%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP052^1 : 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 08:04:13 AM UTC 2026
% Result : Theorem 0.59s 0.45s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 9 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 135 ( 10 ~; 6 |; 1 &; 116 @)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 5 con; 0-5 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
product_prod_nat_nat: $tType ).
thf(decl_sort2,type,
capacity: $tType ).
thf(decl_sort3,type,
list_P559422087at_nat: $tType ).
thf(decl_sort4,type,
nat: $tType ).
thf(decl_sort5,type,
set_Pr1986765409at_nat: $tType ).
thf(decl_25,type,
augmen1090971539pacity: ( product_prod_nat_nat > capacity ) > nat > nat > ( product_prod_nat_nat > capacity ) > list_P559422087at_nat > $o ).
thf(decl_29,type,
isSimp1359852763pacity: ( product_prod_nat_nat > capacity ) > nat > list_P559422087at_nat > nat > $o ).
thf(decl_33,type,
inf_in586391887at_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(decl_34,type,
set_Pr2131844118at_nat: list_P559422087at_nat > set_Pr1986765409at_nat ).
thf(decl_52,type,
bot_bo2130386637at_nat: set_Pr1986765409at_nat ).
thf(decl_61,type,
converse_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
thf(decl_65,type,
residu203630698pacity: ( product_prod_nat_nat > capacity ) > ( product_prod_nat_nat > capacity ) > product_prod_nat_nat > capacity ).
thf(decl_70,type,
c: product_prod_nat_nat > capacity ).
thf(decl_71,type,
f: product_prod_nat_nat > capacity ).
thf(decl_72,type,
p: list_P559422087at_nat ).
thf(decl_73,type,
s: nat ).
thf(decl_74,type,
t: nat ).
thf(conj_1,conjecture,
( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
= bot_bo2130386637at_nat ),
file('/export/starexec/sandbox/tmp/tmp.9FTNwvcdoa/E---3.1_3821822.p',conj_1) ).
thf(fact_57_Graph_OisSPath__nt__parallel__pf,axiom,
! [X51: product_prod_nat_nat > capacity,X1: nat,X2: list_P559422087at_nat,X3: nat] :
( ( isSimp1359852763pacity @ X51 @ X1 @ X2 @ X3 )
=> ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ X2 ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ X2 ) ) )
= bot_bo2130386637at_nat ) ),
file('/export/starexec/sandbox/tmp/tmp.9FTNwvcdoa/E---3.1_3821822.p',fact_57_Graph_OisSPath__nt__parallel__pf) ).
thf(fact_5_isAugmentingPath__def,axiom,
! [X2: list_P559422087at_nat] :
( ( augmen1090971539pacity @ c @ s @ t @ f @ X2 )
<=> ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ X2 @ t ) ),
file('/export/starexec/sandbox/tmp/tmp.9FTNwvcdoa/E---3.1_3821822.p',fact_5_isAugmentingPath__def) ).
thf(conj_0,hypothesis,
augmen1090971539pacity @ c @ s @ t @ f @ p,
file('/export/starexec/sandbox/tmp/tmp.9FTNwvcdoa/E---3.1_3821822.p',conj_0) ).
thf(c_0_4,negated_conjecture,
( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
!= bot_bo2130386637at_nat ),
inference(assume_negation,[status(cth)],[conj_1]) ).
thf(c_0_5,negated_conjecture,
( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
!= bot_bo2130386637at_nat ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_6,plain,
! [X1232: product_prod_nat_nat > capacity,X1233: nat,X1234: list_P559422087at_nat,X1235: nat] :
( ~ ( isSimp1359852763pacity @ X1232 @ X1233 @ X1234 @ X1235 )
| ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ X1234 ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ X1234 ) ) )
= bot_bo2130386637at_nat ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_57_Graph_OisSPath__nt__parallel__pf])])]) ).
