % Success case prop solver time : 0.000
% 0.46/0.46 % Current number of processed clauses : 151
% 0.46/0.46 % Positive orientable unit clauses : 34
% 0.46/0.46 % Positive unorientable unit clauses: 0
% 0.46/0.46 % Negative unit clauses : 7
% 0.46/0.46 % Non-unit-clauses : 110
% 0.46/0.46 % Current number of unprocessed clauses: 409
% 0.46/0.46 % ...number of literals in the above : 1512
% 0.46/0.46 % Current number of archived formulas : 0
% 0.46/0.46 % Current number of archived clauses : 461
% 0.46/0.46 % Clause-clause subsumption calls (NU) : 56814
% 0.46/0.46 % Rec. Clause-clause subsumption calls : 18934
% 0.46/0.46 % Non-unit clause-clause subsumptions : 195
% 0.46/0.46 % Unit Clause-clause subsumption calls : 298
% 0.46/0.46 % Rewrite failures with RHS unbound : 0
% 0.46/0.46 % BW rewrite match attempts : 8
% 0.46/0.46 % BW rewrite match successes : 3
% 0.46/0.46 % Condensation attempts : 873
% 0.46/0.46 % Condensation successes : 16
% 0.46/0.46 % Termbank termtop insertions : 77179
% 0.46/0.46 % Search garbage collected termcells : 17394
% 0.46/0.46
% 0.46/0.46 % -------------------------------------------------
% 0.46/0.46 % User time : 0.147 s
% 0.46/0.46 % System time : 0.009 s
% 0.46/0.46 % Total time : 0.156 s
% 0.46/0.46 % Maximum resident set size: 7208 pages
% 0.46/0.46
% 0.46/0.46 % -------------------------------------------------
% 0.46/0.46 % User time : 0.473 s
% 0.46/0.46 % System time : 0.054 s
% 0.46/0.46 % Total time : 0.527 s
% 0.46/0.46 % Maximum resident set size: 5888 pages
% 0.46/0.46 % E exiting
%------------------------------------------------------------------------------