%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP053^1 : 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 : n020.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 0.23s 0.35s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 26 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 178 ( 8 ~; 2 |; 0 &; 167 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 4 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 17 ( 2 ^; 15 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
product_prod_nat_nat: $tType ).
thf(decl_sort2,type,
capacity: $tType ).
thf(decl_sort3,type,
nat: $tType ).
thf(decl_sort4,type,
list_P559422087at_nat: $tType ).
thf(decl_28,type,
min_dist_capacity: ( product_prod_nat_nat > capacity ) > nat > nat > nat ).
thf(decl_29,type,
one_one_nat: nat ).
thf(decl_30,type,
plus_plus_nat: nat > nat > nat ).
thf(decl_33,type,
size_s1990949619at_nat: list_P559422087at_nat > nat ).
thf(decl_50,type,
c: product_prod_nat_nat > capacity ).
thf(decl_51,type,
p: list_P559422087at_nat ).
thf(decl_52,type,
p1: list_P559422087at_nat ).
thf(decl_53,type,
p2: list_P559422087at_nat ).
thf(decl_55,type,
s: nat ).
thf(decl_56,type,
t: nat ).
thf(decl_57,type,
u: nat ).
thf(conj_0,conjecture,
( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VyGWLV3VNu/E---3.1_1498248.p',conj_0) ).
thf(fact_23_add_Ocommute,axiom,
( plus_plus_nat
= ( ^ [X13: nat,X14: nat] : ( plus_plus_nat @ X14 @ X13 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VyGWLV3VNu/E---3.1_1498248.p',fact_23_add_Ocommute) ).
thf(fact_2__092_060open_062min__dist_As_At_A_061_Alength_Ap1_A_L_A_I1_A_L_Alength_Ap2_J_A_092_060Longrightarrow_062_Amin__dist_Au_At_A_061_A1_A_L_Alength_Ap2_092_060close_062,axiom,
( ( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
=> ( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VyGWLV3VNu/E---3.1_1498248.p',fact_2__092_060open_062min__dist_As_At_A_061_Alength_Ap1_A_L_A_I1_A_L_Alength_Ap2_J_A_092_060Longrightarrow_062_Amin__dist_Au_At_A_061_A1_A_L_Alength_Ap2_092_060close_062) ).
thf(fact_0_MIN_H,axiom,
( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ one_one_nat ) @ ( size_s1990949619at_nat @ p2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VyGWLV3VNu/E---3.1_1498248.p',fact_0_MIN_H) ).
thf(fact_4_MIN,axiom,
( ( min_dist_capacity @ c @ s @ t )
= ( size_s1990949619at_nat @ p ) ),
file('/export/starexec/sandbox2/tmp/tmp.VyGWLV3VNu/E---3.1_1498248.p',fact_4_MIN) ).
thf(fact_22_add_Oleft__commute,axiom,
! [X7: nat,X6: nat,X8: nat] :
( ( plus_plus_nat @ X7 @ ( plus_plus_nat @ X6 @ X8 ) )
= ( plus_plus_nat @ X6 @ ( plus_plus_nat @ X7 @ X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VyGWLV3VNu/E---3.1_1498248.p',fact_22_add_Oleft__commute) ).
thf(c_0_6,negated_conjecture,
( ( min_dist_capacity @ c @ u @ t )
!= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_7,negated_conjecture,
( ( min_dist_capacity @ c @ u @ t )
!= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
thf(c_0_8,plain,
! [X1013: nat,X1014: nat] :
( ( plus_plus_nat @ X1013 @ X1014 )
= ( plus_plus_nat @ X1014 @ X1013 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_23_add_Ocommute])]) ).
thf(c_0_9,plain,
( ( ( min_dist_capacity @ c @ s @ t )
!= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) )
| ( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2__092_060open_062min__dist_As_At_A_061_Alength_Ap1_A_L_A_I1_A_L_Alength_Ap2_J_A_092_060Longrightarrow_062_Amin__dist_Au_At_A_061_A1_A_L_Alength_Ap2_092_060close_062])]) ).
thf(c_0_10,negated_conjecture,
( ( min_dist_capacity @ c @ u @ t )
!= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
( ( min_dist_capacity @ c @ s @ t )
= ( plus_plus_nat @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ one_one_nat ) @ ( size_s1990949619at_nat @ p2 ) ) ),
inference(split_conjunct,[status(thm)],[fact_0_MIN_H]) ).
