%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM925^1 : 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 : n015.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 08:17:12 AM UTC 2026
% Result : Theorem 0.23s 0.29s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 44 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 179 ( 16 ~; 6 |; 4 &; 151 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 31 ( 0 ^; 31 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
int: $tType ).
thf(decl_sort2,type,
nat: $tType ).
thf(decl_23,type,
one_one_int: int ).
thf(decl_25,type,
plus_plus_int: int > int > int ).
thf(decl_27,type,
zero_zero_int: int ).
thf(decl_28,type,
zero_zero_nat: nat ).
thf(decl_29,type,
bit0: int > int ).
thf(decl_30,type,
bit1: int > int ).
thf(decl_31,type,
pls: int ).
thf(decl_33,type,
number_number_of_nat: int > nat ).
thf(decl_34,type,
semiri1621563631at_int: nat > int ).
thf(decl_36,type,
ord_less_int: int > int > $o ).
thf(decl_38,type,
power_power_int: int > nat > int ).
thf(decl_40,type,
n: nat ).
thf(fact_85_zadd__0,axiom,
! [X15: int] :
( ( plus_plus_int @ zero_zero_int @ X15 )
= X15 ),
file('/export/starexec/sandbox/tmp/tmp.vGMk9ny6QI/E---3.1_3485536.p',fact_85_zadd__0) ).
thf(fact_99_Bit1__def,axiom,
! [X7: int] :
( ( bit1 @ X7 )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ X7 ) @ X7 ) ),
file('/export/starexec/sandbox/tmp/tmp.vGMk9ny6QI/E---3.1_3485536.p',fact_99_Bit1__def) ).
thf(fact_52_zadd__commute,axiom,
! [X15: int,X10: int] :
( ( plus_plus_int @ X15 @ X10 )
= ( plus_plus_int @ X10 @ X15 ) ),
file('/export/starexec/sandbox/tmp/tmp.vGMk9ny6QI/E---3.1_3485536.p',fact_52_zadd__commute) ).
thf(fact_84_zadd__0__right,axiom,
! [X15: int] :
( ( plus_plus_int @ X15 @ zero_zero_int )
= X15 ),
file('/export/starexec/sandbox/tmp/tmp.vGMk9ny6QI/E---3.1_3485536.p',fact_84_zadd__0__right) ).
thf(fact_92_power__eq__0__iff__number__of,axiom,
! [X38: int,X39: int] :
( ( ( power_power_int @ X38 @ ( number_number_of_nat @ X39 ) )
= zero_zero_int )
<=> ( ( X38 = zero_zero_int )
& ( ( number_number_of_nat @ X39 )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vGMk9ny6QI/E---3.1_3485536.p',fact_92_power__eq__0__iff__number__of) ).
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.vGMk9ny6QI/E---3.1_3485536.p',conj_0) ).
thf(fact_78_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/tmp/tmp.vGMk9ny6QI/E---3.1_3485536.p',fact_78_Pls__def) ).
thf(fact_83_Bit0__def,axiom,
! [X7: int] :
( ( bit0 @ X7 )
= ( plus_plus_int @ X7 @ X7 ) ),
file('/export/starexec/sandbox/tmp/tmp.vGMk9ny6QI/E---3.1_3485536.p',fact_83_Bit0__def) ).
thf(fact_62_bin__less__0__simps_I1_J,axiom,
~ ( ord_less_int @ pls @ zero_zero_int ),
file('/export/starexec/sandbox/tmp/tmp.vGMk9ny6QI/E---3.1_3485536.p',fact_62_bin__less__0__simps_I1_J) ).
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.vGMk9ny6QI/E---3.1_3485536.p',fact_0_n1pos) ).
thf(c_0_10,plain,
! [X164: int] :
( ( plus_plus_int @ zero_zero_int @ X164 )
= X164 ),
inference(variable_rename,[status(thm)],[fact_85_zadd__0]) ).
thf(c_0_11,plain,
! [X248: int] :
( ( bit1 @ X248 )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ X248 ) @ X248 ) ),
inference(variable_rename,[status(thm)],[fact_99_Bit1__def]) ).
thf(c_0_12,plain,
! [X226: int,X227: int] :
( ( plus_plus_int @ X226 @ X227 )
= ( plus_plus_int @ X227 @ X226 ) ),
inference(variable_rename,[status(thm)],[fact_52_zadd__commute]) ).
thf(c_0_13,plain,
! [X163: int] :
( ( plus_plus_int @ X163 @ zero_zero_int )
= X163 ),
inference(variable_rename,[status(thm)],[fact_84_zadd__0__right]) ).
thf(c_0_14,plain,
! [X38: int,X39: int] :
( ( ( power_power_int @ X38 @ ( number_number_of_nat @ X39 ) )
= zero_zero_int )
<=> ( ( X38 = zero_zero_int )
& ( ( number_number_of_nat @ X39 )
!= zero_zero_nat ) ) ),
inference(fof_simplification,[status(thm)],[fact_92_power__eq__0__iff__number__of]) ).
