%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP103^1 : 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 : n004.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 08:04:22 AM UTC 2026
% Result : Theorem 0.22s 0.35s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 31 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 232 ( 32 ~; 17 |; 2 &; 173 @)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 50 ( 2 ^; 48 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
list_a: $tType ).
thf(decl_23,type,
times_times_nat: nat > nat > nat ).
thf(decl_24,type,
zero_zero_nat: nat ).
thf(decl_29,type,
suc: nat > nat ).
thf(decl_34,type,
size_size_list_a: list_a > nat ).
thf(decl_35,type,
ord_less_nat: nat > nat > $o ).
thf(decl_37,type,
divide_divide_nat: nat > nat > nat ).
thf(decl_38,type,
k: nat ).
thf(decl_39,type,
n: nat ).
thf(decl_40,type,
xs: list_a ).
thf(conj_2,conjecture,
ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ),
file('/export/starexec/sandbox/tmp/tmp.PGlt0NV4r9/E---3.1_1757087.p',conj_2) ).
thf(fact_133_mult_Ocommute,axiom,
( times_times_nat
= ( ^ [X40: nat,X41: nat] : ( times_times_nat @ X41 @ X40 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PGlt0NV4r9/E---3.1_1757087.p',fact_133_mult_Ocommute) ).
thf(fact_93_Euclidean__Division_Oless__mult__imp__div__less,axiom,
! [X2: nat,X27: nat,X1: nat] :
( ( ord_less_nat @ X2 @ ( times_times_nat @ X27 @ X1 ) )
=> ( ord_less_nat @ ( divide_divide_nat @ X2 @ X1 ) @ X27 ) ),
file('/export/starexec/sandbox/tmp/tmp.PGlt0NV4r9/E---3.1_1757087.p',fact_93_Euclidean__Division_Oless__mult__imp__div__less) ).
thf(fact_29_linorder__neqE__nat,axiom,
! [X11: nat,X12: nat] :
( ( X11 != X12 )
=> ( ~ ( ord_less_nat @ X11 @ X12 )
=> ( ord_less_nat @ X12 @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PGlt0NV4r9/E---3.1_1757087.p',fact_29_linorder__neqE__nat) ).
thf(fact_32_less__irrefl__nat,axiom,
! [X1: nat] :
~ ( ord_less_nat @ X1 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.PGlt0NV4r9/E---3.1_1757087.p',fact_32_less__irrefl__nat) ).
thf(conj_0,hypothesis,
( ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k )
= ( suc @ n ) ),
file('/export/starexec/sandbox/tmp/tmp.PGlt0NV4r9/E---3.1_1757087.p',conj_0) ).
thf(fact_68_less__Suc__eq,axiom,
! [X2: nat,X1: nat] :
( ( ord_less_nat @ X2 @ ( suc @ X1 ) )
<=> ( ( ord_less_nat @ X2 @ X1 )
| ( X2 = X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PGlt0NV4r9/E---3.1_1757087.p',fact_68_less__Suc__eq) ).
thf(fact_99_nonzero__mult__div__cancel__left,axiom,
! [X8: nat,X10: nat] :
( ( X8 != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ X8 @ X10 ) @ X8 )
= X10 ) ),
file('/export/starexec/sandbox/tmp/tmp.PGlt0NV4r9/E---3.1_1757087.p',fact_99_nonzero__mult__div__cancel__left) ).
thf(fact_27_n__not__Suc__n,axiom,
! [X1: nat] :
( X1
!= ( suc @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.PGlt0NV4r9/E---3.1_1757087.p',fact_27_n__not__Suc__n) ).
thf(conj_1,hypothesis,
k != zero_zero_nat,
file('/export/starexec/sandbox/tmp/tmp.PGlt0NV4r9/E---3.1_1757087.p',conj_1) ).
thf(c_0_10,negated_conjecture,
~ ( ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ) ),
inference(assume_negation,[status(cth)],[conj_2]) ).
thf(c_0_11,negated_conjecture,
~ ( ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
thf(c_0_12,plain,
! [X461: nat,X462: nat] :
( ( times_times_nat @ X461 @ X462 )
= ( times_times_nat @ X462 @ X461 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_133_mult_Ocommute])]) ).
