%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM925^3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:17:48 AM UTC 2026
% Result : Theorem 1.09s 0.75s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 41 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 188 ( 18 ~; 7 |; 4 &; 155 @)
% ( 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 : 18 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 0 ^; 23 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
int: $tType ).
thf(decl_30,type,
one_one_int: int ).
thf(decl_31,type,
one_one_nat: nat ).
thf(decl_33,type,
plus_plus_int: int > int > int ).
thf(decl_34,type,
plus_plus_nat: nat > nat > nat ).
thf(decl_39,type,
zero_zero_int: int ).
thf(decl_46,type,
bit0: int > int ).
thf(decl_47,type,
bit1: int > int ).
thf(decl_49,type,
pls: int ).
thf(decl_50,type,
nat_1: int > nat ).
thf(decl_51,type,
number_number_of_int: int > int ).
thf(decl_52,type,
number_number_of_nat: int > nat ).
thf(decl_55,type,
semiri1621563631at_int: nat > int ).
thf(decl_58,type,
ord_less_int: int > int > $o ).
thf(decl_61,type,
ord_less_eq_int: int > int > $o ).
thf(decl_64,type,
power_power_int: int > nat > int ).
thf(decl_74,type,
n: nat ).
thf(fact_25_semiring__norm_I110_J,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OB5HQtBO9O/E---3.1_557968.p',fact_25_semiring__norm_I110_J) ).
thf(fact_98_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/tmp/tmp.OB5HQtBO9O/E---3.1_557968.p',fact_98_Pls__def) ).
thf(fact_177_number__of__is__id,axiom,
! [X10: int] :
( ( number_number_of_int @ X10 )
= X10 ),
file('/export/starexec/sandbox2/tmp/tmp.OB5HQtBO9O/E---3.1_557968.p',fact_177_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/sandbox2/tmp/tmp.OB5HQtBO9O/E---3.1_557968.p',conj_0) ).
thf(fact_55_Numeral1__eq1__nat,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OB5HQtBO9O/E---3.1_557968.p',fact_55_Numeral1__eq1__nat) ).
thf(fact_768_transfer__nat__int__numerals_I2_J,axiom,
( one_one_nat
= ( nat_1 @ one_one_int ) ),
file('/export/starexec/sandbox2/tmp/tmp.OB5HQtBO9O/E---3.1_557968.p',fact_768_transfer__nat__int__numerals_I2_J) ).
thf(fact_103_Bit0__def,axiom,
! [X10: int] :
( ( bit0 @ X10 )
= ( plus_plus_int @ X10 @ X10 ) ),
file('/export/starexec/sandbox2/tmp/tmp.OB5HQtBO9O/E---3.1_557968.p',fact_103_Bit0__def) ).
thf(fact_231_field__power__not__zero,axiom,
! [X141: nat,X142: int] :
( ( X142 != zero_zero_int )
=> ( ( power_power_int @ X142 @ X141 )
!= zero_zero_int ) ),
file('/export/starexec/sandbox2/tmp/tmp.OB5HQtBO9O/E---3.1_557968.p',fact_231_field__power__not__zero) ).
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/sandbox2/tmp/tmp.OB5HQtBO9O/E---3.1_557968.p',fact_19_semiring__one__add__one__is__two) ).
thf(fact_718_zless__le,axiom,
! [X18: int,X13: int] :
( ( ord_less_int @ X18 @ X13 )
<=> ( ( ord_less_eq_int @ X18 @ X13 )
& ( X18 != X13 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OB5HQtBO9O/E---3.1_557968.p',fact_718_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/sandbox2/tmp/tmp.OB5HQtBO9O/E---3.1_557968.p',fact_0_n1pos) ).
thf(c_0_11,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(split_conjunct,[status(thm)],[fact_25_semiring__norm_I110_J]) ).
thf(c_0_12,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_98_Pls__def]) ).
