%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM925^2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:17:13 AM UTC 2026
% Result : Theorem 1.46s 0.61s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 39 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 177 ( 19 ~; 8 |; 4 &; 142 @)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 25 ( 0 ^; 25 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
int: $tType ).
thf(decl_sort2,type,
nat: $tType ).
thf(decl_23,type,
one_one_int: int ).
thf(decl_24,type,
one_one_nat: nat ).
thf(decl_26,type,
plus_plus_int: int > int > int ).
thf(decl_27,type,
plus_plus_nat: nat > nat > nat ).
thf(decl_30,type,
zero_zero_int: int ).
thf(decl_34,type,
bit0: int > int ).
thf(decl_35,type,
bit1: int > int ).
thf(decl_36,type,
pls: int ).
thf(decl_37,type,
number_number_of_int: int > int ).
thf(decl_38,type,
number_number_of_nat: int > nat ).
thf(decl_41,type,
semiri1621563631at_int: nat > int ).
thf(decl_45,type,
ord_less_int: int > int > $o ).
thf(decl_48,type,
ord_less_eq_int: int > int > $o ).
thf(decl_51,type,
power_power_int: int > nat > int ).
thf(decl_55,type,
n: nat ).
thf(fact_176_number__of__is__id,axiom,
! [X10: int] :
( ( number_number_of_int @ X10 )
= X10 ),
file('/export/starexec/sandbox/tmp/tmp.iTKpBHxXMX/E---3.1_312515.p',fact_176_number__of__is__id) ).
thf(conj_0,conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ),
file('/export/starexec/sandbox/tmp/tmp.iTKpBHxXMX/E---3.1_312515.p',conj_0) ).
thf(fact_25_semiring__norm_I110_J,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iTKpBHxXMX/E---3.1_312515.p',fact_25_semiring__norm_I110_J) ).
thf(fact_231_field__power__not__zero,axiom,
! [X141: nat,X143: int] :
( ( X143 != zero_zero_int )
=> ( ( power_power_int @ X143 @ X141 )
!= zero_zero_int ) ),
file('/export/starexec/sandbox/tmp/tmp.iTKpBHxXMX/E---3.1_312515.p',fact_231_field__power__not__zero) ).
thf(fact_16_one__add__one__is__two,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iTKpBHxXMX/E---3.1_312515.p',fact_16_one__add__one__is__two) ).
thf(fact_98_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/tmp/tmp.iTKpBHxXMX/E---3.1_312515.p',fact_98_Pls__def) ).
thf(fact_103_Bit0__def,axiom,
! [X10: int] :
( ( bit0 @ X10 )
= ( plus_plus_int @ X10 @ X10 ) ),
file('/export/starexec/sandbox/tmp/tmp.iTKpBHxXMX/E---3.1_312515.p',fact_103_Bit0__def) ).
thf(fact_19_semiring__one__add__one__is__two,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iTKpBHxXMX/E---3.1_312515.p',fact_19_semiring__one__add__one__is__two) ).
thf(fact_447_zless__le,axiom,
! [X18: int,X13: int] :
( ( ord_less_int @ X18 @ X13 )
<=> ( ( ord_less_eq_int @ X18 @ X13 )
& ( X18 != X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.iTKpBHxXMX/E---3.1_312515.p',fact_447_zless__le) ).
thf(fact_0_n1pos,axiom,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ),
file('/export/starexec/sandbox/tmp/tmp.iTKpBHxXMX/E---3.1_312515.p',fact_0_n1pos) ).
thf(c_0_10,plain,
! [X2335: int] :
( ( number_number_of_int @ X2335 )
= X2335 ),
inference(variable_rename,[status(thm)],[fact_176_number__of__is__id]) ).
thf(c_0_11,negated_conjecture,
~ ( ( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_12,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(split_conjunct,[status(thm)],[fact_25_semiring__norm_I110_J]) ).
thf(c_0_13,plain,
! [X1: int] :
( ( number_number_of_int @ X1 )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
! [X141: nat,X143: int] :
( ( X143 != zero_zero_int )
=> ( ( power_power_int @ X143 @ X141 )
!= zero_zero_int ) ),
inference(fof_simplification,[status(thm)],[fact_231_field__power__not__zero]) ).
thf(c_0_15,negated_conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(split_conjunct,[status(thm)],[fact_16_one__add__one__is__two]) ).
thf(c_0_17,plain,
( ( bit1 @ pls )
= one_one_int ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_18,plain,
! [X2436: nat,X2437: int] :
( ( X2437 = zero_zero_int )
| ( ( power_power_int @ X2437 @ X2436 )
!= zero_zero_int ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
thf(c_0_19,negated_conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_20,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_98_Pls__def]) ).
