%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP276_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:55:12 PM UTC 2026
% Result : ContradictoryAxioms 4.79s 3.16s
% Output : CNFRefutation 4.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 14 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
fun_nat_bool: $tType ).
tff(decl_sort2,type,
nat: $tType ).
tff(decl_sort3,type,
fun_nat_nat: $tType ).
tff(decl_sort4,type,
fun_nat_fun_nat_bool: $tType ).
tff(decl_sort5,type,
num: $tType ).
tff(decl_sort6,type,
bool: $tType ).
tff(decl_sort7,type,
fun_num_nat: $tType ).
tff(decl_sort8,type,
fun_num_num: $tType ).
tff(decl_989,type,
one_one_nat: nat ).
tff(decl_1029,type,
zero_zero_nat: nat ).
tff(decl_1388,type,
suc: fun_nat_nat ).
tff(decl_1476,type,
bit0: fun_num_num ).
tff(decl_1478,type,
one: num ).
tff(decl_1486,type,
numeral_numeral_nat: fun_num_nat ).
tff(decl_1547,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(decl_2005,type,
aa_nat_bool: ( nat * fun_nat_bool ) > bool ).
tff(decl_2008,type,
aa_nat_nat: ( nat * fun_nat_nat ) > nat ).
tff(decl_2034,type,
aa_nat_fun_nat_bool: ( nat * fun_nat_fun_nat_bool ) > fun_nat_bool ).
tff(decl_2060,type,
aa_num_nat: ( num * fun_num_nat ) > nat ).
tff(decl_2061,type,
aa_num_num: ( num * fun_num_num ) > num ).
tff(decl_2411,type,
pp: bool > $o ).
tff(decl_2414,type,
deg: nat ).
tff(fact_103_Suc__n__not__le__n,axiom,
! [X176: nat] : ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(suc,X176)),X176)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Suc__n__not__le__n) ).
tff(fact_75__C1_C_I2_J,axiom,
deg = aa_nat_nat(suc,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75__C1_C_I2_J) ).
tff(fact_1158_One__nat__def,axiom,
one_one_nat = aa_nat_nat(suc,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1158_One__nat__def) ).
tff(fact_2986_a0,axiom,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2986_a0) ).
tff(fact_3212_Suc__1,axiom,
aa_nat_nat(suc,one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3212_Suc__1) ).
tff(c_0_5,plain,
! [X176: nat] : ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(suc,X176)),X176)),
inference(fof_simplification,[status(thm)],[fact_103_Suc__n__not__le__n]) ).
tcf(c_0_6,plain,
deg = aa_nat_nat(suc,zero_zero_nat),
inference(split_conjunct,[status(thm)],[fact_75__C1_C_I2_J]) ).
tcf(c_0_7,plain,
one_one_nat = aa_nat_nat(suc,zero_zero_nat),
inference(split_conjunct,[status(thm)],[fact_1158_One__nat__def]) ).
tff(c_0_8,plain,
! [X19789: nat] : ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(suc,X19789)),X19789)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_5])]) ).
tcf(c_0_9,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg)),
inference(split_conjunct,[status(thm)],[fact_2986_a0]) ).
tcf(c_0_10,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_3212_Suc__1]) ).
tcf(c_0_11,plain,
deg = one_one_nat,
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
tcf(c_0_12,plain,
! [X3: nat] : ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(suc,X3)),X3)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP276_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 20 22:28:59 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 4.79/3.16 % Version: 3.5.1
% 4.79/3.16 % Preprocessing class: FMLLSMLLSSSNFFN.
% 4.79/3.16 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 4.79/3.16 % Starting new_bool_3 with 897s (3) cores
% 4.79/3.16 % Starting new_bool_1 with 897s (3) cores
% 4.79/3.16 % Starting sh5l with 299s (1) cores
% 4.79/3.16 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 299s (1) cores
% 4.79/3.16 % new_bool_3 with pid 327830 completed with status 0
% 4.79/3.16 % Result found by new_bool_3
% 4.79/3.16 % Preprocessing class: FMLLSMLLSSSNFFN.
% 4.79/3.16 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 4.79/3.16 % Starting new_bool_3 with 897s (3) cores
% 4.79/3.16 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 4.79/3.16 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.79/3.16 % Search class: FGHSM-SMLM32-DFFFFFNN
% 4.79/3.16 % Scheduled 13 strats onto 3 cores with 897 seconds (897 total)
% 4.79/3.16 % Starting SubtermCWHack with 81s (1) cores
% 4.79/3.16 % Starting new_bool_3 with 90s (1) cores
% 4.79/3.16 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 4.79/3.16 % SubtermCWHack with pid 327834 completed with status 0
% 4.79/3.16 % Result found by SubtermCWHack
% 4.79/3.16 % Preprocessing class: FMLLSMLLSSSNFFN.