thf(c_0_7,plain,
! [X1149: list_P559422087at_nat] :
( ( ~ ( augmen1090971539pacity @ c @ s @ t @ f @ X1149 )
| ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ X1149 @ t ) )
& ( ~ ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ X1149 @ t )
| ( augmen1090971539pacity @ c @ s @ t @ f @ X1149 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_isAugmentingPath__def])])]) ).
thf(c_0_8,negated_conjecture,
( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
!= bot_bo2130386637at_nat ),
inference(fof_nnf,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
! [X1: nat,X2: list_P559422087at_nat,X37: product_prod_nat_nat > capacity,X3: nat] :
( ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ X2 ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ X2 ) ) )
= bot_bo2130386637at_nat )
| ~ ( isSimp1359852763pacity @ X37 @ X1 @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
! [X2: list_P559422087at_nat] :
( ( isSimp1359852763pacity @ ( residu203630698pacity @ c @ f ) @ s @ X2 @ t )
| ~ ( augmen1090971539pacity @ c @ s @ t @ f @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ p ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ p ) ) )
!= bot_bo2130386637at_nat ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X2: list_P559422087at_nat] :
( ( ( inf_in586391887at_nat @ ( set_Pr2131844118at_nat @ X2 ) @ ( converse_nat_nat @ ( set_Pr2131844118at_nat @ X2 ) ) )
= bot_bo2130386637at_nat )
| ~ ( augmen1090971539pacity @ c @ s @ t @ f @ X2 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,hypothesis,
augmen1090971539pacity @ c @ s @ t @ f @ p,
inference(split_conjunct,[status(thm)],[conj_0]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP052^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 19:41:41 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.21/0.28 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.9FTNwvcdoa/E---3.1_3821822.p
% 0.59/0.45 % Version: 3.5.1-ho
% 0.59/0.45 % Preprocessing class: HSLSSMSSSSMNHSA.
% 0.59/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.45 % Starting sh1 with 1500s (5) cores
% 0.59/0.45 % Starting new_ho_8 with 300s (1) cores
% 0.59/0.45 % Starting new_ho_11 with 300s (1) cores
% 0.59/0.45 % Starting sh5l with 300s (1) cores
% 0.59/0.45 % sh1 with pid 3821835 completed with status 0
% 0.59/0.45 % Result found by sh1
% 0.59/0.45 % Preprocessing class: HSLSSMSSSSMNHSA.
% 0.59/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.45 % Starting sh1 with 1500s (5) cores
% 0.59/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.59/0.45 % No SInE strategy applied
% 0.59/0.45 % Search class: HGHSM-FSLM32-MHSFFFBN
% 0.59/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.59/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.59/0.45 % Starting sh1 with 151s (1) cores
% 0.59/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.59/0.45 % Starting full_lambda_10 with 136s (1) cores
% 0.59/0.45 % Starting pre_casc_5 with 136s (1) cores
% 0.59/0.45 % sh1 with pid 3821845 completed with status 0
% 0.59/0.45 % Result found by sh1
% 0.59/0.45 % Preprocessing class: HSLSSMSSSSMNHSA.
% 0.59/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.45 % Starting sh1 with 1500s (5) cores
% 0.59/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.59/0.45 % No SInE strategy applied
% 0.59/0.45 % Search class: HGHSM-FSLM32-MHSFFFBN
% 0.59/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.59/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.59/0.45 % Starting sh1 with 151s (1) cores
% 0.59/0.45 % Preprocessing time : 0.011 s
% 0.59/0.45
% 0.59/0.45 % Proof found!
