%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP051^1 : 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 : n012.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 08:04:12 AM UTC 2026
% Result : ContradictoryAxioms 0.08s 0.20s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 13 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 125 ( 15 ~; 9 |; 4 &; 94 @)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 18 ( 2 ^; 16 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
product_prod_nat_nat: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_sort3,type,
b: $tType ).
thf(decl_sort4,type,
nat: $tType ).
thf(decl_sort5,type,
list_P559422087at_nat: $tType ).
thf(decl_61,type,
min_dist_a: ( product_prod_nat_nat > a ) > nat > nat > nat ).
thf(decl_62,type,
min_dist_b: ( product_prod_nat_nat > b ) > nat > nat > nat ).
thf(decl_69,type,
size_s1990949619at_nat: list_P559422087at_nat > nat ).
thf(decl_70,type,
ord_less_nat: nat > nat > $o ).
thf(decl_73,type,
ord_less_eq_nat: nat > nat > $o ).
thf(decl_87,type,
c: product_prod_nat_nat > a ).
thf(decl_88,type,
c2: product_prod_nat_nat > b ).
thf(decl_90,type,
p: list_P559422087at_nat ).
thf(decl_91,type,
p2: list_P559422087at_nat ).
thf(decl_92,type,
s: nat ).
thf(decl_93,type,
t: nat ).
thf(fact_103_nat__less__le,axiom,
( ord_less_nat
= ( ^ [X69: nat,X70: nat] :
( ( ord_less_eq_nat @ X69 @ X70 )
& ( X69 != X70 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bhDAb2uP5H/E---3.1_587588.p',fact_103_nat__less__le) ).
thf(fact_6_SHORTER,axiom,
ord_less_nat @ ( min_dist_b @ c2 @ s @ t ) @ ( min_dist_a @ c @ s @ t ),
file('/export/starexec/sandbox/tmp/tmp.bhDAb2uP5H/E---3.1_587588.p',fact_6_SHORTER) ).
thf(fact_2_LENP_H,axiom,
( ( size_s1990949619at_nat @ p2 )
= ( min_dist_b @ c2 @ s @ t ) ),
file('/export/starexec/sandbox/tmp/tmp.bhDAb2uP5H/E---3.1_587588.p',fact_2_LENP_H) ).
thf(fact_1_LENP,axiom,
( ( size_s1990949619at_nat @ p )
= ( min_dist_a @ c @ s @ t ) ),
file('/export/starexec/sandbox/tmp/tmp.bhDAb2uP5H/E---3.1_587588.p',fact_1_LENP) ).
thf(fact_96_le__antisym,axiom,
! [X62: nat,X47: nat] :
( ( ord_less_eq_nat @ X62 @ X47 )
=> ( ( ord_less_eq_nat @ X47 @ X62 )
=> ( X62 = X47 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bhDAb2uP5H/E---3.1_587588.p',fact_96_le__antisym) ).
thf(fact_13__092_060open_062length_Ap_A_060_Alength_Ap_H_092_060close_062,axiom,
ord_less_nat @ ( size_s1990949619at_nat @ p ) @ ( size_s1990949619at_nat @ p2 ),
file('/export/starexec/sandbox/tmp/tmp.bhDAb2uP5H/E---3.1_587588.p',fact_13__092_060open_062length_Ap_A_060_Alength_Ap_H_092_060close_062) ).
thf(fact_122_less__not__refl,axiom,
! [X47: nat] :
~ ( ord_less_nat @ X47 @ X47 ),
file('/export/starexec/sandbox/tmp/tmp.bhDAb2uP5H/E---3.1_587588.p',fact_122_less__not__refl) ).
thf(c_0_7,plain,
! [X874: nat,X875: nat] :
( ( ord_less_nat @ X874 @ X875 )
<=> ( ( ord_less_eq_nat @ X874 @ X875 )
& ( X874 != X875 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_103_nat__less__le])])]) ).
thf(c_0_8,plain,
! [X1111: nat,X1112: nat] :
( ( ( ord_less_eq_nat @ X1111 @ X1112 )
| ~ ( ord_less_nat @ X1111 @ X1112 ) )
& ( ( X1111 != X1112 )
| ~ ( ord_less_nat @ X1111 @ X1112 ) )
& ( ~ ( ord_less_eq_nat @ X1111 @ X1112 )
| ( X1111 = X1112 )
| ( ord_less_nat @ X1111 @ X1112 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
thf(c_0_9,plain,
ord_less_nat @ ( min_dist_b @ c2 @ s @ t ) @ ( min_dist_a @ c @ s @ t ),
inference(split_conjunct,[status(thm)],[fact_6_SHORTER]) ).