thf(c_0_12,plain,
( ( min_dist_capacity @ c @ s @ t )
= ( size_s1990949619at_nat @ p ) ),
inference(split_conjunct,[status(thm)],[fact_4_MIN]) ).
thf(c_0_13,plain,
! [X1094: nat,X1095: nat] :
( ( plus_plus_nat @ X1094 @ X1095 )
= ( plus_plus_nat @ X1095 @ X1094 ) ),
inference(variable_rename,[status(thm)],[c_0_8]) ).
thf(c_0_14,plain,
( ( ( min_dist_capacity @ c @ u @ t )
= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) )
| ( ( min_dist_capacity @ c @ s @ t )
!= ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,negated_conjecture,
( ( min_dist_capacity @ c @ u @ t )
!= ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,plain,
! [X1091: nat,X1092: nat,X1093: nat] :
( ( plus_plus_nat @ X1091 @ ( plus_plus_nat @ X1092 @ X1093 ) )
= ( plus_plus_nat @ X1092 @ ( plus_plus_nat @ X1091 @ X1093 ) ) ),
inference(variable_rename,[status(thm)],[fact_22_add_Oleft__commute]) ).
thf(c_0_17,plain,
( ( plus_plus_nat @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ one_one_nat ) @ ( size_s1990949619at_nat @ p2 ) )
= ( size_s1990949619at_nat @ p ) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_18,plain,
! [X2: nat,X1: nat] :
( ( plus_plus_nat @ X1 @ X2 )
= ( plus_plus_nat @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,plain,
( ( plus_plus_nat @ ( size_s1990949619at_nat @ p1 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p2 ) ) )
!= ( size_s1990949619at_nat @ p ) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_12]),c_0_15]) ).
thf(c_0_20,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( plus_plus_nat @ X1 @ ( plus_plus_nat @ X2 @ X3 ) )
= ( plus_plus_nat @ X2 @ ( plus_plus_nat @ X1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_21,plain,
( ( plus_plus_nat @ ( size_s1990949619at_nat @ p2 ) @ ( plus_plus_nat @ one_one_nat @ ( size_s1990949619at_nat @ p1 ) ) )
= ( size_s1990949619at_nat @ p ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
thf(c_0_22,plain,
( ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( size_s1990949619at_nat @ p2 ) @ ( size_s1990949619at_nat @ p1 ) ) )
!= ( size_s1990949619at_nat @ p ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_18]) ).
thf(c_0_23,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_20]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP053^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n020.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 19:44:49 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.23/0.26 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.VyGWLV3VNu/E---3.1_1498248.p
% 0.23/0.35 % Version: 3.5.1-ho
% 0.23/0.35 % Preprocessing class: HSLSSMSMSSSNHSA.
% 0.23/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.35 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.35 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.23/0.35 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.23/0.35 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.35 % new_ho_10 with pid 1498261 completed with status 0
% 0.23/0.35 % Result found by new_ho_10
% 0.23/0.35 % Preprocessing class: HSLSSMSMSSSNHSA.
% 0.23/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.35 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.35 % No SInE strategy applied
% 0.23/0.35 % Search class: HGHSM-FSLM31-MHSFFSBC
% 0.23/0.35 % partial match(1): HGHSM-FSLM31-MHSFFSBN
% 0.23/0.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.35 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.35 % Starting new_ho_10 with 151s (1) cores
% 0.23/0.35 % Starting lpo4_lambdas_fix with 136s (1) cores
% 0.23/0.35 % Starting post_as_ho3 with 136s (1) cores
% 0.23/0.35 % Starting full_lambda_10 with 136s (1) cores
% 0.23/0.35 % new_ho_10 with pid 1498268 completed with status 0
% 0.23/0.35 % Result found by new_ho_10
% 0.23/0.35 % Preprocessing class: HSLSSMSMSSSNHSA.
% 0.23/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.35 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.35 % No SInE strategy applied
% 0.23/0.35 % Search class: HGHSM-FSLM31-MHSFFSBC
% 0.23/0.35 % partial match(1): HGHSM-FSLM31-MHSFFSBN
% 0.23/0.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.35 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.35 % Starting new_ho_10 with 151s (1) cores
% 0.23/0.35 % Preprocessing time : 0.008 s
% 0.23/0.35 % Presaturation interreduction done
% 0.23/0.35
% 0.23/0.35 % Proof found!