% 0.59/0.45 % SZS status Theorem
% 0.59/0.45 % SZS output start CNFRefutation
% See solution above
% 0.59/0.45 % Parsed axioms : 338
% 0.59/0.45 % Removed by relevancy pruning/SinE : 0
% 0.59/0.45 % Initial clauses : 524
% 0.59/0.45 % Removed in clause preprocessing : 81
% 0.59/0.45 % Initial clauses in saturation : 443
% 0.59/0.45 % Processed clauses : 689
% 0.59/0.45 % ...of these trivial : 28
% 0.59/0.45 % ...subsumed : 269
% 0.59/0.45 % ...remaining for further processing : 392
% 0.59/0.45 % Other redundant clauses eliminated : 86
% 0.59/0.45 % Clauses deleted for lack of memory : 0
% 0.59/0.45 % Backward-subsumed : 22
% 0.59/0.45 % Backward-rewritten : 1
% 0.59/0.45 % Generated clauses : 2074
% 0.59/0.45 % ...of the previous two non-redundant : 1646
% 0.59/0.45 % ...aggressively subsumed : 0
% 0.59/0.45 % Contextual simplify-reflections : 2
% 0.59/0.45 % Paramodulations : 1758
% 0.59/0.45 % Factorizations : 8
% 0.59/0.45 % NegExts : 13
% 0.59/0.45 % Equation resolutions : 100
% 0.59/0.45 % Disequality decompositions : 0
% 0.59/0.45 % Total rewrite steps : 655
% 0.59/0.45 % ...of those cached : 501
% 0.59/0.45 % Propositional unsat checks : 0
% 0.59/0.45 % Propositional check models : 0
% 0.59/0.45 % Propositional check unsatisfiable : 0
% 0.59/0.45 % Propositional clauses : 0
% 0.59/0.45 % Propositional clauses after purity: 0
% 0.59/0.45 % Propositional unsat core size : 0
% 0.59/0.45 % Propositional preprocessing time : 0.000
% 0.59/0.45 % Propositional encoding time : 0.000
% 0.59/0.45 % Propositional solver time : 0.000
% 0.59/0.45 % Success case prop preproc time : 0.000
% 0.59/0.45 % Success case prop encoding time : 0.000
% 0.59/0.45 % Success case prop solver time : 0.000
% 0.59/0.45 % Current number of processed clauses : 336
% 0.59/0.45 % Positive orientable unit clauses : 55
% 0.59/0.45 % Positive unorientable unit clauses: 2
% 0.59/0.45 % Negative unit clauses : 14
% 0.59/0.45 % Non-unit-clauses : 265
% 0.59/0.45 % Current number of unprocessed clauses: 1345
% 0.59/0.45 % ...number of literals in the above : 4341
% 0.59/0.45 % Current number of archived formulas : 0
% 0.59/0.45 % Current number of archived clauses : 33
% 0.59/0.45 % Clause-clause subsumption calls (NU) : 23455
% 0.59/0.45 % Rec. Clause-clause subsumption calls : 13215
% 0.59/0.45 % Non-unit clause-clause subsumptions : 238
% 0.59/0.45 % Unit Clause-clause subsumption calls : 1421
% 0.59/0.45 % Rewrite failures with RHS unbound : 0
% 0.59/0.45 % BW rewrite match attempts : 77
% 0.59/0.45 % BW rewrite match successes : 13
% 0.59/0.45 % Condensation attempts : 0
% 0.59/0.45 % Condensation successes : 0
% 0.59/0.45 % Termbank termtop insertions : 61487
% 0.59/0.45 % Search garbage collected termcells : 9464
% 0.59/0.45
% 0.59/0.45 % -------------------------------------------------
% 0.59/0.45 % User time : 0.139 s
% 0.59/0.45 % System time : 0.010 s
% 0.59/0.45 % Total time : 0.149 s
% 0.59/0.45 % Maximum resident set size: 6032 pages
% 0.59/0.45
% 0.59/0.45 % -------------------------------------------------
% 0.59/0.45 % User time : 0.511 s
% 0.59/0.45 % System time : 0.056 s
% 0.59/0.45 % Total time : 0.568 s
% 0.59/0.45 % Maximum resident set size: 5376 pages
% 0.59/0.45 % E exiting
%------------------------------------------------------------------------------