%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM924^3 : 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 : n010.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 0.99s 0.79s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 25 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 246 ( 7 ~; 0 |; 0 &; 239 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
int: $tType ).
thf(decl_sort2,type,
nat: $tType ).
thf(decl_28,type,
one_one_int: int ).
thf(decl_31,type,
plus_plus_int: int > int > int ).
thf(decl_34,type,
times_times_int: int > int > int ).
thf(decl_37,type,
zero_zero_int: int ).
thf(decl_45,type,
bit0: int > int ).
thf(decl_46,type,
bit1: int > int ).
thf(decl_48,type,
pls: int ).
thf(decl_49,type,
number_number_of_int: int > int ).
thf(decl_50,type,
number_number_of_nat: int > nat ).
thf(decl_52,type,
ord_less_int: int > int > $o ).
thf(decl_58,type,
power_power_int: int > nat > int ).
thf(decl_75,type,
m: int ).
thf(decl_77,type,
s: int ).
thf(decl_78,type,
t: int ).
thf(conj_0,conjecture,
ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int,
file('/export/starexec/sandbox/tmp/tmp.PA8apRu9Tf/E---3.1_2816592.p',conj_0) ).
thf(fact_160_one__is__num__one,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PA8apRu9Tf/E---3.1_2816592.p',fact_160_one__is__num__one) ).
thf(fact_172_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/tmp/tmp.PA8apRu9Tf/E---3.1_2816592.p',fact_172_Pls__def) ).
thf(fact_34_number__of__is__id,axiom,
! [X23: int] :
( ( number_number_of_int @ X23 )
= X23 ),
file('/export/starexec/sandbox/tmp/tmp.PA8apRu9Tf/E---3.1_2816592.p',fact_34_number__of__is__id) ).
thf(fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X201: int] :
( ( times_times_int @ X201 @ X201 )
= ( power_power_int @ X201 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PA8apRu9Tf/E---3.1_2816592.p',fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(fact_134_zadd__commute,axiom,
! [X24: int,X22: int] :
( ( plus_plus_int @ X24 @ X22 )
= ( plus_plus_int @ X22 @ X24 ) ),
file('/export/starexec/sandbox/tmp/tmp.PA8apRu9Tf/E---3.1_2816592.p',fact_134_zadd__commute) ).
thf(fact_35_zmult__commute,axiom,
! [X24: int,X22: int] :
( ( times_times_int @ X24 @ X22 )
= ( times_times_int @ X22 @ X24 ) ),
file('/export/starexec/sandbox/tmp/tmp.PA8apRu9Tf/E---3.1_2816592.p',fact_35_zmult__commute) ).
thf(fact_3_t,axiom,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
file('/export/starexec/sandbox/tmp/tmp.PA8apRu9Tf/E---3.1_2816592.p',fact_3_t) ).
thf(fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X376: int] :
( ( times_times_int @ X376 @ zero_zero_int )
= zero_zero_int ),
file('/export/starexec/sandbox/tmp/tmp.PA8apRu9Tf/E---3.1_2816592.p',fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
thf(fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096,axiom,
ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ),
file('/export/starexec/sandbox/tmp/tmp.PA8apRu9Tf/E---3.1_2816592.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
thf(c_0_10,negated_conjecture,
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_11,negated_conjecture,
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
thf(c_0_12,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(split_conjunct,[status(thm)],[fact_160_one__is__num__one]) ).
thf(c_0_13,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_172_Pls__def]) ).
thf(c_0_14,plain,
! [X4413: int] :
( ( number_number_of_int @ X4413 )
= X4413 ),
inference(variable_rename,[status(thm)],[fact_34_number__of__is__id]) ).
thf(c_0_15,plain,
! [X4775: int] :
( ( times_times_int @ X4775 @ X4775 )
= ( power_power_int @ X4775 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(variable_rename,[status(thm)],[fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
thf(c_0_16,negated_conjecture,
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
thf(c_0_17,plain,
( ( number_number_of_int @ ( bit1 @ zero_zero_int ) )
= one_one_int ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_18,plain,
! [X3: int] :
( ( number_number_of_int @ X3 )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,plain,
! [X4596: int,X4597: int] :
( ( plus_plus_int @ X4596 @ X4597 )
= ( plus_plus_int @ X4597 @ X4596 ) ),
inference(variable_rename,[status(thm)],[fact_134_zadd__commute]) ).
thf(c_0_20,plain,
! [X4414: int,X4415: int] :
( ( times_times_int @ X4414 @ X4415 )
= ( times_times_int @ X4415 @ X4414 ) ),
inference(variable_rename,[status(thm)],[fact_35_zmult__commute]) ).
