%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP232_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 : 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 12:56:56 PM UTC 2026
% Result : Theorem 6.78s 3.35s
% Output : CNFRefutation 6.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 11 ~; 2 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 7 !; 4 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
fun_VEBT_VEBT_bool: $tType ).
tff(decl_sort2,type,
fun_nat_nat: $tType ).
tff(decl_sort3,type,
fun_nat_bool: $tType ).
tff(decl_sort4,type,
fun_nat_fun_nat_nat: $tType ).
tff(decl_sort5,type,
nat: $tType ).
tff(decl_sort6,type,
vEBT_VEBT: $tType ).
tff(decl_sort7,type,
fun_VE3763956218935105199t_bool: $tType ).
tff(decl_sort8,type,
bool: $tType ).
tff(decl_sort9,type,
list_VEBT_VEBT: $tType ).
tff(decl_1185,type,
nth_VEBT_VEBT: ( nat * list_VEBT_VEBT ) > vEBT_VEBT ).
tff(decl_1603,type,
vEBT_V8194947554948674370ptions: fun_VE3763956218935105199t_bool ).
tff(decl_1604,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
tff(decl_1620,type,
vEBT_VEBT_minNull: fun_VEBT_VEBT_bool ).
tff(decl_1712,type,
aa_nat_bool: ( nat * fun_nat_bool ) > bool ).
tff(decl_1714,type,
aa_nat_nat: ( nat * fun_nat_nat ) > nat ).
tff(decl_1741,type,
aa_nat_fun_nat_nat: ( nat * fun_nat_fun_nat_nat ) > fun_nat_nat ).
tff(decl_1839,type,
aa_VEBT_VEBT_bool: ( vEBT_VEBT * fun_VEBT_VEBT_bool ) > bool ).
tff(decl_1851,type,
aa_VEB4832260192069861672t_bool: ( vEBT_VEBT * fun_VE3763956218935105199t_bool ) > fun_nat_bool ).
tff(decl_2075,type,
pp: bool > $o ).
tff(decl_2078,type,
m: nat ).
tff(decl_2080,type,
mi: nat ).
tff(decl_2081,type,
na: nat ).
tff(decl_2083,type,
treeList: list_VEBT_VEBT ).
tff(decl_2205,type,
esk116_1: vEBT_VEBT > nat ).
tff(conj_0,conjecture,
? [X252: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na))),X252)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(fact_1_False,axiom,
~ pp(aa_VEBT_VEBT_bool(vEBT_VEBT_minNull,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_False) ).
tff(fact_0_not__min__Null__member,axiom,
! [X1: vEBT_VEBT] :
( ~ pp(aa_VEBT_VEBT_bool(vEBT_VEBT_minNull,X1))
=> ? [X2: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_not__min__Null__member) ).
tff(fact_3__C8_C,axiom,
na = m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__C8_C) ).
tff(c_0_4,negated_conjecture,
~ ? [X252: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na))),X252)),
inference(assume_negation,[status(cth)],[conj_0]) ).
tff(c_0_5,plain,
~ pp(aa_VEBT_VEBT_bool(vEBT_VEBT_minNull,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)))),
inference(fof_simplification,[status(thm)],[fact_1_False]) ).
tff(c_0_6,negated_conjecture,
! [X18596: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na))),X18596)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
tff(c_0_7,plain,
! [X1: vEBT_VEBT] :
( ~ pp(aa_VEBT_VEBT_bool(vEBT_VEBT_minNull,X1))
=> ? [X2: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X1),X2)) ),
inference(fof_simplification,[status(thm)],[fact_0_not__min__Null__member]) ).
tff(c_0_8,plain,
~ pp(aa_VEBT_VEBT_bool(vEBT_VEBT_minNull,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)))),
inference(fof_nnf,[status(thm)],[c_0_5]) ).
tcf(c_0_9,negated_conjecture,
! [X2: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na))),X2)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
tcf(c_0_10,plain,
na = m,
inference(split_conjunct,[status(thm)],[fact_3__C8_C]) ).
tff(c_0_11,plain,
! [X19206: vEBT_VEBT] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X19206),esk116_1(X19206)))
| pp(aa_VEBT_VEBT_bool(vEBT_VEBT_minNull,X19206)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
tcf(c_0_12,plain,
~ pp(aa_VEBT_VEBT_bool(vEBT_VEBT_minNull,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),na)))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_13,negated_conjecture,
! [X2: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),m))),X2)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
tcf(c_0_14,plain,
! [X1: vEBT_VEBT] :
( pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,X1),esk116_1(X1)))
| pp(aa_VEBT_VEBT_bool(vEBT_VEBT_minNull,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_15,plain,
~ pp(aa_VEBT_VEBT_bool(vEBT_VEBT_minNull,nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,mi),m)))),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP232_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 % Computer : n004.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sun Sep 20 22:13:19 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.46 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
% 6.78/3.35 % Version: 3.5.1
% 6.78/3.35 % Preprocessing class: FMLLSMLLSSSNFFN.
% 6.78/3.35 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 6.78/3.35 % Starting new_bool_3 with 897s (3) cores
% 6.78/3.35 % Starting new_bool_1 with 897s (3) cores
% 6.78/3.35 % Starting sh5l with 299s (1) cores
% 6.78/3.35 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 299s (1) cores
% 6.78/3.35 % new_bool_1 with pid 1595072 completed with status 0
% 6.78/3.35 % Result found by new_bool_1
% 6.78/3.35 % Preprocessing class: FMLLSMLLSSSNFFN.
