%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP112^1 : 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 : 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 08:04:23 AM UTC 2026
% Result : Theorem 84.87s 28.67s
% Output : CNFRefutation 84.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 6 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 143 ( 9 ~; 3 |; 0 &; 129 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 38 ( 16 ^; 22 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
extended_ereal: $tType ).
thf(decl_sort2,type,
filter_nat: $tType ).
thf(decl_sort3,type,
nat: $tType ).
thf(decl_sort4,type,
filter2049122004_ereal: $tType ).
thf(decl_sort5,type,
a: $tType ).
thf(decl_26,type,
at_top_nat: filter_nat ).
thf(decl_28,type,
filter1531173832_ereal: ( nat > extended_ereal ) > filter2049122004_ereal > filter_nat > $o ).
thf(decl_44,type,
comp_a1112243075al_nat: ( a > extended_ereal ) > ( nat > a ) > nat > extended_ereal ).
thf(decl_54,type,
uminus1208298309_ereal: extended_ereal > extended_ereal ).
thf(decl_95,type,
topolo2140997059_ereal: extended_ereal > filter2049122004_ereal ).
thf(decl_102,type,
a2: extended_ereal ).
thf(decl_103,type,
f: a > extended_ereal ).
thf(decl_105,type,
x: nat > a ).
thf(conj_0,conjecture,
( filter1531173832_ereal
@ ^ [X811: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ X811 ) ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
@ at_top_nat ),
file('/export/starexec/sandbox/tmp/tmp.yYhQMz4qbz/E---3.1_3845510.p',conj_0) ).
thf(fact_4_tendsto__uminus__ereal,axiom,
! [X4: nat > extended_ereal,X5: extended_ereal,X1: filter_nat] :
( ( filter1531173832_ereal @ X4 @ ( topolo2140997059_ereal @ X5 ) @ X1 )
=> ( filter1531173832_ereal
@ ^ [X2: nat] : ( uminus1208298309_ereal @ ( X4 @ X2 ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ X5 ) )
@ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.yYhQMz4qbz/E---3.1_3845510.p',fact_4_tendsto__uminus__ereal) ).
thf(fact_36_comp__apply,axiom,
( comp_a1112243075al_nat
= ( ^ [X63: a > extended_ereal,X64: nat > a,X2: nat] : ( X63 @ ( X64 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yYhQMz4qbz/E---3.1_3845510.p',fact_36_comp__apply) ).
thf(fact_1_x__def_I2_J,axiom,
filter1531173832_ereal @ ( comp_a1112243075al_nat @ f @ x ) @ ( topolo2140997059_ereal @ a2 ) @ at_top_nat,
file('/export/starexec/sandbox/tmp/tmp.yYhQMz4qbz/E---3.1_3845510.p',fact_1_x__def_I2_J) ).
thf(c_0_4,negated_conjecture,
~ ( filter1531173832_ereal
@ ^ [X811: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ X811 ) ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
@ at_top_nat ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_5,negated_conjecture,
~ ( filter1531173832_ereal
@ ^ [Z0: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ Z0 ) ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
@ at_top_nat ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_4])]) ).
thf(c_0_6,plain,
! [X4: nat > extended_ereal,X5: extended_ereal,X1: filter_nat] :
( ( filter1531173832_ereal @ X4 @ ( topolo2140997059_ereal @ X5 ) @ X1 )
=> ( filter1531173832_ereal
@ ^ [Z0: nat] : ( uminus1208298309_ereal @ ( X4 @ Z0 ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ X5 ) )
@ X1 ) ),
inference(fof_simplification,[status(thm)],[fact_4_tendsto__uminus__ereal]) ).
thf(c_0_7,negated_conjecture,
~ ( filter1531173832_ereal
@ ^ [Z0: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ Z0 ) ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
@ at_top_nat ),
inference(fof_nnf,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
! [X1167: nat > extended_ereal,X1168: extended_ereal,X1169: filter_nat] :
( ~ ( filter1531173832_ereal @ X1167 @ ( topolo2140997059_ereal @ X1168 ) @ X1169 )
| ( filter1531173832_ereal
@ ^ [Z0: nat] : ( uminus1208298309_ereal @ ( X1167 @ Z0 ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ X1168 ) )
@ X1169 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_9,negated_conjecture,
~ ( filter1531173832_ereal
@ ^ [Z0: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ Z0 ) ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ a2 ) )
@ at_top_nat ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X5: extended_ereal,X4: nat > extended_ereal,X1: filter_nat] :
( ( filter1531173832_ereal
@ ^ [Z0: nat] : ( uminus1208298309_ereal @ ( X4 @ Z0 ) )
@ ( topolo2140997059_ereal @ ( uminus1208298309_ereal @ X5 ) )
@ X1 )
| ~ ( filter1531173832_ereal @ X4 @ ( topolo2140997059_ereal @ X5 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,plain,
! [X1106: a > extended_ereal,X1107: nat > a,X1108: nat] :
( ( comp_a1112243075al_nat @ X1106 @ X1107 @ X1108 )
= ( X1106 @ ( X1107 @ X1108 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_36_comp__apply])]) ).
