%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP270_1 : TPTP v9.3.1. Released v8.0.0.
% 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 : Thu Sep 24 12:57:19 PM UTC 2026
% Result : Theorem 0.18s 26.31s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 10 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 41 ( 19 ~; 15 |; 3 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 12 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
fun_nat_bool: $tType ).
tff(decl_sort2,type,
fun_nat_nat: $tType ).
tff(decl_sort3,type,
fun_nat_fun_nat_bool: $tType ).
tff(decl_sort4,type,
fun_nat_fun_nat_nat: $tType ).
tff(decl_sort5,type,
nat: $tType ).
tff(decl_sort6,type,
num: $tType ).
tff(decl_sort7,type,
bool: $tType ).
tff(decl_sort8,type,
fun_num_num: $tType ).
tff(decl_sort9,type,
fun_num_nat: $tType ).
tff(decl_901,type,
one_one_nat: nat ).
tff(decl_1142,type,
suc: fun_nat_nat ).
tff(decl_1206,type,
bit0: fun_num_num ).
tff(decl_1208,type,
one: num ).
tff(decl_1216,type,
numeral_numeral_nat: fun_num_nat ).
tff(decl_1256,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(decl_1271,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(decl_1319,type,
power_power_nat: fun_nat_fun_nat_nat ).
tff(decl_1722,type,
aa_nat_bool: ( nat * fun_nat_bool ) > bool ).
tff(decl_1725,type,
aa_nat_nat: ( nat * fun_nat_nat ) > nat ).
tff(decl_1747,type,
aa_nat_fun_nat_bool: ( nat * fun_nat_fun_nat_bool ) > fun_nat_bool ).
tff(decl_1750,type,
aa_nat_fun_nat_nat: ( nat * fun_nat_fun_nat_nat ) > fun_nat_nat ).
tff(decl_1772,type,
aa_num_nat: ( num * fun_num_nat ) > nat ).
tff(decl_1773,type,
aa_num_num: ( num * fun_num_num ) > num ).
tff(decl_2009,type,
pp: bool > $o ).
tff(decl_2010,type,
deg: nat ).
tff(decl_2012,type,
ma: nat ).
tff(decl_2013,type,
mi: nat ).
tff(decl_2017,type,
x: nat ).
tff(fact_523_nless__le,axiom,
! [X1078: nat,X1079: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X1078),X1079))
<=> ( ( X1078 = X1079 )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X1078),X1079)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_nless__le) ).
tff(conj_0,conjecture,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(fact_382_dual__order_Ostrict__trans,axiom,
! [X735: nat,X736: nat,X737: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X735),X736))
=> ( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X737),X735))
=> pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X737),X736)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_dual__order_Ostrict__trans) ).
tff(fact_24__092_060open_062x_A_092_060le_062_Ama_A_092_060and_062_Ami_A_092_060le_062_Ax_092_060close_062,axiom,
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,mi),x))
& pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,x),ma)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24__092_060open_062x_A_092_060le_062_Ama_A_092_060and_062_Ami_A_092_060le_062_Ax_092_060close_062) ).
tff(fact_1__C5_Ohyps_C_I8_J,axiom,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,ma),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__C5_Ohyps_C_I8_J) ).
tff(fact_2973_Suc__1,axiom,
aa_nat_nat(suc,one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2973_Suc__1) ).
tff(c_0_6,plain,
! [X1078: nat,X1079: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X1078),X1079))
<=> ( ( X1078 = X1079 )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X1078),X1079)) ) ),
inference(fof_simplification,[status(thm)],[fact_523_nless__le]) ).
tff(c_0_7,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(assume_negation,[status(cth)],[conj_0]) ).
tff(c_0_8,plain,
! [X19449: nat,X19450: nat] :
( ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19449),X19450))
| ( X19449 != X19450 ) )
& ( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19449),X19450))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X19449),X19450)) )
& ( ( X19449 = X19450 )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X19449),X19450))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19449),X19450)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
tff(c_0_9,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
tff(c_0_10,plain,
! [X19389: nat,X19390: nat,X19391: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19391),X19390))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19391),X19389))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X19389),X19390)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_382_dual__order_Ostrict__trans])])]) ).