thf(c_0_10,plain,
( ( size_s1990949619at_nat @ p2 )
= ( min_dist_b @ c2 @ s @ t ) ),
inference(split_conjunct,[status(thm)],[fact_2_LENP_H]) ).
thf(c_0_11,plain,
( ( size_s1990949619at_nat @ p )
= ( min_dist_a @ c @ s @ t ) ),
inference(split_conjunct,[status(thm)],[fact_1_LENP]) ).
thf(c_0_12,plain,
! [X1097: nat,X1098: nat] :
( ~ ( ord_less_eq_nat @ X1097 @ X1098 )
| ~ ( ord_less_eq_nat @ X1098 @ X1097 )
| ( X1097 = X1098 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_96_le__antisym])])]) ).
thf(c_0_13,plain,
! [X5: nat,X6: nat] :
( ( ord_less_eq_nat @ X5 @ X6 )
| ~ ( ord_less_nat @ X5 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,plain,
ord_less_nat @ ( size_s1990949619at_nat @ p2 ) @ ( size_s1990949619at_nat @ p ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
thf(c_0_15,plain,
ord_less_nat @ ( size_s1990949619at_nat @ p ) @ ( size_s1990949619at_nat @ p2 ),
inference(split_conjunct,[status(thm)],[fact_13__092_060open_062length_Ap_A_060_Alength_Ap_H_092_060close_062]) ).
thf(c_0_16,plain,
! [X47: nat] :
~ ( ord_less_nat @ X47 @ X47 ),
inference(fof_simplification,[status(thm)],[fact_122_less__not__refl]) ).
thf(c_0_17,plain,
! [X6: nat,X5: nat] :
( ( X5 = X6 )
| ~ ( ord_less_eq_nat @ X5 @ X6 )
| ~ ( ord_less_eq_nat @ X6 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,plain,
ord_less_eq_nat @ ( size_s1990949619at_nat @ p2 ) @ ( size_s1990949619at_nat @ p ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_19,plain,
ord_less_eq_nat @ ( size_s1990949619at_nat @ p ) @ ( size_s1990949619at_nat @ p2 ),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
thf(c_0_20,plain,
! [X1193: nat] :
~ ( ord_less_nat @ X1193 @ X1193 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_16])]) ).
thf(c_0_21,plain,
( ( size_s1990949619at_nat @ p2 )
= ( size_s1990949619at_nat @ p ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
thf(c_0_22,plain,
! [X5: nat] :
~ ( ord_less_nat @ X5 @ X5 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_23,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_21]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP051^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 19:43:18 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.15 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.bhDAb2uP5H/E---3.1_587588.p
% 0.08/0.20 % Version: 3.5.1-ho
% 0.08/0.20 % Preprocessing class: HSLSSMSSSSMNHFA.
% 0.08/0.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting pre_casc_2 with 1500s (5) cores
% 0.08/0.20 % Starting sh3 with 300s (1) cores
% 0.08/0.20 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.08/0.20 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.20 % new_bool_3 with pid 587604 completed with status 9
% 0.08/0.20 % new_ho_10_cnf2 with pid 587603 completed with status 0
% 0.08/0.20 % Result found by new_ho_10_cnf2
% 0.08/0.20 % Preprocessing class: HSLSSMSSSSMNHFA.
% 0.08/0.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting pre_casc_2 with 1500s (5) cores
% 0.08/0.20 % Starting sh3 with 300s (1) cores
% 0.08/0.20 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.08/0.20 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.20 % No SInE strategy applied
% 0.08/0.20 % Search class: HGHSM-FSLM32-SHFFFSBN
% 0.08/0.20 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.20 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.20 % SubtermCWHack with pid 587621 completed with status 0
% 0.08/0.20 % Result found by SubtermCWHack
% 0.08/0.20 % Preprocessing class: HSLSSMSSSSMNHFA.
% 0.08/0.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.20 % Starting pre_casc_2 with 1500s (5) cores
% 0.08/0.20 % Starting sh3 with 300s (1) cores
% 0.08/0.20 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.08/0.20 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.20 % No SInE strategy applied
% 0.08/0.20 % Search class: HGHSM-FSLM32-SHFFFSBN
% 0.08/0.20 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.20 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.20 % Preprocessing time : 0.004 s
% 0.08/0.20
% 0.08/0.20 % Proof found!
