%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP048^1 : 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 : n010.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 08:05:22 AM UTC 2026
% Result : Theorem 1.16s 0.44s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 13 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 294 ( 20 ~; 14 |; 1 &; 252 @)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 40 ( 2 ^; 38 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
product_prod_nat_nat: $tType ).
thf(decl_sort2,type,
nat: $tType ).
thf(decl_sort3,type,
capacity: $tType ).
thf(decl_sort4,type,
list_P559422087at_nat: $tType ).
thf(decl_34,type,
min_dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat ).
thf(decl_37,type,
plus_plus_nat: nat > nat > nat ).
thf(decl_38,type,
size_s1990949619at_nat: list_P559422087at_nat > nat ).
thf(decl_40,type,
ord_less_nat: nat > nat > $o ).
thf(decl_41,type,
ord_less_eq_nat: nat > nat > $o ).
thf(decl_44,type,
c: product_prod_nat_nat > capacity ).
thf(decl_48,type,
p1a: list_P559422087at_nat ).
thf(decl_50,type,
p2_a: list_P559422087at_nat ).
thf(decl_52,type,
s: nat ).
thf(decl_53,type,
t: nat ).
thf(decl_55,type,
ua: nat ).
thf(conj_0,conjecture,
ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ),
file('/export/starexec/sandbox2/tmp/tmp.qzEIEOgEqR/E---3.1_3313106.p',conj_0) ).
thf(fact_75_add_Ocommute,axiom,
( plus_plus_nat
= ( ^ [X32: nat,X33: nat] : ( plus_plus_nat @ X33 @ X32 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qzEIEOgEqR/E---3.1_3313106.p',fact_75_add_Ocommute) ).
thf(fact_99_add__strict__mono,axiom,
! [X5: nat,X6: nat,X4: nat,X13: nat] :
( ( ord_less_nat @ X5 @ X6 )
=> ( ( ord_less_nat @ X4 @ X13 )
=> ( ord_less_nat @ ( plus_plus_nat @ X5 @ X4 ) @ ( plus_plus_nat @ X6 @ X13 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qzEIEOgEqR/E---3.1_3313106.p',fact_99_add__strict__mono) ).
thf(fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062,axiom,
( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( min_dist_capacity @ c @ ua @ t ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qzEIEOgEqR/E---3.1_3313106.p',fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062) ).
thf(fact_56_le__neq__implies__less,axiom,
! [X2: nat,X3: nat] :
( ( ord_less_eq_nat @ X2 @ X3 )
=> ( ( X2 != X3 )
=> ( ord_less_nat @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qzEIEOgEqR/E---3.1_3313106.p',fact_56_le__neq__implies__less) ).
thf(fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062,axiom,
ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( size_s1990949619at_nat @ p1a ),
file('/export/starexec/sandbox2/tmp/tmp.qzEIEOgEqR/E---3.1_3313106.p',fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062) ).
thf(fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062,axiom,
ord_less_eq_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( size_s1990949619at_nat @ p2_a ),
file('/export/starexec/sandbox2/tmp/tmp.qzEIEOgEqR/E---3.1_3313106.p',fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062) ).
thf(fact_3_nat__add__left__cancel__less,axiom,
! [X1: nat,X2: nat,X3: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ X1 @ X2 ) @ ( plus_plus_nat @ X1 @ X3 ) )
<=> ( ord_less_nat @ X2 @ X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.qzEIEOgEqR/E---3.1_3313106.p',fact_3_nat__add__left__cancel__less) ).
thf(c_0_8,negated_conjecture,
~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_9,plain,
! [X715: nat,X716: nat] :
( ( plus_plus_nat @ X715 @ X716 )
= ( plus_plus_nat @ X716 @ X715 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_75_add_Ocommute])]) ).
thf(c_0_10,negated_conjecture,
~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
thf(c_0_11,plain,
! [X991: nat,X992: nat] :
( ( plus_plus_nat @ X991 @ X992 )
= ( plus_plus_nat @ X992 @ X991 ) ),
inference(variable_rename,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) ),
inference(fof_nnf,[status(thm)],[c_0_10]) ).
thf(c_0_13,plain,
! [X1044: nat,X1045: nat,X1046: nat,X1047: nat] :
( ~ ( ord_less_nat @ X1044 @ X1045 )
| ~ ( ord_less_nat @ X1046 @ X1047 )
| ( ord_less_nat @ ( plus_plus_nat @ X1044 @ X1046 ) @ ( plus_plus_nat @ X1045 @ X1047 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_99_add__strict__mono])])]) ).
thf(c_0_14,plain,
( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( min_dist_capacity @ c @ ua @ t ) ) ),
inference(split_conjunct,[status(thm)],[fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062]) ).