thf(c_0_21,plain,
! [X3: int] :
( ( times_times_int @ X3 @ X3 )
= ( power_power_int @ X3 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_22,negated_conjecture,
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_23,plain,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
inference(split_conjunct,[status(thm)],[fact_3_t]) ).
thf(c_0_24,plain,
( one_one_int
= ( bit1 @ zero_zero_int ) ),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_25,plain,
! [X4: int,X3: int] :
( ( plus_plus_int @ X3 @ X4 )
= ( plus_plus_int @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_26,plain,
! [X4: int,X3: int] :
( ( times_times_int @ X3 @ X4 )
= ( times_times_int @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_27,plain,
! [X3: int] :
( ( times_times_int @ X3 @ X3 )
= ( power_power_int @ X3 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) ) ),
inference(rw,[status(thm)],[c_0_21,c_0_13]) ).
thf(c_0_28,plain,
! [X4984: int] :
( ( times_times_int @ X4984 @ zero_zero_int )
= zero_zero_int ),
inference(variable_rename,[status(thm)],[fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).
thf(c_0_29,negated_conjecture,
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) ) @ one_one_int ) @ zero_zero_int ),
inference(rw,[status(thm)],[c_0_22,c_0_13]) ).
thf(c_0_30,plain,
ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ),
inference(split_conjunct,[status(thm)],[fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096]) ).
thf(c_0_31,plain,
( ( times_times_int @ t @ ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( times_times_int @ ( bit0 @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) @ m ) ) )
= ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( times_times_int @ s @ s ) ) ),
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)],[inference(rw,[status(thm)],[c_0_23,c_0_13]),c_0_18]),c_0_24]),c_0_25]),c_0_26]),c_0_13]),c_0_27]),c_0_24]),c_0_25]) ).
thf(c_0_32,plain,
! [X3: int] :
( ( times_times_int @ X3 @ zero_zero_int )
= zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_33,negated_conjecture,
~ ( ord_less_int @ ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ zero_zero_int ) ) ) ) ) @ zero_zero_int ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_25]),c_0_24]) ).
thf(c_0_34,plain,
ord_less_int @ ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( times_times_int @ s @ s ) ) @ 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_13]),c_0_18]),c_0_24]),c_0_25]),c_0_26]),c_0_31]),c_0_13]),c_0_18]),c_0_24]),c_0_25]),c_0_32]) ).
thf(c_0_35,negated_conjecture,
~ ( ord_less_int @ ( plus_plus_int @ ( bit1 @ zero_zero_int ) @ ( times_times_int @ s @ s ) ) @ zero_zero_int ),
inference(rw,[status(thm)],[c_0_33,c_0_27]) ).
thf(c_0_36,plain,
$false,
inference(sr,[status(thm)],[c_0_34,c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM924^3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n010.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:05:48 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.31/0.37 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.PA8apRu9Tf/E---3.1_2816592.p
% 0.99/0.79 % Version: 3.5.1-ho
% 0.99/0.79 % Preprocessing class: HMLSSMSMSSSNSFA.
% 0.99/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.99/0.79 % Starting sh3 with 1500s (5) cores
% 0.99/0.79 % Starting lpo1_def_fix with 300s (1) cores
% 0.99/0.79 % Starting lpo8_s with 300s (1) cores
% 0.99/0.79 % Starting lpo1_lambda_fix with 300s (1) cores
% 0.99/0.79 % sh3 with pid 2816605 completed with status 0
% 0.99/0.79 % Result found by sh3
% 0.99/0.79 % Preprocessing class: HMLSSMSMSSSNSFA.
% 0.99/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.99/0.79 % Starting sh3 with 1500s (5) cores
% 0.99/0.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.99/0.79 % No SInE strategy applied
% 0.99/0.79 % Search class: HGHSM-SSLM32-DSFFFFBN
% 0.99/0.79 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.99/0.79 % Starting SubtermCWHack with 151s (1) cores
% 0.99/0.79 % Starting sh3 with 750s (1) cores
% 0.99/0.79 % Starting lpo1_def_fix with 188s (1) cores
% 0.99/0.79 % Starting lpo8_s with 188s (1) cores
% 0.99/0.79 % Starting lpo1_lambda_fix with 188s (1) cores
% 0.99/0.79 % sh3 with pid 2816613 completed with status 0
% 0.99/0.79 % Result found by sh3
% 0.99/0.79 % Preprocessing class: HMLSSMSMSSSNSFA.
