%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP113^1 : 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 : n007.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 08:04:24 AM UTC 2026
% Result : Theorem 0.41s 0.39s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 4 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 134 ( 16 ~; 6 |; 3 &; 108 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 17 !; 1 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
product_prod_a_real: $tType ).
thf(decl_sort2,type,
set_Pr1928503567a_real: $tType ).
thf(decl_sort3,type,
set_a: $tType ).
thf(decl_sort4,type,
real: $tType ).
thf(decl_sort5,type,
extended_ereal: $tType ).
thf(decl_sort6,type,
a: $tType ).
thf(decl_30,type,
lower_930854854raph_a: set_a > ( a > extended_ereal ) > set_Pr1928503567a_real ).
thf(decl_33,type,
ord_less_real: real > real > $o ).
thf(decl_62,type,
top_top_set_a: set_a ).
thf(decl_78,type,
product_Pair_a_real: a > real > product_prod_a_real ).
thf(decl_79,type,
real_V404783528a_real: product_prod_a_real > product_prod_a_real > real ).
thf(decl_87,type,
member1103263856a_real: product_prod_a_real > set_Pr1928503567a_real > $o ).
thf(decl_90,type,
e: real ).
thf(decl_91,type,
f: a > extended_ereal ).
thf(decl_92,type,
thesis: $o ).
thf(decl_93,type,
x: a ).
thf(decl_94,type,
y: real ).
thf(decl_132,type,
esk37_0: product_prod_a_real ).
thf(decl_135,type,
esk40_1: product_prod_a_real > a ).
thf(decl_136,type,
esk41_1: product_prod_a_real > real ).
thf(conj_1,conjecture,
thesis,
file('/export/starexec/sandbox2/tmp/tmp.W4uEfIWJgv/E---3.1_3848186.p',conj_1) ).
thf(conj_0,hypothesis,
! [X794: a,X795: real] :
( ( ( member1103263856a_real @ ( product_Pair_a_real @ X794 @ X795 ) @ ( lower_930854854raph_a @ top_top_set_a @ f ) )
& ( ord_less_real @ ( real_V404783528a_real @ ( product_Pair_a_real @ X794 @ X795 ) @ ( product_Pair_a_real @ x @ y ) ) @ e ) )
=> thesis ),
file('/export/starexec/sandbox2/tmp/tmp.W4uEfIWJgv/E---3.1_3848186.p',conj_0) ).
thf(fact_280_old_Oprod_Oexhaust,axiom,
! [X23: product_prod_a_real] :
~ ! [X722: a,X250: real] :
( X23
!= ( product_Pair_a_real @ X722 @ X250 ) ),
file('/export/starexec/sandbox2/tmp/tmp.W4uEfIWJgv/E---3.1_3848186.p',fact_280_old_Oprod_Oexhaust) ).
thf(fact_0__092_060open_062_092_060exists_062ya_092_060in_062Epigraph_AUNIV_Af_O_Adist_Aya_A_Ix_M_Ay_J_A_060_Ae_092_060close_062,axiom,
? [X1: product_prod_a_real] :
( ( member1103263856a_real @ X1 @ ( lower_930854854raph_a @ top_top_set_a @ f ) )
& ( ord_less_real @ ( real_V404783528a_real @ X1 @ ( product_Pair_a_real @ x @ y ) ) @ e ) ),
file('/export/starexec/sandbox2/tmp/tmp.W4uEfIWJgv/E---3.1_3848186.p',fact_0__092_060open_062_092_060exists_062ya_092_060in_062Epigraph_AUNIV_Af_O_Adist_Aya_A_Ix_M_Ay_J_A_060_Ae_092_060close_062) ).
thf(c_0_4,negated_conjecture,
~ thesis,
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(c_0_5,negated_conjecture,
~ thesis,
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_6,hypothesis,
! [X996: a,X997: real] :
( ~ ( member1103263856a_real @ ( product_Pair_a_real @ X996 @ X997 ) @ ( lower_930854854raph_a @ top_top_set_a @ f ) )
| ~ ( ord_less_real @ ( real_V404783528a_real @ ( product_Pair_a_real @ X996 @ X997 ) @ ( product_Pair_a_real @ x @ y ) ) @ e )
| thesis ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])])]) ).
thf(c_0_7,negated_conjecture,
~ thesis,
inference(fof_nnf,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
! [X23: product_prod_a_real] :
~ ! [X722: a,X250: real] :
( X23
!= ( product_Pair_a_real @ X722 @ X250 ) ),
inference(fof_simplification,[status(thm)],[fact_280_old_Oprod_Oexhaust]) ).