thf(c_0_15,plain,
! [X2: nat,X1: nat] :
( ( plus_plus_nat @ X1 @ X2 )
= ( plus_plus_nat @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,negated_conjecture,
~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1a ) @ ( size_s1990949619at_nat @ p2_a ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,plain,
! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ X1 @ X3 ) @ ( plus_plus_nat @ X2 @ X4 ) )
| ~ ( ord_less_nat @ X1 @ X2 )
| ~ ( ord_less_nat @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,plain,
( ( plus_plus_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( min_dist_capacity @ c @ s @ ua ) )
= ( min_dist_capacity @ c @ s @ t ) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,plain,
! [X2: nat,X3: nat] :
( ( ord_less_eq_nat @ X2 @ X3 )
=> ( ( X2 != X3 )
=> ( ord_less_nat @ X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[fact_56_le__neq__implies__less]) ).
thf(c_0_20,negated_conjecture,
~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p2_a ) @ ( size_s1990949619at_nat @ p1a ) ) ),
inference(rw,[status(thm)],[c_0_16,c_0_15]) ).
thf(c_0_21,plain,
! [X2: nat,X1: nat] :
( ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ X1 @ X2 ) )
| ~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ X2 )
| ~ ( ord_less_nat @ ( min_dist_capacity @ c @ ua @ t ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_22,plain,
ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ ( size_s1990949619at_nat @ p1a ),
inference(split_conjunct,[status(thm)],[fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062]) ).
thf(c_0_23,plain,
! [X748: nat,X749: nat] :
( ~ ( ord_less_eq_nat @ X748 @ X749 )
| ( X748 = X749 )
| ( ord_less_nat @ X748 @ X749 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
thf(c_0_24,negated_conjecture,
~ ( ord_less_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( size_s1990949619at_nat @ p2_a ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
thf(c_0_25,plain,
! [X1: nat,X2: nat] :
( ( X1 = X2 )
| ( ord_less_nat @ X1 @ X2 )
| ~ ( ord_less_eq_nat @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_26,plain,
ord_less_eq_nat @ ( min_dist_capacity @ c @ ua @ t ) @ ( size_s1990949619at_nat @ p2_a ),
inference(split_conjunct,[status(thm)],[fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062]) ).
thf(c_0_27,plain,
! [X886: nat,X887: nat,X888: nat] :
( ( ~ ( ord_less_nat @ ( plus_plus_nat @ X886 @ X887 ) @ ( plus_plus_nat @ X886 @ X888 ) )
| ( ord_less_nat @ X887 @ X888 ) )
& ( ~ ( ord_less_nat @ X887 @ X888 )
| ( ord_less_nat @ ( plus_plus_nat @ X886 @ X887 ) @ ( plus_plus_nat @ X886 @ X888 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_3_nat__add__left__cancel__less])])]) ).
thf(c_0_28,negated_conjecture,
( ( min_dist_capacity @ c @ ua @ t )
= ( size_s1990949619at_nat @ p2_a ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
thf(c_0_29,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ X3 @ X1 ) @ ( plus_plus_nat @ X3 @ X2 ) )
| ~ ( ord_less_nat @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_30,plain,
( ( plus_plus_nat @ ( size_s1990949619at_nat @ p2_a ) @ ( min_dist_capacity @ c @ s @ ua ) )
= ( min_dist_capacity @ c @ s @ t ) ),
inference(rw,[status(thm)],[c_0_18,c_0_28]) ).
thf(c_0_31,plain,
! [X1: nat] :
( ( ord_less_nat @ ( min_dist_capacity @ c @ s @ t ) @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p2_a ) @ X1 ) )
| ~ ( ord_less_nat @ ( min_dist_capacity @ c @ s @ ua ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_31]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP048^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n010.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 19:42:18 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.23 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.qzEIEOgEqR/E---3.1_3313106.p
% 1.16/0.44 % Version: 3.5.1-ho
% 1.16/0.44 % Preprocessing class: HSLSSMSMSSMCHSA.
% 1.16/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.16/0.44 % Starting post_as_ho6 with 1500s (5) cores
% 1.16/0.44 % Starting post_as_ho8 with 300s (1) cores
% 1.16/0.44 % Starting new_bool_3 with 300s (1) cores
% 1.16/0.44 % Starting new_bool_1 with 300s (1) cores
% 1.16/0.44 % post_as_ho6 with pid 3313143 completed with status 0
% 1.16/0.44 % Result found by post_as_ho6
% 1.16/0.44 % Preprocessing class: HSLSSMSMSSMCHSA.
% 1.16/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.16/0.44 % Starting post_as_ho6 with 1500s (5) cores
% 1.16/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true))
% 1.16/0.44 % SinE strategy is GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true)
% 1.16/0.44 % Search class: HGHSM-FSLM32-SHSFFSBC
% 1.16/0.44 % partial match(1): HGHSM-FSLM32-MHSFFSBC
% 1.16/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.16/0.44 % Starting SubtermCWHack with 136s (1) cores
% 1.16/0.44 % Starting post_as_ho6 with 151s (1) cores
% 1.16/0.44 % Starting post_as_ho12 with 228s (1) cores
% 1.16/0.44 % Starting sh1 with 136s (1) cores
% 1.16/0.44 % Starting almost_fo_4 with 136s (1) cores
% 1.16/0.44 % post_as_ho6 with pid 3313154 completed with status 0
% 1.16/0.44 % Result found by post_as_ho6
% 1.16/0.44 % Preprocessing class: HSLSSMSMSSMCHSA.