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(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_16,plain,
! [X1: int] :
( ( plus_plus_int @ zero_zero_int @ X1 )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_17,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_78_Pls__def]) ).
thf(c_0_18,plain,
! [X1: int] :
( ( bit1 @ X1 )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ X1 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_19,plain,
! [X2: int,X1: int] :
( ( plus_plus_int @ X1 @ X2 )
= ( plus_plus_int @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_20,plain,
! [X1: int] :
( ( plus_plus_int @ X1 @ zero_zero_int )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_21,plain,
! [X171: int,X172: int] :
( ( ( X171 = zero_zero_int )
| ( ( power_power_int @ X171 @ ( number_number_of_nat @ X172 ) )
!= zero_zero_int ) )
& ( ( ( number_number_of_nat @ X172 )
!= zero_zero_nat )
| ( ( power_power_int @ X171 @ ( number_number_of_nat @ X172 ) )
!= zero_zero_int ) )
& ( ( X171 != zero_zero_int )
| ( ( number_number_of_nat @ X172 )
= zero_zero_nat )
| ( ( power_power_int @ X171 @ ( number_number_of_nat @ X172 ) )
= zero_zero_int ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
thf(c_0_22,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_15]) ).
thf(c_0_23,plain,
! [X1: int] :
( ( plus_plus_int @ pls @ X1 )
= X1 ),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_24,plain,
! [X1: int] :
( ( plus_plus_int @ X1 @ ( plus_plus_int @ one_one_int @ X1 ) )
= ( bit1 @ X1 ) ),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_25,plain,
! [X1: int] :
( ( plus_plus_int @ X1 @ pls )
= X1 ),
inference(rw,[status(thm)],[c_0_20,c_0_17]) ).
thf(c_0_26,plain,
! [X199: int] :
( ( bit0 @ X199 )
= ( plus_plus_int @ X199 @ X199 ) ),
inference(variable_rename,[status(thm)],[fact_83_Bit0__def]) ).
thf(c_0_27,plain,
~ ( ord_less_int @ pls @ zero_zero_int ),
inference(fof_simplification,[status(thm)],[fact_62_bin__less__0__simps_I1_J]) ).
thf(c_0_28,plain,
! [X1: int,X2: int] :
( ( X1 = zero_zero_int )
| ( ( power_power_int @ X1 @ ( number_number_of_nat @ X2 ) )
!= zero_zero_int ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_29,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_22]) ).
thf(c_0_30,plain,
( ( bit1 @ pls )
= one_one_int ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
thf(c_0_31,plain,
! [X1: int] :
( ( bit0 @ X1 )
= ( plus_plus_int @ X1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_32,plain,
~ ( ord_less_int @ pls @ zero_zero_int ),
inference(fof_nnf,[status(thm)],[c_0_27]) ).
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,X2: int] :
( ( X1 = pls )
| ( ( power_power_int @ X1 @ ( number_number_of_nat @ X2 ) )
!= pls ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_17]),c_0_17]) ).
thf(c_0_35,negated_conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( plus_plus_int @ one_one_int @ one_one_int ) ) )
= pls ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_17]) ).
thf(c_0_36,plain,
~ ( ord_less_int @ pls @ zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_37,plain,
ord_less_int @ pls @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ),
inference(rw,[status(thm)],[c_0_33,c_0_17]) ).
thf(c_0_38,negated_conjecture,
( ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) )
= pls ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
thf(c_0_39,plain,
~ ( ord_less_int @ pls @ pls ),
inference(rw,[status(thm)],[c_0_36,c_0_17]) ).
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 : NUM925^1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n015.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 13:09:02 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.26 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.vGMk9ny6QI/E---3.1_3485536.p
% 0.23/0.29 % Version: 3.5.1-ho
% 0.23/0.29 % Preprocessing class: HSLSSMSSSSSNFFN.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.29 % Starting sh5l with 300s (1) cores
% 0.23/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.29 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.29 % new_bool_1 with pid 3485576 completed with status 0
% 0.23/0.29 % Result found by new_bool_1
% 0.23/0.29 % Preprocessing class: HSLSSMSSSSSNFFN.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.29 % Starting sh5l with 300s (1) cores
% 0.23/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.29 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.29 % Search class: HGHSM-FFMM21-MFFFFFNN
% 0.23/0.29 % partial match(1): FGHSM-FFMM21-MFFFFFNN
% 0.23/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.29 % SubtermCWHack with pid 3485580 completed with status 0
% 0.23/0.29 % Result found by SubtermCWHack
% 0.23/0.29 % Preprocessing class: HSLSSMSSSSSNFFN.