thf(c_0_21,plain,
! [X2248: int] :
( ( bit0 @ X2248 )
= ( plus_plus_int @ X2248 @ X2248 ) ),
inference(variable_rename,[status(thm)],[fact_103_Bit0__def]) ).
thf(c_0_22,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(split_conjunct,[status(thm)],[fact_19_semiring__one__add__one__is__two]) ).
thf(c_0_23,plain,
( ( bit0 @ one_one_int )
= ( plus_plus_int @ one_one_int @ one_one_int ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_13]),c_0_17]) ).
thf(c_0_24,plain,
! [X18: int,X13: int] :
( ( ord_less_int @ X18 @ X13 )
<=> ( ( ord_less_eq_int @ X18 @ X13 )
& ( X18 != X13 ) ) ),
inference(fof_simplification,[status(thm)],[fact_447_zless__le]) ).
thf(c_0_25,plain,
! [X1: int,X16: nat] :
( ( X1 = zero_zero_int )
| ( ( power_power_int @ X1 @ X16 )
!= zero_zero_int ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_26,negated_conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= pls ),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_27,plain,
! [X1: int] :
( ( bit0 @ X1 )
= ( plus_plus_int @ X1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_28,plain,
( ( number_number_of_nat @ ( plus_plus_int @ one_one_int @ one_one_int ) )
= ( plus_plus_nat @ one_one_nat @ one_one_nat ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_17]),c_0_23]) ).
thf(c_0_29,plain,
! [X2888: int,X2889: int] :
( ( ( ord_less_eq_int @ X2888 @ X2889 )
| ~ ( ord_less_int @ X2888 @ X2889 ) )
& ( ( X2888 != X2889 )
| ~ ( ord_less_int @ X2888 @ X2889 ) )
& ( ~ ( ord_less_eq_int @ X2888 @ X2889 )
| ( X2888 = X2889 )
| ( ord_less_int @ X2888 @ X2889 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
thf(c_0_30,plain,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
thf(c_0_31,plain,
! [X1: int,X16: nat] :
( ( X1 = pls )
| ( ( power_power_int @ X1 @ X16 )
!= pls ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_20]),c_0_20]) ).
thf(c_0_32,negated_conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
= pls ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_17]),c_0_27]),c_0_28]) ).
thf(c_0_33,plain,
! [X1: int,X2: int] :
( ( X1 != X2 )
| ~ ( ord_less_int @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_34,plain,
ord_less_int @ pls @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ),
inference(rw,[status(thm)],[c_0_30,c_0_20]) ).
thf(c_0_35,negated_conjecture,
( ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) )
= pls ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_36,plain,
! [X1: int] :
~ ( ord_less_int @ X1 @ X1 ),
inference(er,[status(thm)],[c_0_33]) ).
thf(c_0_37,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925^2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n016.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 13:09:49 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 Running higher-order theorem proving
% 0.23/0.31 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.iTKpBHxXMX/E---3.1_312515.p
% 1.46/0.61 % Version: 3.5.1-ho
% 1.46/0.61 % Preprocessing class: HSLSSMSMSSSNSFA.
% 1.46/0.61 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.46/0.61 % Starting new_ho_10 with 900s (3) cores
% 1.46/0.61 % Starting sh2lt with 300s (1) cores
% 1.46/0.61 % Starting new_ho_5 with 300s (1) cores
% 1.46/0.61 % Starting full_lambda_5 with 300s (1) cores
% 1.46/0.61 % Starting sh9 with 300s (1) cores
% 1.46/0.61 % Starting ehoh_best8_lambda with 300s (1) cores
% 1.46/0.61 % new_ho_10 with pid 312528 completed with status 0
% 1.46/0.61 % Result found by new_ho_10
% 1.46/0.61 % Preprocessing class: HSLSSMSMSSSNSFA.
% 1.46/0.61 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.46/0.61 % Starting new_ho_10 with 900s (3) cores
% 1.46/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.46/0.61 % No SInE strategy applied
% 1.46/0.61 % Search class: HGHSM-FSLM31-DSFFFFBN
% 1.46/0.61 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 1.46/0.61 % Starting SubtermCWHack with 82s (1) cores
% 1.46/0.61 % Starting new_ho_10 with 91s (1) cores
% 1.46/0.61 % Starting lpo5_fix with 136s (1) cores
% 1.46/0.61 % new_ho_10 with pid 312538 completed with status 0
% 1.46/0.61 % Result found by new_ho_10
% 1.46/0.61 % Preprocessing class: HSLSSMSMSSSNSFA.