% 1.16/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.16/0.44 % Starting post_as_ho6 with 1500s (5) cores
% 1.16/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true))
% 1.16/0.44 % SinE strategy is GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true)
% 1.16/0.44 % Search class: HGHSM-FSLM32-SHSFFSBC
% 1.16/0.44 % partial match(1): HGHSM-FSLM32-MHSFFSBC
% 1.16/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.16/0.44 % Starting SubtermCWHack with 136s (1) cores
% 1.16/0.44 % Starting post_as_ho6 with 151s (1) cores
% 1.16/0.44 % Preprocessing time : 0.007 s
% 1.16/0.44 % Presaturation interreduction done
% 1.16/0.44
% 1.16/0.44 % Proof found!
% 1.16/0.44 % SZS status Theorem
% 1.16/0.44 % SZS output start CNFRefutation
% See solution above
% 1.16/0.44 % Parsed axioms : 315
% 1.16/0.44 % Removed by relevancy pruning/SinE : 107
% 1.16/0.44 % Initial clauses : 364
% 1.16/0.44 % Removed in clause preprocessing : 17
% 1.16/0.44 % Initial clauses in saturation : 347
% 1.16/0.44 % Processed clauses : 920
% 1.16/0.44 % ...of these trivial : 28
% 1.16/0.44 % ...subsumed : 360
% 1.16/0.44 % ...remaining for further processing : 532
% 1.16/0.44 % Other redundant clauses eliminated : 81
% 1.16/0.44 % Clauses deleted for lack of memory : 0
% 1.16/0.44 % Backward-subsumed : 12
% 1.16/0.44 % Backward-rewritten : 32
% 1.16/0.44 % Generated clauses : 4454
% 1.16/0.44 % ...of the previous two non-redundant : 4202
% 1.16/0.44 % ...aggressively subsumed : 0
% 1.16/0.44 % Contextual simplify-reflections : 4
% 1.16/0.44 % Paramodulations : 4360
% 1.16/0.44 % Factorizations : 6
% 1.16/0.44 % NegExts : 0
% 1.16/0.44 % Equation resolutions : 86
% 1.16/0.44 % Disequality decompositions : 0
% 1.16/0.44 % Total rewrite steps : 619
% 1.16/0.44 % ...of those cached : 463
% 1.16/0.44 % Propositional unsat checks : 0
% 1.16/0.44 % Propositional check models : 0
% 1.16/0.44 % Propositional check unsatisfiable : 0
% 1.16/0.44 % Propositional clauses : 0
% 1.16/0.44 % Propositional clauses after purity: 0
% 1.16/0.44 % Propositional unsat core size : 0
% 1.16/0.44 % Propositional preprocessing time : 0.000
% 1.16/0.44 % Propositional encoding time : 0.000
% 1.16/0.44 % Propositional solver time : 0.000
% 1.16/0.44 % Success case prop preproc time : 0.000
% 1.16/0.44 % Success case prop encoding time : 0.000
% 1.16/0.44 % Success case prop solver time : 0.000
% 1.16/0.44 % Current number of processed clauses : 279
% 1.16/0.44 % Positive orientable unit clauses : 46
% 1.16/0.44 % Positive unorientable unit clauses: 2
% 1.16/0.44 % Negative unit clauses : 27
% 1.16/0.44 % Non-unit-clauses : 204
% 1.16/0.44 % Current number of unprocessed clauses: 3773
% 1.16/0.44 % ...number of literals in the above : 10087
% 1.16/0.44 % Current number of archived formulas : 0
% 1.16/0.44 % Current number of archived clauses : 200
% 1.16/0.44 % Clause-clause subsumption calls (NU) : 7117
% 1.16/0.44 % Rec. Clause-clause subsumption calls : 5825
% 1.16/0.44 % Non-unit clause-clause subsumptions : 265
% 1.16/0.44 % Unit Clause-clause subsumption calls : 544
% 1.16/0.44 % Rewrite failures with RHS unbound : 0
% 1.16/0.44 % BW rewrite match attempts : 77
% 1.16/0.44 % BW rewrite match successes : 43
% 1.16/0.44 % Condensation attempts : 920
% 1.16/0.44 % Condensation successes : 16
% 1.16/0.44 % Termbank termtop insertions : 99120
% 1.16/0.44 % Search garbage collected termcells : 8401
% 1.16/0.44
% 1.16/0.44 % -------------------------------------------------
% 1.16/0.44 % User time : 0.146 s
% 1.16/0.44 % System time : 0.009 s
% 1.16/0.44 % Total time : 0.155 s
% 1.16/0.44 % Maximum resident set size: 5356 pages
% 1.16/0.44
% 1.16/0.44 % -------------------------------------------------
% 1.16/0.44 % User time : 0.712 s
% 1.16/0.44 % System time : 0.053 s
% 1.16/0.44 % Total time : 0.765 s
% 1.16/0.44 % Maximum resident set size: 5376 pages
% 1.16/0.44 % E exiting
%------------------------------------------------------------------------------