thf(c_0_9,hypothesis,
! [X4: a,X3: real] :
( thesis
| ~ ( member1103263856a_real @ ( product_Pair_a_real @ X4 @ X3 ) @ ( lower_930854854raph_a @ top_top_set_a @ f ) )
| ~ ( ord_less_real @ ( real_V404783528a_real @ ( product_Pair_a_real @ X4 @ X3 ) @ ( product_Pair_a_real @ x @ y ) ) @ e ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
~ thesis,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X1169: product_prod_a_real] :
( X1169
= ( product_Pair_a_real @ ( esk40_1 @ X1169 ) @ ( esk41_1 @ X1169 ) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
thf(c_0_12,hypothesis,
! [X4: a,X3: real] :
( ~ ( ord_less_real @ ( real_V404783528a_real @ ( product_Pair_a_real @ X4 @ X3 ) @ ( product_Pair_a_real @ x @ y ) ) @ e )
| ~ ( member1103263856a_real @ ( product_Pair_a_real @ X4 @ X3 ) @ ( lower_930854854raph_a @ top_top_set_a @ f ) ) ),
inference(sr,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,plain,
! [X1: product_prod_a_real] :
( X1
= ( product_Pair_a_real @ ( esk40_1 @ X1 ) @ ( esk41_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,plain,
( ( member1103263856a_real @ esk37_0 @ ( lower_930854854raph_a @ top_top_set_a @ f ) )
& ( ord_less_real @ ( real_V404783528a_real @ esk37_0 @ ( product_Pair_a_real @ x @ y ) ) @ e ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_0__092_060open_062_092_060exists_062ya_092_060in_062Epigraph_AUNIV_Af_O_Adist_Aya_A_Ix_M_Ay_J_A_060_Ae_092_060close_062])]) ).
thf(c_0_15,hypothesis,
! [X1: product_prod_a_real] :
( ~ ( ord_less_real @ ( real_V404783528a_real @ X1 @ ( product_Pair_a_real @ x @ y ) ) @ e )
| ~ ( member1103263856a_real @ X1 @ ( lower_930854854raph_a @ top_top_set_a @ f ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,plain,
member1103263856a_real @ esk37_0 @ ( lower_930854854raph_a @ top_top_set_a @ f ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,plain,
ord_less_real @ ( real_V404783528a_real @ esk37_0 @ ( product_Pair_a_real @ x @ y ) ) @ e,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP113^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n007.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 19:54:11 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.21/0.28 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.W4uEfIWJgv/E---3.1_3848186.p
% 0.41/0.39 % Version: 3.5.1-ho
% 0.41/0.39 % Preprocessing class: HSLSSMSMSSMNHSA.
% 0.41/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.41/0.39 % Starting ehoh_best2 with 1500s (5) cores
% 0.41/0.39 % Starting additional_ho_6 with 300s (1) cores
% 0.41/0.39 % Starting new_bool_5 with 300s (1) cores
% 0.41/0.39 % Starting new_bool_1 with 300s (1) cores
% 0.41/0.39 % new_bool_5 with pid 3848250 completed with status 0
% 0.41/0.39 % Result found by new_bool_5
% 0.41/0.39 % Preprocessing class: HSLSSMSMSSMNHSA.
% 0.41/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.41/0.39 % Starting ehoh_best2 with 1500s (5) cores
% 0.41/0.39 % Starting additional_ho_6 with 300s (1) cores
% 0.41/0.39 % Starting new_bool_5 with 300s (1) cores
% 0.41/0.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.41/0.39 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.41/0.39 % Search class: HGHSM-FFMS32-SHSFFSBN
% 0.41/0.39 % partial match(3): HGHSM-FSLS32-MHSFFSBN
% 0.41/0.39 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.41/0.39 % Starting SubtermCWHack with 28s (1) cores
% 0.41/0.39 % SubtermCWHack with pid 3848257 completed with status 0
% 0.41/0.39 % Result found by SubtermCWHack
% 0.41/0.39 % Preprocessing class: HSLSSMSMSSMNHSA.
% 0.41/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.41/0.39 % Starting ehoh_best2 with 1500s (5) cores
% 0.41/0.39 % Starting additional_ho_6 with 300s (1) cores
% 0.41/0.39 % Starting new_bool_5 with 300s (1) cores
% 0.41/0.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.41/0.39 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.41/0.39 % Search class: HGHSM-FFMS32-SHSFFSBN
% 0.41/0.39 % partial match(3): HGHSM-FSLS32-MHSFFSBN
% 0.41/0.39 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.41/0.39 % Starting SubtermCWHack with 28s (1) cores
% 0.41/0.39 % Preprocessing time : 0.002 s
% 0.41/0.39
% 0.41/0.39 % Proof found!