thf(c_0_13,plain,
! [X715: nat,X716: nat,X717: nat] :
( ~ ( ord_less_nat @ X715 @ ( times_times_nat @ X716 @ X717 ) )
| ( ord_less_nat @ ( divide_divide_nat @ X715 @ X717 ) @ X716 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_93_Euclidean__Division_Oless__mult__imp__div__less])])]) ).
thf(c_0_14,negated_conjecture,
~ ( ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ) ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
! [X801: nat,X802: nat] :
( ( times_times_nat @ X801 @ X802 )
= ( times_times_nat @ X802 @ X801 ) ),
inference(variable_rename,[status(thm)],[c_0_12]) ).
thf(c_0_16,plain,
! [X11: nat,X12: nat] :
( ( X11 != X12 )
=> ( ~ ( ord_less_nat @ X11 @ X12 )
=> ( ord_less_nat @ X12 @ X11 ) ) ),
inference(fof_simplification,[status(thm)],[fact_29_linorder__neqE__nat]) ).
thf(c_0_17,plain,
! [X1: nat] :
~ ( ord_less_nat @ X1 @ X1 ),
inference(fof_simplification,[status(thm)],[fact_32_less__irrefl__nat]) ).
thf(c_0_18,plain,
! [X1: nat,X2: nat,X3: nat] :
( ( ord_less_nat @ ( divide_divide_nat @ X1 @ X3 ) @ X2 )
| ~ ( ord_less_nat @ X1 @ ( times_times_nat @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,hypothesis,
( ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k )
= ( suc @ n ) ),
inference(split_conjunct,[status(thm)],[conj_0]) ).
thf(c_0_20,negated_conjecture,
~ ( ord_less_nat @ ( times_times_nat @ n @ k ) @ ( size_size_list_a @ xs ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_21,plain,
! [X2: nat,X1: nat] :
( ( times_times_nat @ X1 @ X2 )
= ( times_times_nat @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_22,plain,
! [X528: nat,X529: nat] :
( ( X528 = X529 )
| ( ord_less_nat @ X528 @ X529 )
| ( ord_less_nat @ X529 @ X528 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])]) ).
thf(c_0_23,plain,
! [X538: nat] :
~ ( ord_less_nat @ X538 @ X538 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_17])]) ).
thf(c_0_24,plain,
! [X626: nat,X627: nat] :
( ( ~ ( ord_less_nat @ X626 @ ( suc @ X627 ) )
| ( ord_less_nat @ X626 @ X627 )
| ( X626 = X627 ) )
& ( ~ ( ord_less_nat @ X626 @ X627 )
| ( ord_less_nat @ X626 @ ( suc @ X627 ) ) )
& ( ( X626 != X627 )
| ( ord_less_nat @ X626 @ ( suc @ X627 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_68_less__Suc__eq])])])]) ).
thf(c_0_25,plain,
! [X8: nat,X10: nat] :
( ( X8 != zero_zero_nat )
=> ( ( divide_divide_nat @ ( times_times_nat @ X8 @ X10 ) @ X8 )
= X10 ) ),
inference(fof_simplification,[status(thm)],[fact_99_nonzero__mult__div__cancel__left]) ).
thf(c_0_26,hypothesis,
! [X1: nat] :
( ( ord_less_nat @ ( suc @ n ) @ X1 )
| ~ ( ord_less_nat @ ( size_size_list_a @ xs ) @ ( times_times_nat @ X1 @ k ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_27,negated_conjecture,
~ ( ord_less_nat @ ( times_times_nat @ k @ n ) @ ( size_size_list_a @ xs ) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_28,plain,
! [X2: nat,X1: nat] :
( ( X1 = X2 )
| ( ord_less_nat @ X1 @ X2 )
| ( ord_less_nat @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_29,plain,
! [X1: nat] :
~ ( ord_less_nat @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_30,plain,
! [X1: nat,X2: nat] :
( ( ord_less_nat @ X1 @ ( suc @ X2 ) )
| ~ ( ord_less_nat @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_31,plain,
! [X1: nat] :
( X1
!= ( suc @ X1 ) ),
inference(fof_simplification,[status(thm)],[fact_27_n__not__Suc__n]) ).