% 0.23/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.29 % Starting sh5l with 300s (1) cores
% 0.23/0.29 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.23/0.29 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.23/0.29 % Search class: HGHSM-FFMM21-MFFFFFNN
% 0.23/0.29 % partial match(1): FGHSM-FFMM21-MFFFFFNN
% 0.23/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.29 % Preprocessing time : 0.002 s
% 0.23/0.29
% 0.23/0.29 % Proof found!
% 0.23/0.29 % SZS status Theorem
% 0.23/0.29 % SZS output start CNFRefutation
% See solution above
% 0.23/0.29 % Parsed axioms : 128
% 0.23/0.29 % Removed by relevancy pruning/SinE : 38
% 0.23/0.29 % Initial clauses : 130
% 0.23/0.29 % Removed in clause preprocessing : 8
% 0.23/0.29 % Initial clauses in saturation : 122
% 0.23/0.29 % Processed clauses : 266
% 0.23/0.29 % ...of these trivial : 18
% 0.23/0.29 % ...subsumed : 123
% 0.23/0.29 % ...remaining for further processing : 125
% 0.23/0.29 % Other redundant clauses eliminated : 7
% 0.23/0.29 % Clauses deleted for lack of memory : 0
% 0.23/0.29 % Backward-subsumed : 1
% 0.23/0.29 % Backward-rewritten : 10
% 0.23/0.29 % Generated clauses : 474
% 0.23/0.29 % ...of the previous two non-redundant : 329
% 0.23/0.29 % ...aggressively subsumed : 0
% 0.23/0.29 % Contextual simplify-reflections : 0
% 0.23/0.29 % Paramodulations : 461
% 0.23/0.29 % Factorizations : 2
% 0.23/0.29 % NegExts : 0
% 0.23/0.29 % Equation resolutions : 11
% 0.23/0.29 % Disequality decompositions : 0
% 0.23/0.29 % Total rewrite steps : 263
% 0.23/0.29 % ...of those cached : 214
% 0.23/0.29 % Propositional unsat checks : 0
% 0.23/0.29 % Propositional check models : 0
% 0.23/0.29 % Propositional check unsatisfiable : 0
% 0.23/0.29 % Propositional clauses : 0
% 0.23/0.29 % Propositional clauses after purity: 0
% 0.23/0.29 % Propositional unsat core size : 0
% 0.23/0.29 % Propositional preprocessing time : 0.000
% 0.23/0.29 % Propositional encoding time : 0.000
% 0.23/0.29 % Propositional solver time : 0.000
% 0.23/0.29 % Success case prop preproc time : 0.000
% 0.23/0.29 % Success case prop encoding time : 0.000
% 0.23/0.29 % Success case prop solver time : 0.000
% 0.23/0.29 % Current number of processed clauses : 107
% 0.23/0.29 % Positive orientable unit clauses : 29
% 0.23/0.29 % Positive unorientable unit clauses: 2
% 0.23/0.29 % Negative unit clauses : 19
% 0.23/0.29 % Non-unit-clauses : 57
% 0.23/0.29 % Current number of unprocessed clauses: 183
% 0.23/0.29 % ...number of literals in the above : 343
% 0.23/0.29 % Current number of archived formulas : 0
% 0.23/0.29 % Current number of archived clauses : 11
% 0.23/0.29 % Clause-clause subsumption calls (NU) : 764
% 0.23/0.29 % Rec. Clause-clause subsumption calls : 699
% 0.23/0.29 % Non-unit clause-clause subsumptions : 47
% 0.23/0.29 % Unit Clause-clause subsumption calls : 386
% 0.23/0.29 % Rewrite failures with RHS unbound : 0
% 0.23/0.29 % BW rewrite match attempts : 21
% 0.23/0.29 % BW rewrite match successes : 18
% 0.23/0.29 % Condensation attempts : 0
% 0.23/0.29 % Condensation successes : 0
% 0.23/0.29 % Termbank termtop insertions : 11214
% 0.23/0.29 % Search garbage collected termcells : 1375
% 0.23/0.29
% 0.23/0.29 % -------------------------------------------------
% 0.23/0.29 % User time : 0.016 s
% 0.23/0.29 % System time : 0.007 s
% 0.23/0.29 % Total time : 0.023 s
% 0.23/0.29 % Maximum resident set size: 3960 pages
% 0.23/0.29
% 0.23/0.29 % -------------------------------------------------
% 0.23/0.29 % User time : 0.018 s
% 0.23/0.29 % System time : 0.011 s
% 0.23/0.29 % Total time : 0.029 s
% 0.23/0.29 % Maximum resident set size: 4864 pages
% 0.23/0.29 % E exiting
%------------------------------------------------------------------------------