% 4.79/3.16 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 4.79/3.16 % Starting new_bool_3 with 897s (3) cores
% 4.79/3.16 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 4.79/3.16 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 4.79/3.16 % Search class: FGHSM-SMLM32-DFFFFFNN
% 4.79/3.16 % Scheduled 13 strats onto 3 cores with 897 seconds (897 total)
% 4.79/3.16 % Starting SubtermCWHack with 81s (1) cores
% 4.79/3.16 % Preprocessing time : 0.133 s
% 4.79/3.16
% 4.79/3.16 % Proof found!
% 4.79/3.16 % SZS status ContradictoryAxioms
% 4.79/3.16 % SZS output start CNFRefutation
% See solution above
% 4.79/3.17 % Parsed axioms : 13312
% 4.79/3.17 % Removed by relevancy pruning/SinE : 10984
% 4.79/3.17 % Initial clauses : 7116
% 4.79/3.17 % Removed in clause preprocessing : 1889
% 4.79/3.17 % Initial clauses in saturation : 5227
% 4.79/3.17 % Processed clauses : 788
% 4.79/3.17 % ...of these trivial : 79
% 4.79/3.17 % ...subsumed : 216
% 4.79/3.17 % ...remaining for further processing : 492
% 4.79/3.17 % Other redundant clauses eliminated : 202
% 4.79/3.17 % Clauses deleted for lack of memory : 0
% 4.79/3.17 % Backward-subsumed : 7
% 4.79/3.17 % Backward-rewritten : 12
% 4.79/3.17 % Generated clauses : 596
% 4.79/3.17 % ...of the previous two non-redundant : 313
% 4.79/3.17 % ...aggressively subsumed : 0
% 4.79/3.17 % Contextual simplify-reflections : 0
% 4.79/3.17 % Paramodulations : 396
% 4.79/3.17 % Factorizations : 0
% 4.79/3.17 % NegExts : 0
% 4.79/3.17 % Equation resolutions : 210
% 4.79/3.17 % Disequality decompositions : 0
% 4.79/3.17 % Total rewrite steps : 348
% 4.79/3.17 % ...of those cached : 219
% 4.79/3.17 % Propositional unsat checks : 0
% 4.79/3.17 % Propositional check models : 0
% 4.79/3.17 % Propositional check unsatisfiable : 0
% 4.79/3.17 % Propositional clauses : 0
% 4.79/3.17 % Propositional clauses after purity: 0
% 4.79/3.17 % Propositional unsat core size : 0
% 4.79/3.17 % Propositional preprocessing time : 0.000
% 4.79/3.17 % Propositional encoding time : 0.000
% 4.79/3.17 % Propositional solver time : 0.000
% 4.79/3.17 % Success case prop preproc time : 0.000
% 4.79/3.17 % Success case prop encoding time : 0.000
% 4.79/3.17 % Success case prop solver time : 0.000
% 4.79/3.17 % Current number of processed clauses : 302
% 4.79/3.17 % Positive orientable unit clauses : 165
% 4.79/3.17 % Positive unorientable unit clauses: 0
% 4.79/3.17 % Negative unit clauses : 45
% 4.79/3.17 % Non-unit-clauses : 92
% 4.79/3.17 % Current number of unprocessed clauses: 4752
% 4.79/3.17 % ...number of literals in the above : 20939
% 4.79/3.17 % Current number of archived formulas : 0
% 4.79/3.17 % Current number of archived clauses : 19
% 4.79/3.17 % Clause-clause subsumption calls (NU) : 5572
% 4.79/3.17 % Rec. Clause-clause subsumption calls : 5002
% 4.79/3.17 % Non-unit clause-clause subsumptions : 108
% 4.79/3.17 % Unit Clause-clause subsumption calls : 623
% 4.79/3.17 % Rewrite failures with RHS unbound : 0
% 4.79/3.17 % BW rewrite match attempts : 237
% 4.79/3.17 % BW rewrite match successes : 12
% 4.79/3.17 % Condensation attempts : 0
% 4.79/3.17 % Condensation successes : 0
% 4.79/3.17 % Termbank termtop insertions : 885053
% 4.79/3.17 % Search garbage collected termcells : 189535
% 4.79/3.17
% 4.79/3.17 % -------------------------------------------------
% 4.79/3.17 % User time : 0.678 s
% 4.79/3.17 % System time : 0.098 s
% 4.79/3.17 % Total time : 0.775 s
% 4.79/3.17 % Maximum resident set size: 47720 pages
% 4.79/3.17
% 4.79/3.17 % -------------------------------------------------
% 4.79/3.17 % User time : 2.797 s
% 4.79/3.17 % System time : 0.282 s
% 4.79/3.17 % Total time : 3.078 s
% 4.79/3.17 % Maximum resident set size: 33024 pages
% 4.79/3.17 % E exiting
%------------------------------------------------------------------------------