thf(c_0_32,hypothesis,
k != zero_zero_nat,
inference(fof_simplification,[status(thm)],[conj_1]) ).
thf(c_0_33,plain,
! [X729: nat,X730: nat] :
( ( X729 = zero_zero_nat )
| ( ( divide_divide_nat @ ( times_times_nat @ X729 @ X730 ) @ X729 )
= X730 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).
thf(c_0_34,hypothesis,
! [X1: nat] :
( ( ord_less_nat @ ( suc @ n ) @ X1 )
| ~ ( ord_less_nat @ ( size_size_list_a @ xs ) @ ( times_times_nat @ k @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
thf(c_0_35,negated_conjecture,
( ( ( times_times_nat @ k @ n )
= ( size_size_list_a @ xs ) )
| ( ord_less_nat @ ( size_size_list_a @ xs ) @ ( times_times_nat @ k @ n ) ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_36,plain,
! [X1: nat] :
~ ( ord_less_nat @ ( suc @ X1 ) @ X1 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_37,plain,
! [X525: nat] :
( X525
!= ( suc @ X525 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_31])]) ).
thf(c_0_38,hypothesis,
k != zero_zero_nat,
inference(fof_nnf,[status(thm)],[c_0_32]) ).
thf(c_0_39,plain,
! [X1: nat,X2: nat] :
( ( X1 = zero_zero_nat )
| ( ( divide_divide_nat @ ( times_times_nat @ X1 @ X2 ) @ X1 )
= X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_40,negated_conjecture,
( ( times_times_nat @ k @ n )
= ( size_size_list_a @ xs ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
thf(c_0_41,plain,
! [X1: nat] :
( X1
!= ( suc @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_42,hypothesis,
k != zero_zero_nat,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_19]),c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP103^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n004.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 19:53:52 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.25 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.PGlt0NV4r9/E---3.1_1757087.p
% 0.22/0.35 % Version: 3.5.1-ho
% 0.22/0.35 % Preprocessing class: HSLSSMSSSSSNSFA.
% 0.22/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.35 % Starting new_ho_11 with 1500s (5) cores
% 0.22/0.35 % Starting post_as_ho6 with 300s (1) cores
% 0.22/0.35 % Starting sh9 with 300s (1) cores
% 0.22/0.35 % Starting sh5l with 300s (1) cores
% 0.22/0.35 % new_ho_11 with pid 1757100 completed with status 0
% 0.22/0.35 % Result found by new_ho_11
% 0.22/0.35 % Preprocessing class: HSLSSMSSSSSNSFA.
% 0.22/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.35 % Starting new_ho_11 with 1500s (5) cores
% 0.22/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.35 % No SInE strategy applied
% 0.22/0.35 % Search class: HGHSM-FSLF31-MSFFFSBN
% 0.22/0.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.35 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.35 % Starting new_ho_11 with 151s (1) cores
% 0.22/0.35 % Starting sh5l with 136s (1) cores
% 0.22/0.35 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.22/0.35 % Starting sh3l with 136s (1) cores
% 0.22/0.35 % sh3l with pid 1757108 completed with status 0
% 0.22/0.35 % Result found by sh3l
% 0.22/0.35 % Preprocessing class: HSLSSMSSSSSNSFA.
% 0.22/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.35 % Starting new_ho_11 with 1500s (5) cores
% 0.22/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.35 % No SInE strategy applied
% 0.22/0.35 % Search class: HGHSM-FSLF31-MSFFFSBN
% 0.22/0.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.35 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.35 % Starting new_ho_11 with 151s (1) cores
% 0.22/0.35 % Starting sh5l with 136s (1) cores
% 0.22/0.35 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.22/0.35 % Starting sh3l with 136s (1) cores
% 0.22/0.35 % Preprocessing time : 0.003 s
% 0.22/0.35 % Presaturation interreduction done
% 0.22/0.35
% 0.22/0.35 % Proof found!