thf(c_0_12,plain,
! [X4: nat > extended_ereal] :
( ( ( ^ [Z0: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ Z0 ) ) ) )
!= ( ^ [Z0: nat] : ( uminus1208298309_ereal @ ( X4 @ Z0 ) ) ) )
| ~ ( filter1531173832_ereal @ X4 @ ( topolo2140997059_ereal @ a2 ) @ at_top_nat ) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_9,c_0_10])])]) ).
thf(c_0_13,plain,
filter1531173832_ereal @ ( comp_a1112243075al_nat @ f @ x ) @ ( topolo2140997059_ereal @ a2 ) @ at_top_nat,
inference(split_conjunct,[status(thm)],[fact_1_x__def_I2_J]) ).
thf(c_0_14,plain,
! [X1392: a > extended_ereal,X1393: nat > a,X1394: nat] :
( ( comp_a1112243075al_nat @ X1392 @ X1393 @ X1394 )
= ( X1392 @ ( X1393 @ X1394 ) ) ),
inference(variable_rename,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
( ( ^ [Z0: nat] : ( uminus1208298309_ereal @ ( comp_a1112243075al_nat @ f @ x @ Z0 ) ) )
!= ( ^ [Z0: nat] : ( uminus1208298309_ereal @ ( f @ ( x @ Z0 ) ) ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,plain,
! [X63: a > extended_ereal,X36: nat > a,X2: nat] :
( ( comp_a1112243075al_nat @ X63 @ X36 @ X2 )
= ( X63 @ ( X36 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_15]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP112^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n007.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 19:53:11 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.yYhQMz4qbz/E---3.1_3845510.p
% 84.87/28.67 % Version: 3.5.1-ho
% 84.87/28.67 % Preprocessing class: HSLSSMSSSSLNHSA.
% 84.87/28.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.87/28.67 % Starting pre_casc_6 with 1200s (4) cores
% 84.87/28.67 % Starting sh4 with 600s (2) cores
% 84.87/28.67 % Starting pre_casc_4 with 300s (1) cores
% 84.87/28.67 % Starting full_lambda_7 with 300s (1) cores
% 84.87/28.67 % pre_casc_4 with pid 3845525 completed with status 0
% 84.87/28.67 % Result found by pre_casc_4
% 84.87/28.67 % Preprocessing class: HSLSSMSSSSLNHSA.
% 84.87/28.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.87/28.67 % Starting pre_casc_6 with 1200s (4) cores
% 84.87/28.67 % Starting sh4 with 600s (2) cores
% 84.87/28.67 % Starting pre_casc_4 with 300s (1) cores
% 84.87/28.67 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 84.87/28.67 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 84.87/28.67 % Search class: HGUSM-FSLF32-MHSFFSBN
% 84.87/28.67 % partial match(1): HGUSM-FSLM32-MHSFFSBN
% 84.87/28.67 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 84.87/28.67 % Starting SubtermCWHack with 28s (1) cores
% 84.87/28.67 % SubtermCWHack with pid 3845527 completed with status 8
% 84.87/28.67 % Starting pre_casc_4 with 31s (1) cores
% 84.87/28.67 % pre_casc_4 with pid 3846208 completed with status 0
% 84.87/28.67 % Result found by pre_casc_4
% 84.87/28.67 % Preprocessing class: HSLSSMSSSSLNHSA.
% 84.87/28.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.87/28.67 % Starting pre_casc_6 with 1200s (4) cores
% 84.87/28.67 % Starting sh4 with 600s (2) cores
% 84.87/28.67 % Starting pre_casc_4 with 300s (1) cores
% 84.87/28.67 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 84.87/28.67 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 84.87/28.67 % Search class: HGUSM-FSLF32-MHSFFSBN
% 84.87/28.67 % partial match(1): HGUSM-FSLM32-MHSFFSBN
% 84.87/28.67 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 84.87/28.67 % Starting SubtermCWHack with 28s (1) cores
% 84.87/28.67 % SubtermCWHack with pid 3845527 completed with status 8
% 84.87/28.67 % Starting pre_casc_4 with 31s (1) cores
% 84.87/28.67 % Preprocessing time : 0.007 s
% 84.87/28.67 % Presaturation interreduction done
% 84.87/28.67
% 84.87/28.67 % Proof found!