% 0.23/0.35 % SZS status Theorem
% 0.23/0.35 % SZS output start CNFRefutation
% See solution above
% 0.23/0.35 % Parsed axioms : 302
% 0.23/0.35 % Removed by relevancy pruning/SinE : 0
% 0.23/0.35 % Initial clauses : 474
% 0.23/0.35 % Removed in clause preprocessing : 69
% 0.23/0.35 % Initial clauses in saturation : 405
% 0.23/0.35 % Processed clauses : 189
% 0.23/0.35 % ...of these trivial : 3
% 0.23/0.35 % ...subsumed : 56
% 0.23/0.35 % ...remaining for further processing : 129
% 0.23/0.35 % Other redundant clauses eliminated : 27
% 0.23/0.35 % Clauses deleted for lack of memory : 0
% 0.23/0.35 % Backward-subsumed : 3
% 0.23/0.35 % Backward-rewritten : 7
% 0.23/0.35 % Generated clauses : 27
% 0.23/0.35 % ...of the previous two non-redundant : 17
% 0.23/0.35 % ...aggressively subsumed : 0
% 0.23/0.35 % Contextual simplify-reflections : 0
% 0.23/0.35 % Paramodulations : 0
% 0.23/0.35 % Factorizations : 0
% 0.23/0.35 % NegExts : 0
% 0.23/0.35 % Equation resolutions : 27
% 0.23/0.35 % Disequality decompositions : 0
% 0.23/0.35 % Total rewrite steps : 29
% 0.23/0.35 % ...of those cached : 11
% 0.23/0.35 % Propositional unsat checks : 0
% 0.23/0.35 % Propositional check models : 0
% 0.23/0.35 % Propositional check unsatisfiable : 0
% 0.23/0.35 % Propositional clauses : 0
% 0.23/0.35 % Propositional clauses after purity: 0
% 0.23/0.35 % Propositional unsat core size : 0
% 0.23/0.35 % Propositional preprocessing time : 0.000
% 0.23/0.35 % Propositional encoding time : 0.000
% 0.23/0.35 % Propositional solver time : 0.000
% 0.23/0.35 % Success case prop preproc time : 0.000
% 0.23/0.35 % Success case prop encoding time : 0.000
% 0.23/0.35 % Success case prop solver time : 0.000
% 0.23/0.35 % Current number of processed clauses : 92
% 0.23/0.35 % Positive orientable unit clauses : 33
% 0.23/0.35 % Positive unorientable unit clauses: 2
% 0.23/0.35 % Negative unit clauses : 6
% 0.23/0.35 % Non-unit-clauses : 51
% 0.23/0.35 % Current number of unprocessed clauses: 233
% 0.23/0.35 % ...number of literals in the above : 766
% 0.23/0.35 % Current number of archived formulas : 0
% 0.23/0.35 % Current number of archived clauses : 10
% 0.23/0.35 % Clause-clause subsumption calls (NU) : 814
% 0.23/0.35 % Rec. Clause-clause subsumption calls : 801
% 0.23/0.35 % Non-unit clause-clause subsumptions : 47
% 0.23/0.35 % Unit Clause-clause subsumption calls : 84
% 0.23/0.35 % Rewrite failures with RHS unbound : 0
% 0.23/0.35 % BW rewrite match attempts : 42
% 0.23/0.35 % BW rewrite match successes : 29
% 0.23/0.35 % Condensation attempts : 189
% 0.23/0.35 % Condensation successes : 0
% 0.23/0.35 % Termbank termtop insertions : 34445
% 0.23/0.35 % Search garbage collected termcells : 9442
% 0.23/0.35
% 0.23/0.35 % -------------------------------------------------
% 0.23/0.35 % User time : 0.043 s
% 0.23/0.35 % System time : 0.008 s
% 0.23/0.35 % Total time : 0.051 s
% 0.23/0.35 % Maximum resident set size: 5860 pages
% 0.23/0.35
% 0.23/0.35 % -------------------------------------------------
% 0.23/0.35 % User time : 0.095 s
% 0.23/0.35 % System time : 0.035 s
% 0.23/0.35 % Total time : 0.130 s
% 0.23/0.35 % Maximum resident set size: 5120 pages
% 0.23/0.35 % E exiting
%------------------------------------------------------------------------------