thf(c_0_13,plain,
! [X4358: int] :
( ( number_number_of_int @ X4358 )
= X4358 ),
inference(variable_rename,[status(thm)],[fact_177_number__of__is__id]) ).
thf(c_0_14,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_15,plain,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
inference(split_conjunct,[status(thm)],[fact_55_Numeral1__eq1__nat]) ).
thf(c_0_16,plain,
( one_one_nat
= ( nat_1 @ one_one_int ) ),
inference(split_conjunct,[status(thm)],[fact_768_transfer__nat__int__numerals_I2_J]) ).
thf(c_0_17,plain,
( ( number_number_of_int @ ( bit1 @ zero_zero_int ) )
= one_one_int ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_18,plain,
! [X1: int] :
( ( number_number_of_int @ X1 )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
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(fof_simplification,[status(thm)],[c_0_14]) ).
thf(c_0_20,plain,
( ( nat_1 @ one_one_int )
= ( number_number_of_nat @ ( bit1 @ zero_zero_int ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_12]) ).
thf(c_0_21,plain,
( one_one_int
= ( bit1 @ zero_zero_int ) ),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_22,plain,
! [X4271: int] :
( ( bit0 @ X4271 )
= ( plus_plus_int @ X4271 @ X4271 ) ),
inference(variable_rename,[status(thm)],[fact_103_Bit0__def]) ).
thf(c_0_23,plain,
! [X141: nat,X142: int] :
( ( X142 != zero_zero_int )
=> ( ( power_power_int @ X142 @ X141 )
!= zero_zero_int ) ),
inference(fof_simplification,[status(thm)],[fact_231_field__power__not__zero]) ).
thf(c_0_24,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_19]) ).
thf(c_0_25,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_26,plain,
( ( nat_1 @ ( bit1 @ zero_zero_int ) )
= ( number_number_of_nat @ ( bit1 @ zero_zero_int ) ) ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_27,plain,
! [X1: int] :
( ( bit0 @ X1 )
= ( plus_plus_int @ X1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_28,plain,
! [X18: int,X13: int] :
( ( ord_less_int @ X18 @ X13 )
<=> ( ( ord_less_eq_int @ X18 @ X13 )
& ( X18 != X13 ) ) ),
inference(fof_simplification,[status(thm)],[fact_718_zless__le]) ).
thf(c_0_29,plain,
! [X4457: nat,X4458: int] :
( ( X4458 = zero_zero_int )
| ( ( power_power_int @ X4458 @ X4457 )
!= zero_zero_int ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
thf(c_0_30,negated_conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) )
= zero_zero_int ),
inference(rw,[status(thm)],[c_0_24,c_0_12]) ).
thf(c_0_31,plain,
( ( number_number_of_nat @ ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( bit1 @ zero_zero_int ) ) )
= ( plus_plus_nat @ ( number_number_of_nat @ ( bit1 @ zero_zero_int ) ) @ ( number_number_of_nat @ ( bit1 @ zero_zero_int ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_16]),c_0_21]),c_0_26]),c_0_16]),c_0_21]),c_0_26]),c_0_12]),c_0_27]) ).
thf(c_0_32,plain,
! [X5614: int,X5615: int] :
( ( ( ord_less_eq_int @ X5614 @ X5615 )
| ~ ( ord_less_int @ X5614 @ X5615 ) )
& ( ( X5614 != X5615 )
| ~ ( ord_less_int @ X5614 @ X5615 ) )
& ( ~ ( ord_less_eq_int @ X5614 @ X5615 )
| ( X5614 = X5615 )
| ( ord_less_int @ X5614 @ X5615 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
thf(c_0_33,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_34,plain,
! [X1: int,X16: nat] :
( ( X1 = zero_zero_int )
| ( ( power_power_int @ X1 @ X16 )
!= zero_zero_int ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_35,negated_conjecture,
( ( power_power_int @ ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( semiri1621563631at_int @ n ) ) @ ( plus_plus_nat @ ( number_number_of_nat @ ( bit1 @ zero_zero_int ) ) @ ( number_number_of_nat @ ( bit1 @ zero_zero_int ) ) ) )
= zero_zero_int ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_21]),c_0_27]),c_0_31]) ).