% 0.99/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.99/0.79 % Starting sh3 with 1500s (5) cores
% 0.99/0.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.99/0.79 % No SInE strategy applied
% 0.99/0.79 % Search class: HGHSM-SSLM32-DSFFFFBN
% 0.99/0.79 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.99/0.79 % Starting SubtermCWHack with 151s (1) cores
% 0.99/0.79 % Starting sh3 with 750s (1) cores
% 0.99/0.79 % Preprocessing time : 0.026 s
% 0.99/0.79 % Presaturation interreduction done
% 0.99/0.79
% 0.99/0.79 % Proof found!
% 0.99/0.79 % SZS status Theorem
% 0.99/0.79 % SZS output start CNFRefutation
% See solution above
% 0.99/0.79 % Parsed axioms : 1259
% 0.99/0.79 % Removed by relevancy pruning/SinE : 0
% 0.99/0.79 % Initial clauses : 1788
% 0.99/0.79 % Removed in clause preprocessing : 150
% 0.99/0.79 % Initial clauses in saturation : 1638
% 0.99/0.79 % Processed clauses : 1807
% 0.99/0.79 % ...of these trivial : 183
% 0.99/0.79 % ...subsumed : 327
% 0.99/0.79 % ...remaining for further processing : 1296
% 0.99/0.79 % Other redundant clauses eliminated : 151
% 0.99/0.79 % Clauses deleted for lack of memory : 0
% 0.99/0.79 % Backward-subsumed : 6
% 0.99/0.79 % Backward-rewritten : 39
% 0.99/0.79 % Generated clauses : 144
% 0.99/0.79 % ...of the previous two non-redundant : 95
% 0.99/0.79 % ...aggressively subsumed : 0
% 0.99/0.79 % Contextual simplify-reflections : 3
% 0.99/0.79 % Paramodulations : 13
% 0.99/0.79 % Factorizations : 0
% 0.99/0.79 % NegExts : 0
% 0.99/0.79 % Equation resolutions : 151
% 0.99/0.79 % Disequality decompositions : 0
% 0.99/0.79 % Total rewrite steps : 1577
% 0.99/0.79 % ...of those cached : 1298
% 0.99/0.79 % Propositional unsat checks : 0
% 0.99/0.79 % Propositional check models : 0
% 0.99/0.79 % Propositional check unsatisfiable : 0
% 0.99/0.79 % Propositional clauses : 0
% 0.99/0.79 % Propositional clauses after purity: 0
% 0.99/0.79 % Propositional unsat core size : 0
% 0.99/0.79 % Propositional preprocessing time : 0.000
% 0.99/0.79 % Propositional encoding time : 0.000
% 0.99/0.79 % Propositional solver time : 0.000
% 0.99/0.79 % Success case prop preproc time : 0.000
% 0.99/0.79 % Success case prop encoding time : 0.000
% 0.99/0.79 % Success case prop solver time : 0.000
% 0.99/0.79 % Current number of processed clauses : 76
% 0.99/0.79 % Positive orientable unit clauses : 40
% 0.99/0.79 % Positive unorientable unit clauses: 0
% 0.99/0.79 % Negative unit clauses : 24
% 0.99/0.79 % Non-unit-clauses : 12
% 0.99/0.79 % Current number of unprocessed clauses: 971
% 0.99/0.79 % ...number of literals in the above : 2381
% 0.99/0.79 % Current number of archived formulas : 0
% 0.99/0.79 % Current number of archived clauses : 1090
% 0.99/0.79 % Clause-clause subsumption calls (NU) : 136846
% 0.99/0.79 % Rec. Clause-clause subsumption calls : 81630
% 0.99/0.79 % Non-unit clause-clause subsumptions : 253
% 0.99/0.79 % Unit Clause-clause subsumption calls : 1224
% 0.99/0.79 % Rewrite failures with RHS unbound : 0
% 0.99/0.79 % BW rewrite match attempts : 336
% 0.99/0.79 % BW rewrite match successes : 193
% 0.99/0.79 % Condensation attempts : 0
% 0.99/0.79 % Condensation successes : 0
% 0.99/0.79 % Termbank termtop insertions : 156228
% 0.99/0.79 % Search garbage collected termcells : 30002
% 0.99/0.79
% 0.99/0.79 % -------------------------------------------------
% 0.99/0.79 % User time : 0.353 s
% 0.99/0.79 % System time : 0.026 s
% 0.99/0.79 % Total time : 0.379 s
% 0.99/0.79 % Maximum resident set size: 11660 pages
% 0.99/0.79
% 0.99/0.79 % -------------------------------------------------
% 0.99/0.79 % User time : 1.142 s
% 0.99/0.79 % System time : 0.110 s
% 0.99/0.79 % Total time : 1.252 s
% 0.99/0.79 % Maximum resident set size: 7168 pages
% 0.99/0.79 % E exiting
%------------------------------------------------------------------------------