%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP157^1 : 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 : n001.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 08:04:32 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 14 ( 0 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 66 ( 6 ~; 2 |; 0 &; 57 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
set_Product_prod_a_a: $tType ).
thf(decl_sort2,type,
product_prod_a_a: $tType ).
thf(decl_sort3,type,
set_a: $tType ).
thf(decl_sort4,type,
a: $tType ).
thf(decl_69,type,
prefer161218362good_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(decl_89,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(decl_158,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(decl_159,type,
member_a: a > set_a > $o ).
thf(decl_160,type,
b: set_a ).
thf(decl_161,type,
pr: set_Product_prod_a_a ).
thf(decl_162,type,
y: a ).
thf(decl_163,type,
z: a ).
thf(conj_0,conjecture,
member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr,
file('/export/starexec/sandbox/tmp/tmp.M9dpj5mXbZ/E---3.1_1747526.p',conj_0) ).
thf(fact_8_at__lst__asgd__ge,axiom,
! [X29: a,X30: a,X31: set_a,X32: set_Product_prod_a_a] :
( ( member_a @ X29 @ ( prefer161218362good_a @ X30 @ X31 @ X32 ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ X29 @ X30 ) @ X32 ) ),
file('/export/starexec/sandbox/tmp/tmp.M9dpj5mXbZ/E---3.1_1747526.p',fact_8_at__lst__asgd__ge) ).
thf(fact_0_assms,axiom,
member_a @ z @ ( prefer161218362good_a @ y @ b @ pr ),
file('/export/starexec/sandbox/tmp/tmp.M9dpj5mXbZ/E---3.1_1747526.p',fact_0_assms) ).
thf(c_0_3,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_4,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
thf(c_0_5,plain,
! [X1299: a,X1300: a,X1301: set_a,X1302: set_Product_prod_a_a] :
( ~ ( member_a @ X1299 @ ( prefer161218362good_a @ X1300 @ X1301 @ X1302 ) )
| ( member449909584od_a_a @ ( product_Pair_a_a @ X1299 @ X1300 ) @ X1302 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_8_at__lst__asgd__ge])])]) ).
thf(c_0_6,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr ),
inference(fof_nnf,[status(thm)],[c_0_4]) ).
thf(c_0_7,plain,
! [X29: a,X31: set_a,X30: a,X27: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X29 @ X30 ) @ X27 )
| ~ ( member_a @ X29 @ ( prefer161218362good_a @ X30 @ X31 @ X27 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
member_a @ z @ ( prefer161218362good_a @ y @ b @ pr ),
inference(split_conjunct,[status(thm)],[fact_0_assms]) ).
thf(c_0_9,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP157^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n001.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 20:09:45 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.25 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.M9dpj5mXbZ/E---3.1_1747526.p
% 0.22/0.30 % Version: 3.5.1-ho
% 0.22/0.30 % Preprocessing class: HSLMSMSMSSLNSFA.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting new_ho_10 with 1200s (4) cores
% 0.22/0.30 % Starting post_as_ho9 with 600s (2) cores
% 0.22/0.30 % Starting full_lambda_7 with 300s (1) cores
% 0.22/0.30 % Starting post_as_ho6 with 300s (1) cores
% 0.22/0.30 % full_lambda_7 with pid 1747541 completed with status 0
% 0.22/0.30 % Result found by full_lambda_7
% 0.22/0.30 % Preprocessing class: HSLMSMSMSSLNSFA.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting new_ho_10 with 1200s (4) cores
% 0.22/0.30 % Starting post_as_ho9 with 600s (2) cores
% 0.22/0.30 % Starting full_lambda_7 with 300s (1) cores
% 0.22/0.30 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,2.5,,3,20000,1.0,true))
% 0.22/0.30 % SinE strategy is GSinE(CountTerms,hypos,2.5,,3,20000,1.0,true)
% 0.22/0.30 % Search class: HGHSM-FFMS31-DSFFFSBN
% 0.22/0.30 % partial match(2): HGHSM-FFMM31-DSFFFFBN
% 0.22/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.30 % SubtermCWHack with pid 1747546 completed with status 0
% 0.22/0.30 % Result found by SubtermCWHack
% 0.22/0.30 % Preprocessing class: HSLMSMSMSSLNSFA.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting new_ho_10 with 1200s (4) cores
% 0.22/0.30 % Starting post_as_ho9 with 600s (2) cores
% 0.22/0.30 % Starting full_lambda_7 with 300s (1) cores
% 0.22/0.30 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,2.5,,3,20000,1.0,true))
% 0.22/0.30 % SinE strategy is GSinE(CountTerms,hypos,2.5,,3,20000,1.0,true)
% 0.22/0.30 % Search class: HGHSM-FFMS31-DSFFFSBN
% 0.22/0.30 % partial match(2): HGHSM-FFMM31-DSFFFFBN
% 0.22/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.30 % Preprocessing time : 0.004 s
% 0.22/0.30
% 0.22/0.30 % Proof found!