thf(c_0_36,plain,
! [X1: int,X2: int] :
( ( X1 != X2 )
| ~ ( ord_less_int @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_37,plain,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( semiri1621563631at_int @ n ) ),
inference(rw,[status(thm)],[c_0_33,c_0_21]) ).
thf(c_0_38,negated_conjecture,
( ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( semiri1621563631at_int @ n ) )
= zero_zero_int ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_39,plain,
! [X1: int] :
~ ( ord_less_int @ X1 @ X1 ),
inference(er,[status(thm)],[c_0_36]) ).
thf(c_0_40,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925^3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:08:27 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.31/0.39 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.OB5HQtBO9O/E---3.1_557968.p
% 1.09/0.75 % Version: 3.5.1-ho
% 1.09/0.75 % Preprocessing class: HMLSSMSMSSSNSFA.
% 1.09/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.75 % Starting sh3 with 1500s (5) cores
% 1.09/0.75 % Starting lpo1_def_fix with 300s (1) cores
% 1.09/0.75 % Starting lpo8_s with 300s (1) cores
% 1.09/0.75 % Starting lpo1_lambda_fix with 300s (1) cores
% 1.09/0.75 % sh3 with pid 558051 completed with status 0
% 1.09/0.75 % Result found by sh3
% 1.09/0.75 % Preprocessing class: HMLSSMSMSSSNSFA.
% 1.09/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.75 % Starting sh3 with 1500s (5) cores
% 1.09/0.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.09/0.75 % No SInE strategy applied
% 1.09/0.75 % Search class: HGHSM-SSLM31-DSFFFFBN
% 1.09/0.75 % partial match(1): HGHSM-FSLM31-DSFFFFBN
% 1.09/0.75 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.09/0.75 % Starting SubtermCWHack with 136s (1) cores
% 1.09/0.75 % Starting sh3 with 151s (1) cores
% 1.09/0.75 % Starting lpo5_fix with 226s (1) cores
% 1.09/0.75 % Starting new_ho_2_cnf4 with 226s (1) cores
% 1.09/0.75 % Starting full_lambda_5 with 226s (1) cores
% 1.09/0.75 % new_ho_2_cnf4 with pid 558076 completed with status 0
% 1.09/0.75 % Result found by new_ho_2_cnf4
% 1.09/0.75 % Preprocessing class: HMLSSMSMSSSNSFA.
% 1.09/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.09/0.75 % Starting sh3 with 1500s (5) cores
% 1.09/0.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.09/0.75 % No SInE strategy applied
% 1.09/0.75 % Search class: HGHSM-SSLM31-DSFFFFBN
% 1.09/0.75 % partial match(1): HGHSM-FSLM31-DSFFFFBN
% 1.09/0.75 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.09/0.75 % Starting SubtermCWHack with 136s (1) cores
% 1.09/0.75 % Starting sh3 with 151s (1) cores
% 1.09/0.75 % Starting lpo5_fix with 226s (1) cores
% 1.09/0.75 % Starting new_ho_2_cnf4 with 226s (1) cores
% 1.09/0.75 % Preprocessing time : 0.015 s
% 1.09/0.75 % Presaturation interreduction done
% 1.09/0.75
% 1.09/0.75 % Proof found!