% 1.46/0.61 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.46/0.61 % Starting new_ho_10 with 900s (3) cores
% 1.46/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.46/0.61 % No SInE strategy applied
% 1.46/0.61 % Search class: HGHSM-FSLM31-DSFFFFBN
% 1.46/0.61 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 1.46/0.61 % Starting SubtermCWHack with 82s (1) cores
% 1.46/0.61 % Starting new_ho_10 with 91s (1) cores
% 1.46/0.61 % Preprocessing time : 0.014 s
% 1.46/0.61 % Presaturation interreduction done
% 1.46/0.61
% 1.46/0.61 % Proof found!
% 1.46/0.61 % SZS status Theorem
% 1.46/0.61 % SZS output start CNFRefutation
% See solution above
% 1.46/0.61 % Parsed axioms : 741
% 1.46/0.61 % Removed by relevancy pruning/SinE : 0
% 1.46/0.61 % Initial clauses : 1033
% 1.46/0.61 % Removed in clause preprocessing : 128
% 1.46/0.61 % Initial clauses in saturation : 905
% 1.46/0.61 % Processed clauses : 1009
% 1.46/0.61 % ...of these trivial : 128
% 1.46/0.61 % ...subsumed : 229
% 1.46/0.61 % ...remaining for further processing : 652
% 1.46/0.61 % Other redundant clauses eliminated : 75
% 1.46/0.61 % Clauses deleted for lack of memory : 0
% 1.46/0.61 % Backward-subsumed : 18
% 1.46/0.61 % Backward-rewritten : 22
% 1.46/0.61 % Generated clauses : 94
% 1.46/0.61 % ...of the previous two non-redundant : 60
% 1.46/0.61 % ...aggressively subsumed : 0
% 1.46/0.61 % Contextual simplify-reflections : 2
% 1.46/0.61 % Paramodulations : 30
% 1.46/0.61 % Factorizations : 0
% 1.46/0.61 % NegExts : 0
% 1.46/0.61 % Equation resolutions : 75
% 1.46/0.61 % Disequality decompositions : 0
% 1.46/0.61 % Total rewrite steps : 933
% 1.46/0.61 % ...of those cached : 810
% 1.46/0.61 % Propositional unsat checks : 0
% 1.46/0.61 % Propositional check models : 0
% 1.46/0.61 % Propositional check unsatisfiable : 0
% 1.46/0.61 % Propositional clauses : 0
% 1.46/0.61 % Propositional clauses after purity: 0
% 1.46/0.61 % Propositional unsat core size : 0
% 1.46/0.61 % Propositional preprocessing time : 0.000
% 1.46/0.61 % Propositional encoding time : 0.000
% 1.46/0.61 % Propositional solver time : 0.000
% 1.46/0.61 % Success case prop preproc time : 0.000
% 1.46/0.61 % Success case prop encoding time : 0.000
% 1.46/0.61 % Success case prop solver time : 0.000
% 1.46/0.61 % Current number of processed clauses : 53
% 1.46/0.61 % Positive orientable unit clauses : 31
% 1.46/0.61 % Positive unorientable unit clauses: 0
% 1.46/0.61 % Negative unit clauses : 16
% 1.46/0.61 % Non-unit-clauses : 6
% 1.46/0.61 % Current number of unprocessed clauses: 452
% 1.46/0.61 % ...number of literals in the above : 967
% 1.46/0.61 % Current number of archived formulas : 0
% 1.46/0.61 % Current number of archived clauses : 536
% 1.46/0.61 % Clause-clause subsumption calls (NU) : 38862
% 1.46/0.61 % Rec. Clause-clause subsumption calls : 33612
% 1.46/0.61 % Non-unit clause-clause subsumptions : 196
% 1.46/0.61 % Unit Clause-clause subsumption calls : 243
% 1.46/0.61 % Rewrite failures with RHS unbound : 0
% 1.46/0.61 % BW rewrite match attempts : 128
% 1.46/0.61 % BW rewrite match successes : 97
% 1.46/0.61 % Condensation attempts : 1009
% 1.46/0.61 % Condensation successes : 1
% 1.46/0.61 % Termbank termtop insertions : 75268
% 1.46/0.61 % Search garbage collected termcells : 15092
% 1.46/0.61
% 1.46/0.61 % -------------------------------------------------
% 1.46/0.61 % User time : 0.163 s
% 1.46/0.61 % System time : 0.022 s
% 1.46/0.61 % Total time : 0.185 s
% 1.46/0.61 % Maximum resident set size: 7652 pages
% 1.46/0.61
% 1.46/0.61 % -------------------------------------------------
% 1.46/0.61 % User time : 0.409 s
% 1.46/0.61 % System time : 0.048 s
% 1.46/0.61 % Total time : 0.456 s
% 1.46/0.61 % Maximum resident set size: 6144 pages
% 1.46/0.61 % E exiting
%------------------------------------------------------------------------------