% 0.08/0.20 % SZS status ContradictoryAxioms
% 0.08/0.20 % SZS output start CNFRefutation
% See solution above
% 0.08/0.20 % Parsed axioms : 430
% 0.08/0.20 % Removed by relevancy pruning/SinE : 0
% 0.08/0.20 % Initial clauses : 590
% 0.08/0.20 % Removed in clause preprocessing : 116
% 0.08/0.20 % Initial clauses in saturation : 474
% 0.08/0.20 % Processed clauses : 402
% 0.08/0.20 % ...of these trivial : 22
% 0.08/0.20 % ...subsumed : 94
% 0.08/0.20 % ...remaining for further processing : 286
% 0.08/0.20 % Other redundant clauses eliminated : 26
% 0.08/0.20 % Clauses deleted for lack of memory : 0
% 0.08/0.20 % Backward-subsumed : 2
% 0.08/0.20 % Backward-rewritten : 40
% 0.08/0.20 % Generated clauses : 601
% 0.08/0.20 % ...of the previous two non-redundant : 474
% 0.08/0.20 % ...aggressively subsumed : 0
% 0.08/0.20 % Contextual simplify-reflections : 2
% 0.08/0.20 % Paramodulations : 565
% 0.08/0.20 % Factorizations : 4
% 0.08/0.20 % NegExts : 0
% 0.08/0.20 % Equation resolutions : 26
% 0.08/0.20 % Disequality decompositions : 0
% 0.08/0.20 % Total rewrite steps : 196
% 0.08/0.20 % ...of those cached : 129
% 0.08/0.20 % Propositional unsat checks : 0
% 0.08/0.20 % Propositional check models : 0
% 0.08/0.20 % Propositional check unsatisfiable : 0
% 0.08/0.20 % Propositional clauses : 0
% 0.08/0.20 % Propositional clauses after purity: 0
% 0.08/0.20 % Propositional unsat core size : 0
% 0.08/0.20 % Propositional preprocessing time : 0.000
% 0.08/0.20 % Propositional encoding time : 0.000
% 0.08/0.20 % Propositional solver time : 0.000
% 0.08/0.20 % Success case prop preproc time : 0.000
% 0.08/0.20 % Success case prop encoding time : 0.000
% 0.08/0.20 % Success case prop solver time : 0.000
% 0.08/0.20 % Current number of processed clauses : 216
% 0.08/0.20 % Positive orientable unit clauses : 60
% 0.08/0.20 % Positive unorientable unit clauses: 0
% 0.08/0.20 % Negative unit clauses : 2
% 0.08/0.20 % Non-unit-clauses : 154
% 0.08/0.20 % Current number of unprocessed clauses: 518
% 0.08/0.20 % ...number of literals in the above : 1502
% 0.08/0.20 % Current number of archived formulas : 0
% 0.08/0.20 % Current number of archived clauses : 44
% 0.08/0.20 % Clause-clause subsumption calls (NU) : 5705
% 0.08/0.20 % Rec. Clause-clause subsumption calls : 5085
% 0.08/0.20 % Non-unit clause-clause subsumptions : 74
% 0.08/0.20 % Unit Clause-clause subsumption calls : 221
% 0.08/0.20 % Rewrite failures with RHS unbound : 0
% 0.08/0.20 % BW rewrite match attempts : 29
% 0.08/0.20 % BW rewrite match successes : 19
% 0.08/0.20 % Condensation attempts : 0
% 0.08/0.20 % Condensation successes : 0
% 0.08/0.20 % Termbank termtop insertions : 45626
% 0.08/0.20 % Search garbage collected termcells : 10029
% 0.08/0.20
% 0.08/0.20 % -------------------------------------------------
% 0.08/0.20 % User time : 0.027 s
% 0.08/0.20 % System time : 0.010 s
% 0.08/0.20 % Total time : 0.038 s
% 0.08/0.20 % Maximum resident set size: 5988 pages
% 0.08/0.20
% 0.08/0.20 % -------------------------------------------------
% 0.08/0.20 % User time : 0.041 s
% 0.08/0.20 % System time : 0.027 s
% 0.08/0.20 % Total time : 0.068 s
% 0.08/0.20 % Maximum resident set size: 5376 pages
% 0.08/0.20 % E exiting
%------------------------------------------------------------------------------