% 6.78/3.35 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 6.78/3.35 % Starting new_bool_3 with 897s (3) cores
% 6.78/3.35 % Starting new_bool_1 with 897s (3) cores
% 6.78/3.35 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 6.78/3.35 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.78/3.35 % Search class: FGHSM-SMLM32-DFFFFFNN
% 6.78/3.35 % Scheduled 13 strats onto 3 cores with 897 seconds (897 total)
% 6.78/3.35 % Starting SubtermCWHack with 81s (1) cores
% 6.78/3.35 % Starting new_bool_1 with 90s (1) cores
% 6.78/3.35 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 6.78/3.35 % G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with pid 1595077 completed with status 0
% 6.78/3.35 % Result found by G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI
% 6.78/3.35 % Preprocessing class: FMLLSMLLSSSNFFN.
% 6.78/3.35 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 6.78/3.35 % Starting new_bool_3 with 897s (3) cores
% 6.78/3.35 % Starting new_bool_1 with 897s (3) cores
% 6.78/3.35 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 6.78/3.35 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.78/3.35 % Search class: FGHSM-SMLM32-DFFFFFNN
% 6.78/3.35 % Scheduled 13 strats onto 3 cores with 897 seconds (897 total)
% 6.78/3.35 % Starting SubtermCWHack with 81s (1) cores
% 6.78/3.35 % Starting new_bool_1 with 90s (1) cores
% 6.78/3.35 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 6.78/3.35 % Preprocessing time : 0.162 s
% 6.78/3.35
% 6.78/3.35 % Proof found!
% 6.78/3.35 % SZS status Theorem
% 6.78/3.35 % SZS output start CNFRefutation
% See solution above
% 6.78/3.35 % Parsed axioms : 12949
% 6.78/3.35 % Removed by relevancy pruning/SinE : 10896
% 6.78/3.35 % Initial clauses : 6758
% 6.78/3.35 % Removed in clause preprocessing : 1847
% 6.78/3.35 % Initial clauses in saturation : 4911
% 6.78/3.35 % Processed clauses : 448
% 6.78/3.35 % ...of these trivial : 45
% 6.78/3.35 % ...subsumed : 70
% 6.78/3.35 % ...remaining for further processing : 333
% 6.78/3.35 % Other redundant clauses eliminated : 134
% 6.78/3.35 % Clauses deleted for lack of memory : 0
% 6.78/3.35 % Backward-subsumed : 7
% 6.78/3.35 % Backward-rewritten : 5
% 6.78/3.35 % Generated clauses : 512
% 6.78/3.35 % ...of the previous two non-redundant : 332
% 6.78/3.35 % ...aggressively subsumed : 0
% 6.78/3.35 % Contextual simplify-reflections : 0
% 6.78/3.35 % Paramodulations : 369
% 6.78/3.35 % Factorizations : 2
% 6.78/3.35 % NegExts : 0
% 6.78/3.35 % Equation resolutions : 141
% 6.78/3.35 % Disequality decompositions : 0
% 6.78/3.35 % Total rewrite steps : 302
% 6.78/3.35 % ...of those cached : 220
% 6.78/3.35 % Propositional unsat checks : 0
% 6.78/3.35 % Propositional check models : 0
% 6.78/3.35 % Propositional check unsatisfiable : 0
% 6.78/3.35 % Propositional clauses : 0
% 6.78/3.35 % Propositional clauses after purity: 0
% 6.78/3.35 % Propositional unsat core size : 0
% 6.78/3.35 % Propositional preprocessing time : 0.000
% 6.78/3.35 % Propositional encoding time : 0.000
% 6.78/3.35 % Propositional solver time : 0.000
% 6.78/3.35 % Success case prop preproc time : 0.000
% 6.78/3.35 % Success case prop encoding time : 0.000
% 6.78/3.35 % Success case prop solver time : 0.000
% 6.78/3.35 % Current number of processed clauses : 194
% 6.78/3.35 % Positive orientable unit clauses : 71
% 6.78/3.35 % Positive unorientable unit clauses: 0
% 6.78/3.35 % Negative unit clauses : 47
% 6.78/3.35 % Non-unit-clauses : 76
% 6.78/3.35 % Current number of unprocessed clauses: 4791
% 6.78/3.35 % ...number of literals in the above : 22189
% 6.78/3.35 % Current number of archived formulas : 0
% 6.78/3.35 % Current number of archived clauses : 12
% 6.78/3.35 % Clause-clause subsumption calls (NU) : 1269
% 6.78/3.35 % Rec. Clause-clause subsumption calls : 1165
% 6.78/3.35 % Non-unit clause-clause subsumptions : 46
% 6.78/3.35 % Unit Clause-clause subsumption calls : 165
% 6.78/3.35 % Rewrite failures with RHS unbound : 0
% 6.78/3.35 % BW rewrite match attempts : 129
% 6.78/3.35 % BW rewrite match successes : 5
% 6.78/3.35 % Condensation attempts : 0
% 6.78/3.35 % Condensation successes : 0
% 6.78/3.35 % Termbank termtop insertions : 836906
% 6.78/3.35 % Search garbage collected termcells : 184405
% 6.78/3.35
% 6.78/3.35 % -------------------------------------------------
% 6.78/3.35 % User time : 1.069 s
% 6.78/3.35 % System time : 0.102 s
% 6.78/3.35 % Total time : 1.171 s
% 6.78/3.35 % Maximum resident set size: 43684 pages
% 6.78/3.35
% 6.78/3.35 % -------------------------------------------------
% 6.78/3.35 % User time : 2.968 s
% 6.78/3.35 % System time : 0.248 s
% 6.78/3.35 % Total time : 3.216 s
% 6.78/3.35 % Maximum resident set size: 31744 pages
% 6.78/3.35 % E exiting
%------------------------------------------------------------------------------