% 0.41/0.39 % SZS status Theorem
% 0.41/0.39 % SZS output start CNFRefutation
% See solution above
% 0.41/0.39 % Parsed axioms : 444
% 0.41/0.39 % Removed by relevancy pruning/SinE : 382
% 0.41/0.39 % Initial clauses : 93
% 0.41/0.39 % Removed in clause preprocessing : 6
% 0.41/0.39 % Initial clauses in saturation : 87
% 0.41/0.39 % Processed clauses : 906
% 0.41/0.39 % ...of these trivial : 29
% 0.41/0.39 % ...subsumed : 433
% 0.41/0.39 % ...remaining for further processing : 444
% 0.41/0.39 % Other redundant clauses eliminated : 30
% 0.41/0.39 % Clauses deleted for lack of memory : 0
% 0.41/0.39 % Backward-subsumed : 2
% 0.41/0.39 % Backward-rewritten : 5
% 0.41/0.39 % Generated clauses : 4226
% 0.41/0.39 % ...of the previous two non-redundant : 3867
% 0.41/0.39 % ...aggressively subsumed : 0
% 0.41/0.39 % Contextual simplify-reflections : 0
% 0.41/0.39 % Paramodulations : 4189
% 0.41/0.39 % Factorizations : 4
% 0.41/0.39 % NegExts : 0
% 0.41/0.39 % Equation resolutions : 33
% 0.41/0.39 % Disequality decompositions : 0
% 0.41/0.39 % Total rewrite steps : 426
% 0.41/0.39 % ...of those cached : 365
% 0.41/0.39 % Propositional unsat checks : 0
% 0.41/0.39 % Propositional check models : 0
% 0.41/0.39 % Propositional check unsatisfiable : 0
% 0.41/0.39 % Propositional clauses : 0
% 0.41/0.39 % Propositional clauses after purity: 0
% 0.41/0.39 % Propositional unsat core size : 0
% 0.41/0.39 % Propositional preprocessing time : 0.000
% 0.41/0.39 % Propositional encoding time : 0.000
% 0.41/0.39 % Propositional solver time : 0.000
% 0.41/0.39 % Success case prop preproc time : 0.000
% 0.41/0.39 % Success case prop encoding time : 0.000
% 0.41/0.39 % Success case prop solver time : 0.000
% 0.41/0.39 % Current number of processed clauses : 417
% 0.41/0.39 % Positive orientable unit clauses : 44
% 0.41/0.39 % Positive unorientable unit clauses: 1
% 0.41/0.39 % Negative unit clauses : 89
% 0.41/0.39 % Non-unit-clauses : 283
% 0.41/0.39 % Current number of unprocessed clauses: 3043
% 0.41/0.39 % ...number of literals in the above : 8918
% 0.41/0.39 % Current number of archived formulas : 0
% 0.41/0.39 % Current number of archived clauses : 7
% 0.41/0.39 % Clause-clause subsumption calls (NU) : 31516
% 0.41/0.39 % Rec. Clause-clause subsumption calls : 22891
% 0.41/0.39 % Non-unit clause-clause subsumptions : 196
% 0.41/0.39 % Unit Clause-clause subsumption calls : 3981
% 0.41/0.39 % Rewrite failures with RHS unbound : 0
% 0.41/0.39 % BW rewrite match attempts : 192
% 0.41/0.39 % BW rewrite match successes : 5
% 0.41/0.39 % Condensation attempts : 0
% 0.41/0.39 % Condensation successes : 0
% 0.41/0.39 % Termbank termtop insertions : 68415
% 0.41/0.39 % Search garbage collected termcells : 5828
% 0.41/0.39
% 0.41/0.39 % -------------------------------------------------
% 0.41/0.39 % User time : 0.066 s
% 0.41/0.39 % System time : 0.005 s
% 0.41/0.39 % Total time : 0.071 s
% 0.41/0.39 % Maximum resident set size: 4888 pages
% 0.41/0.39
% 0.41/0.39 % -------------------------------------------------
% 0.41/0.39 % User time : 0.080 s
% 0.41/0.39 % System time : 0.010 s
% 0.41/0.39 % Total time : 0.090 s
% 0.41/0.39 % Maximum resident set size: 5888 pages
% 0.41/0.39 % E exiting
%------------------------------------------------------------------------------