% 0.22/0.35 % SZS status Theorem
% 0.22/0.35 % SZS output start CNFRefutation
% See solution above
% 0.22/0.35 % Parsed axioms : 210
% 0.22/0.35 % Removed by relevancy pruning/SinE : 0
% 0.22/0.35 % Initial clauses : 349
% 0.22/0.35 % Removed in clause preprocessing : 42
% 0.22/0.35 % Initial clauses in saturation : 307
% 0.22/0.35 % Processed clauses : 586
% 0.22/0.35 % ...of these trivial : 13
% 0.22/0.35 % ...subsumed : 147
% 0.22/0.35 % ...remaining for further processing : 426
% 0.22/0.35 % Other redundant clauses eliminated : 89
% 0.22/0.35 % Clauses deleted for lack of memory : 0
% 0.22/0.35 % Backward-subsumed : 1
% 0.22/0.35 % Backward-rewritten : 10
% 0.22/0.35 % Generated clauses : 2056
% 0.22/0.35 % ...of the previous two non-redundant : 1741
% 0.22/0.35 % ...aggressively subsumed : 0
% 0.22/0.35 % Contextual simplify-reflections : 1
% 0.22/0.35 % Paramodulations : 1916
% 0.22/0.35 % Factorizations : 2
% 0.22/0.35 % NegExts : 0
% 0.22/0.35 % Equation resolutions : 95
% 0.22/0.35 % Disequality decompositions : 0
% 0.22/0.35 % Total rewrite steps : 437
% 0.22/0.35 % ...of those cached : 356
% 0.22/0.35 % Propositional unsat checks : 0
% 0.22/0.35 % Propositional check models : 0
% 0.22/0.35 % Propositional check unsatisfiable : 0
% 0.22/0.35 % Propositional clauses : 0
% 0.22/0.35 % Propositional clauses after purity: 0
% 0.22/0.35 % Propositional unsat core size : 0
% 0.22/0.35 % Propositional preprocessing time : 0.000
% 0.22/0.35 % Propositional encoding time : 0.000
% 0.22/0.35 % Propositional solver time : 0.000
% 0.22/0.35 % Success case prop preproc time : 0.000
% 0.22/0.35 % Success case prop encoding time : 0.000
% 0.22/0.35 % Success case prop solver time : 0.000
% 0.22/0.35 % Current number of processed clauses : 177
% 0.22/0.35 % Positive orientable unit clauses : 29
% 0.22/0.35 % Positive unorientable unit clauses: 2
% 0.22/0.35 % Negative unit clauses : 11
% 0.22/0.35 % Non-unit-clauses : 135
% 0.22/0.35 % Current number of unprocessed clauses: 1622
% 0.22/0.35 % ...number of literals in the above : 4547
% 0.22/0.35 % Current number of archived formulas : 0
% 0.22/0.35 % Current number of archived clauses : 197
% 0.22/0.35 % Clause-clause subsumption calls (NU) : 6327
% 0.22/0.35 % Rec. Clause-clause subsumption calls : 5119
% 0.22/0.35 % Non-unit clause-clause subsumptions : 65
% 0.22/0.35 % Unit Clause-clause subsumption calls : 81
% 0.22/0.35 % Rewrite failures with RHS unbound : 0
% 0.22/0.35 % BW rewrite match attempts : 29
% 0.22/0.35 % BW rewrite match successes : 25
% 0.22/0.35 % Condensation attempts : 0
% 0.22/0.35 % Condensation successes : 0
% 0.22/0.35 % Termbank termtop insertions : 86293
% 0.22/0.35 % Search garbage collected termcells : 6429
% 0.22/0.35
% 0.22/0.35 % -------------------------------------------------
% 0.22/0.35 % User time : 0.058 s
% 0.22/0.35 % System time : 0.007 s
% 0.22/0.35 % Total time : 0.065 s
% 0.22/0.35 % Maximum resident set size: 4860 pages
% 0.22/0.35
% 0.22/0.35 % -------------------------------------------------
% 0.22/0.35 % User time : 0.298 s
% 0.22/0.35 % System time : 0.035 s
% 0.22/0.35 % Total time : 0.334 s
% 0.22/0.35 % Maximum resident set size: 5120 pages
% 0.22/0.35 % E exiting
%------------------------------------------------------------------------------