% 1.09/0.75 % SZS status Theorem
% 1.09/0.75 % SZS output start CNFRefutation
% See solution above
% 1.09/0.75 % Parsed axioms : 1266
% 1.09/0.75 % Removed by relevancy pruning/SinE : 0
% 1.09/0.75 % Initial clauses : 1827
% 1.09/0.75 % Removed in clause preprocessing : 185
% 1.09/0.75 % Initial clauses in saturation : 1642
% 1.09/0.75 % Processed clauses : 1864
% 1.09/0.75 % ...of these trivial : 216
% 1.09/0.75 % ...subsumed : 388
% 1.09/0.75 % ...remaining for further processing : 1259
% 1.09/0.75 % Other redundant clauses eliminated : 162
% 1.09/0.75 % Clauses deleted for lack of memory : 0
% 1.09/0.75 % Backward-subsumed : 13
% 1.09/0.75 % Backward-rewritten : 104
% 1.09/0.75 % Generated clauses : 171
% 1.09/0.75 % ...of the previous two non-redundant : 158
% 1.09/0.75 % ...aggressively subsumed : 0
% 1.09/0.75 % Contextual simplify-reflections : 2
% 1.09/0.75 % Paramodulations : 26
% 1.09/0.75 % Factorizations : 0
% 1.09/0.75 % NegExts : 0
% 1.09/0.75 % Equation resolutions : 162
% 1.09/0.75 % Disequality decompositions : 0
% 1.09/0.75 % Total rewrite steps : 2543
% 1.09/0.75 % ...of those cached : 2115
% 1.09/0.75 % Propositional unsat checks : 0
% 1.09/0.75 % Propositional check models : 0
% 1.09/0.75 % Propositional check unsatisfiable : 0
% 1.09/0.75 % Propositional clauses : 0
% 1.09/0.75 % Propositional clauses after purity: 0
% 1.09/0.75 % Propositional unsat core size : 0
% 1.09/0.75 % Propositional preprocessing time : 0.000
% 1.09/0.75 % Propositional encoding time : 0.000
% 1.09/0.75 % Propositional solver time : 0.000
% 1.09/0.75 % Success case prop preproc time : 0.000
% 1.09/0.75 % Success case prop encoding time : 0.000
% 1.09/0.75 % Success case prop solver time : 0.000
% 1.09/0.75 % Current number of processed clauses : 68
% 1.09/0.75 % Positive orientable unit clauses : 37
% 1.09/0.75 % Positive unorientable unit clauses: 0
% 1.09/0.75 % Negative unit clauses : 25
% 1.09/0.75 % Non-unit-clauses : 6
% 1.09/0.75 % Current number of unprocessed clauses: 866
% 1.09/0.75 % ...number of literals in the above : 1972
% 1.09/0.75 % Current number of archived formulas : 0
% 1.09/0.75 % Current number of archived clauses : 1047
% 1.09/0.75 % Clause-clause subsumption calls (NU) : 141778
% 1.09/0.75 % Rec. Clause-clause subsumption calls : 94344
% 1.09/0.75 % Non-unit clause-clause subsumptions : 331
% 1.09/0.75 % Unit Clause-clause subsumption calls : 1290
% 1.09/0.75 % Rewrite failures with RHS unbound : 0
% 1.09/0.75 % BW rewrite match attempts : 450
% 1.09/0.75 % BW rewrite match successes : 330
% 1.09/0.75 % Condensation attempts : 0
% 1.09/0.75 % Condensation successes : 0
% 1.09/0.75 % Termbank termtop insertions : 160505
% 1.09/0.75 % Search garbage collected termcells : 28795
% 1.09/0.75
% 1.09/0.75 % -------------------------------------------------
% 1.09/0.75 % User time : 0.256 s
% 1.09/0.75 % System time : 0.026 s
% 1.09/0.75 % Total time : 0.282 s
% 1.09/0.75 % Maximum resident set size: 10848 pages
% 1.09/0.75
% 1.09/0.75 % -------------------------------------------------
% 1.09/0.75 % User time : 0.711 s
% 1.09/0.75 % System time : 0.091 s
% 1.09/0.75 % Total time : 0.802 s
% 1.09/0.75 % Maximum resident set size: 7168 pages
% 1.09/0.75 % E exiting
%------------------------------------------------------------------------------