tcf(c_0_11,plain,
! [X1: nat,X17: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,X1),X17))
| ( X1 = X17 )
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X1),X17)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_12,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,x),ma)),
inference(split_conjunct,[status(thm)],[fact_24__092_060open_062x_A_092_060le_062_Ama_A_092_060and_062_Ami_A_092_060le_062_Ax_092_060close_062]) ).
tff(c_0_13,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
tcf(c_0_14,plain,
! [X18: nat,X17: nat,X1: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X18),X1))
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X1),X17))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,X18),X17)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_15,plain,
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),ma))
| ( x = ma ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
tcf(c_0_16,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,ma),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(split_conjunct,[status(thm)],[fact_1__C5_Ohyps_C_I8_J]) ).
tcf(c_0_17,plain,
aa_nat_nat(suc,one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)),
inference(split_conjunct,[status(thm)],[fact_2973_Suc__1]) ).
tcf(c_0_18,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_19,plain,
! [X1: nat] :
( ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,ma),X1))
| pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),X1))
| ( x = ma ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
tcf(c_0_20,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,ma),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),deg))),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
tcf(c_0_21,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,x),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),deg))),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
tcf(c_0_22,plain,
x = ma,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP270_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 20 22:25:04 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/26.31 % Version: 3.5.1
% 0.18/26.31 % Preprocessing class: FMLLSMLLSSSNFFN.
% 0.18/26.31 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 0.18/26.31 % Starting new_bool_3 with 897s (3) cores
% 0.18/26.31 % Starting new_bool_1 with 897s (3) cores
% 0.18/26.31 % Starting sh5l with 299s (1) cores
% 0.18/26.31 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 299s (1) cores
% 0.18/26.31 % new_bool_1 with pid 1618663 completed with status 0
% 0.18/26.31 % Result found by new_bool_1
% 0.18/26.31 % Preprocessing class: FMLLSMLLSSSNFFN.
% 0.18/26.31 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 0.18/26.31 % Starting new_bool_3 with 897s (3) cores
% 0.18/26.31 % Starting new_bool_1 with 897s (3) cores
% 0.18/26.31 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.18/26.31 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.18/26.31 % Search class: FGHSM-SMLM32-DFFFFFNN
% 0.18/26.31 % Scheduled 13 strats onto 3 cores with 896 seconds (896 total)
% 0.18/26.31 % Starting SubtermCWHack with 81s (1) cores
% 0.18/26.31 % Starting new_bool_1 with 90s (1) cores
% 0.18/26.31 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 0.18/26.31 % G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with pid 1618671 completed with status 0
% 0.18/26.31 % Result found by G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI
% 0.18/26.31 % Preprocessing class: FMLLSMLLSSSNFFN.
% 0.18/26.31 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 0.18/26.31 % Starting new_bool_3 with 897s (3) cores
% 0.18/26.31 % Starting new_bool_1 with 897s (3) cores
% 0.18/26.31 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.18/26.31 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.18/26.31 % Search class: FGHSM-SMLM32-DFFFFFNN
% 0.18/26.31 % Scheduled 13 strats onto 3 cores with 896 seconds (896 total)
% 0.18/26.31 % Starting SubtermCWHack with 81s (1) cores
% 0.18/26.31 % Starting new_bool_1 with 90s (1) cores
% 0.18/26.31 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 0.18/26.31 % Preprocessing time : 0.347 s
% 0.18/26.31
% 0.18/26.31 % Proof found!