% 84.87/28.67 % SZS status Theorem
% 84.87/28.67 % SZS output start CNFRefutation
% See solution above
% 84.87/28.67 % Parsed axioms : 451
% 84.87/28.67 % Removed by relevancy pruning/SinE : 358
% 84.87/28.67 % Initial clauses : 270
% 84.87/28.67 % Removed in clause preprocessing : 9
% 84.87/28.67 % Initial clauses in saturation : 261
% 84.87/28.67 % Processed clauses : 357
% 84.87/28.67 % ...of these trivial : 4
% 84.87/28.67 % ...subsumed : 162
% 84.87/28.67 % ...remaining for further processing : 191
% 84.87/28.67 % Other redundant clauses eliminated : 52
% 84.87/28.67 % Clauses deleted for lack of memory : 0
% 84.87/28.67 % Backward-subsumed : 1
% 84.87/28.67 % Backward-rewritten : 3
% 84.87/28.67 % Generated clauses : 223
% 84.87/28.67 % ...of the previous two non-redundant : 141
% 84.87/28.67 % ...aggressively subsumed : 0
% 84.87/28.67 % Contextual simplify-reflections : 0
% 84.87/28.67 % Paramodulations : 148
% 84.87/28.67 % Factorizations : 4
% 84.87/28.67 % NegExts : 7
% 84.87/28.67 % Equation resolutions : 55
% 84.87/28.67 % Disequality decompositions : 0
% 84.87/28.67 % Total rewrite steps : 77
% 84.87/28.67 % ...of those cached : 46
% 84.87/28.67 % Propositional unsat checks : 0
% 84.87/28.67 % Propositional check models : 0
% 84.87/28.67 % Propositional check unsatisfiable : 0
% 84.87/28.67 % Propositional clauses : 0
% 84.87/28.67 % Propositional clauses after purity: 0
% 84.87/28.67 % Propositional unsat core size : 0
% 84.87/28.67 % Propositional preprocessing time : 0.000
% 84.87/28.67 % Propositional encoding time : 0.000
% 84.87/28.67 % Propositional solver time : 0.000
% 84.87/28.67 % Success case prop preproc time : 0.000
% 84.87/28.67 % Success case prop encoding time : 0.000
% 84.87/28.67 % Success case prop solver time : 0.000
% 84.87/28.67 % Current number of processed clauses : 64
% 84.87/28.67 % Positive orientable unit clauses : 10
% 84.87/28.67 % Positive unorientable unit clauses: 0
% 84.87/28.67 % Negative unit clauses : 6
% 84.87/28.67 % Non-unit-clauses : 48
% 84.87/28.67 % Current number of unprocessed clauses: 132
% 84.87/28.67 % ...number of literals in the above : 386
% 84.87/28.67 % Current number of archived formulas : 0
% 84.87/28.67 % Current number of archived clauses : 91
% 84.87/28.67 % Clause-clause subsumption calls (NU) : 1064
% 84.87/28.67 % Rec. Clause-clause subsumption calls : 834
% 84.87/28.67 % Non-unit clause-clause subsumptions : 162
% 84.87/28.67 % Unit Clause-clause subsumption calls : 83
% 84.87/28.67 % Rewrite failures with RHS unbound : 0
% 84.87/28.67 % BW rewrite match attempts : 11
% 84.87/28.67 % BW rewrite match successes : 3
% 84.87/28.67 % Condensation attempts : 0
% 84.87/28.67 % Condensation successes : 0
% 84.87/28.67 % Termbank termtop insertions : 27882
% 84.87/28.67 % Search garbage collected termcells : 8621
% 84.87/28.67
% 84.87/28.67 % -------------------------------------------------
% 84.87/28.67 % User time : 27.451 s
% 84.87/28.67 % System time : 0.663 s
% 84.87/28.67 % Total time : 28.114 s
% 84.87/28.67 % Maximum resident set size: 5588 pages
% 84.87/28.67
% 84.87/28.67 % -------------------------------------------------
% 84.87/28.67 % User time : 27.468 s
% 84.87/28.67 % System time : 0.671 s
% 84.87/28.67 % Total time : 28.140 s
% 84.87/28.67 % Maximum resident set size: 5888 pages
% 84.87/28.67 % E exiting
%------------------------------------------------------------------------------