% 0.22/0.30 % SZS status Theorem
% 0.22/0.30 % SZS output start CNFRefutation
% See solution above
% 0.22/0.31 % Parsed axioms : 527
% 0.22/0.31 % Removed by relevancy pruning/SinE : 488
% 0.22/0.31 % Initial clauses : 68
% 0.22/0.31 % Removed in clause preprocessing : 8
% 0.22/0.31 % Initial clauses in saturation : 60
% 0.22/0.31 % Processed clauses : 86
% 0.22/0.31 % ...of these trivial : 13
% 0.22/0.31 % ...subsumed : 17
% 0.22/0.31 % ...remaining for further processing : 56
% 0.22/0.31 % Other redundant clauses eliminated : 36
% 0.22/0.31 % Clauses deleted for lack of memory : 0
% 0.22/0.31 % Backward-subsumed : 0
% 0.22/0.31 % Backward-rewritten : 10
% 0.22/0.31 % Generated clauses : 121
% 0.22/0.31 % ...of the previous two non-redundant : 57
% 0.22/0.31 % ...aggressively subsumed : 0
% 0.22/0.31 % Contextual simplify-reflections : 0
% 0.22/0.31 % Paramodulations : 79
% 0.22/0.31 % Factorizations : 0
% 0.22/0.31 % NegExts : 0
% 0.22/0.31 % Equation resolutions : 42
% 0.22/0.31 % Disequality decompositions : 0
% 0.22/0.31 % Total rewrite steps : 60
% 0.22/0.31 % ...of those cached : 36
% 0.22/0.31 % Propositional unsat checks : 0
% 0.22/0.31 % Propositional check models : 0
% 0.22/0.31 % Propositional check unsatisfiable : 0
% 0.22/0.31 % Propositional clauses : 0
% 0.22/0.31 % Propositional clauses after purity: 0
% 0.22/0.31 % Propositional unsat core size : 0
% 0.22/0.31 % Propositional preprocessing time : 0.000
% 0.22/0.31 % Propositional encoding time : 0.000
% 0.22/0.31 % Propositional solver time : 0.000
% 0.22/0.31 % Success case prop preproc time : 0.000
% 0.22/0.31 % Success case prop encoding time : 0.000
% 0.22/0.31 % Success case prop solver time : 0.000
% 0.22/0.31 % Current number of processed clauses : 46
% 0.22/0.31 % Positive orientable unit clauses : 19
% 0.22/0.31 % Positive unorientable unit clauses: 0
% 0.22/0.31 % Negative unit clauses : 1
% 0.22/0.31 % Non-unit-clauses : 26
% 0.22/0.31 % Current number of unprocessed clauses: 20
% 0.22/0.31 % ...number of literals in the above : 41
% 0.22/0.31 % Current number of archived formulas : 0
% 0.22/0.31 % Current number of archived clauses : 10
% 0.22/0.31 % Clause-clause subsumption calls (NU) : 59
% 0.22/0.31 % Rec. Clause-clause subsumption calls : 59
% 0.22/0.31 % Non-unit clause-clause subsumptions : 17
% 0.22/0.31 % Unit Clause-clause subsumption calls : 61
% 0.22/0.31 % Rewrite failures with RHS unbound : 0
% 0.22/0.31 % BW rewrite match attempts : 10
% 0.22/0.31 % BW rewrite match successes : 10
% 0.22/0.31 % Condensation attempts : 0
% 0.22/0.31 % Condensation successes : 0
% 0.22/0.31 % Termbank termtop insertions : 11887
% 0.22/0.31 % Search garbage collected termcells : 5635
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.014 s
% 0.22/0.31 % System time : 0.005 s
% 0.22/0.31 % Total time : 0.019 s
% 0.22/0.31 % Maximum resident set size: 5480 pages
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.032 s
% 0.22/0.31 % System time : 0.011 s
% 0.22/0.31 % Total time : 0.043 s
% 0.22/0.31 % Maximum resident set size: 6144 pages
% 0.22/0.31 % E exiting
%------------------------------------------------------------------------------