% 0.18/26.31 % SZS status Theorem
% 0.18/26.31 % SZS output start CNFRefutation
% See solution above
% 0.18/26.31 % Parsed axioms : 13294
% 0.18/26.31 % Removed by relevancy pruning/SinE : 9897
% 0.18/26.31 % Initial clauses : 9448
% 0.18/26.31 % Removed in clause preprocessing : 1947
% 0.18/26.31 % Initial clauses in saturation : 7501
% 0.18/26.31 % Processed clauses : 9209
% 0.18/26.31 % ...of these trivial : 329
% 0.18/26.31 % ...subsumed : 2280
% 0.18/26.31 % ...remaining for further processing : 6600
% 0.18/26.31 % Other redundant clauses eliminated : 2405
% 0.18/26.31 % Clauses deleted for lack of memory : 0
% 0.18/26.31 % Backward-subsumed : 70
% 0.18/26.31 % Backward-rewritten : 139
% 0.18/26.31 % Generated clauses : 214836
% 0.18/26.31 % ...of the previous two non-redundant : 205023
% 0.18/26.31 % ...aggressively subsumed : 0
% 0.18/26.31 % Contextual simplify-reflections : 86
% 0.18/26.31 % Paramodulations : 213037
% 0.18/26.31 % Factorizations : 58
% 0.18/26.31 % NegExts : 0
% 0.18/26.31 % Equation resolutions : 2456
% 0.18/26.31 % Disequality decompositions : 0
% 0.18/26.31 % Total rewrite steps : 42931
% 0.18/26.31 % ...of those cached : 37624
% 0.18/26.31 % Propositional unsat checks : 0
% 0.18/26.31 % Propositional check models : 0
% 0.18/26.31 % Propositional check unsatisfiable : 0
% 0.18/26.31 % Propositional clauses : 0
% 0.18/26.31 % Propositional clauses after purity: 0
% 0.18/26.31 % Propositional unsat core size : 0
% 0.18/26.31 % Propositional preprocessing time : 0.000
% 0.18/26.31 % Propositional encoding time : 0.000
% 0.18/26.31 % Propositional solver time : 0.000
% 0.18/26.31 % Success case prop preproc time : 0.000
% 0.18/26.31 % Success case prop encoding time : 0.000
% 0.18/26.31 % Success case prop solver time : 0.000
% 0.18/26.31 % Current number of processed clauses : 5029
% 0.18/26.31 % Positive orientable unit clauses : 586
% 0.18/26.31 % Positive unorientable unit clauses: 47
% 0.18/26.31 % Negative unit clauses : 575
% 0.18/26.31 % Non-unit-clauses : 3821
% 0.18/26.31 % Current number of unprocessed clauses: 203166
% 0.18/26.31 % ...number of literals in the above : 929596
% 0.18/26.31 % Current number of archived formulas : 0
% 0.18/26.31 % Current number of archived clauses : 209
% 0.18/26.31 % Clause-clause subsumption calls (NU) : 13992349
% 0.18/26.31 % Rec. Clause-clause subsumption calls : 693795
% 0.18/26.31 % Non-unit clause-clause subsumptions : 1606
% 0.18/26.31 % Unit Clause-clause subsumption calls : 235413
% 0.18/26.31 % Rewrite failures with RHS unbound : 0
% 0.18/26.31 % BW rewrite match attempts : 17253
% 0.18/26.31 % BW rewrite match successes : 328
% 0.18/26.31 % Condensation attempts : 0
% 0.18/26.31 % Condensation successes : 0
% 0.18/26.31 % Termbank termtop insertions : 8436971
% 0.18/26.31 % Search garbage collected termcells : 204400
% 0.18/26.31
% 0.18/26.31 % -------------------------------------------------
% 0.18/26.31 % User time : 23.365 s
% 0.18/26.31 % System time : 0.362 s
% 0.18/26.31 % Total time : 23.727 s
% 0.18/26.31 % Maximum resident set size: 55700 pages
% 0.18/26.31
% 0.18/26.31 % -------------------------------------------------
% 0.18/26.31 % User time : 68.498 s
% 0.18/26.31 % System time : 0.983 s
% 0.18/26.31 % Total time : 69.481 s
% 0.18/26.31 % Maximum resident set size: 33024 pages
% 0.18/26.31 % E exiting
%------------------------------------------------------------------------------