%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP233_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 : n003.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 12:54:47 PM UTC 2026
% Result : Theorem 78.42s 13.57s
% Output : CNFRefutation 78.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 5 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 9 ( 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 : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 6 ( 0 sgn 4 !; 2 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
fun_nat_bool: $tType ).
tff(decl_sort2,type,
fun_nat_nat: $tType ).
tff(decl_sort3,type,
fun_VE3763956218935105199t_bool: $tType ).
tff(decl_sort4,type,
nat: $tType ).
tff(decl_sort5,type,
fun_nat_fun_nat_nat: $tType ).
tff(decl_sort6,type,
bool: $tType ).
tff(decl_sort7,type,
list_VEBT_VEBT: $tType ).
tff(decl_sort8,type,
vEBT_VEBT: $tType ).
tff(decl_1172,type,
list_u1324408373059187874T_VEBT: ( vEBT_VEBT * ( nat * list_VEBT_VEBT ) ) > list_VEBT_VEBT ).
tff(decl_1205,type,
nth_VEBT_VEBT: ( nat * list_VEBT_VEBT ) > vEBT_VEBT ).
tff(decl_1724,type,
vEBT_V8194947554948674370ptions: fun_VE3763956218935105199t_bool ).
tff(decl_1727,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
tff(decl_1729,type,
vEBT_VEBT_low: fun_nat_fun_nat_nat ).
tff(decl_1740,type,
vEBT_vebt_insert: ( nat * vEBT_VEBT ) > vEBT_VEBT ).
tff(decl_1847,type,
aa_nat_bool: ( nat * fun_nat_bool ) > bool ).
tff(decl_1850,type,
aa_nat_nat: ( nat * fun_nat_nat ) > nat ).
tff(decl_1882,type,
aa_nat_fun_nat_nat: ( nat * fun_nat_fun_nat_nat ) > fun_nat_nat ).
tff(decl_1977,type,
aa_VEB4832260192069861672t_bool: ( vEBT_VEBT * fun_VE3763956218935105199t_bool ) > fun_nat_bool ).
tff(decl_2162,type,
pp: bool > $o ).
tff(decl_2164,type,
i: nat ).
tff(decl_2168,type,
na: nat ).
tff(decl_2170,type,
treeList: list_VEBT_VEBT ).
tff(decl_2171,type,
xa: nat ).
tff(conj_0,conjecture,
? [X223: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),X223)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(fact_0_True,axiom,
i = aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_True) ).
tff(fact_3__C164_C,axiom,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i) = vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__C164_C) ).
tff(fact_1__C166_C,axiom,
pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__C166_C) ).
tff(c_0_4,negated_conjecture,
~ ? [X223: nat] : pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),X223)),
inference(assume_negation,[status(cth)],[conj_0]) ).
tff(c_0_5,negated_conjecture,
! [X17933: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),X17933)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
tcf(c_0_6,negated_conjecture,
! [X1: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),X1)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
tcf(c_0_7,plain,
i = aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),
inference(split_conjunct,[status(thm)],[fact_0_True]) ).
tcf(c_0_8,plain,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na),vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i) = vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na)),
inference(split_conjunct,[status(thm)],[fact_3__C164_C]) ).
tcf(c_0_9,plain,
pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,xa),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),
inference(split_conjunct,[status(thm)],[fact_1__C166_C]) ).
tcf(c_0_10,negated_conjecture,
! [X1: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,i,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,i),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i)),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_7]) ).
tcf(c_0_11,plain,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,i,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,i),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),i) = vEBT_vebt_insert(nth_VEBT_VEBT(treeList,i),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_7]),c_0_7]),c_0_7]) ).
tcf(c_0_12,plain,
pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,i),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),
inference(rw,[status(thm)],[c_0_9,c_0_7]) ).
tcf(c_0_13,negated_conjecture,
! [X1: nat] : ~ pp(aa_nat_bool(aa_VEB4832260192069861672t_bool(vEBT_V8194947554948674370ptions,vEBT_vebt_insert(nth_VEBT_VEBT(treeList,i),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,xa),na))),X1)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
$false,
inference(sr,[status(thm)],[c_0_12,c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP233_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 % Computer : n003.cluster.edu
% 0.11/0.41 % Model : x86_64 x86_64
% 0.11/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.41 % Memory : 8046.5625MB
% 0.11/0.41 % OS : Linux 6.8.0-71-generic
% 0.11/0.41 % CPULimit : 300
% 0.11/0.42 % WCLimit : 300
% 0.11/0.42 % DateTime : Sun Sep 20 22:14:45 UTC 2026
% 0.11/0.42 % CPUTime :
% 0.11/0.42 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.47 Running first-order theorem proving
% 0.18/0.47 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
% 78.42/13.57 % Version: 3.5.1
% 78.42/13.57 % Preprocessing class: FMLLSMLLSSSNFFN.
% 78.42/13.57 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 78.42/13.57 % Starting new_bool_3 with 897s (3) cores
% 78.42/13.57 % Starting new_bool_1 with 897s (3) cores
% 78.42/13.57 % Starting sh5l with 299s (1) cores
% 78.42/13.57 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 299s (1) cores
% 78.42/13.57 % new_bool_3 with pid 2721403 completed with status 0
% 78.42/13.57 % Result found by new_bool_3
% 78.42/13.57 % Preprocessing class: FMLLSMLLSSSNFFN.
% 78.42/13.57 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 78.42/13.57 % Starting new_bool_3 with 897s (3) cores
% 78.42/13.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 78.42/13.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 78.42/13.57 % Search class: FGHSM-SMLM32-DFFFFFNN
% 78.42/13.57 % Scheduled 13 strats onto 3 cores with 897 seconds (897 total)
% 78.42/13.57 % Starting SubtermCWHack with 81s (1) cores
% 78.42/13.57 % Starting new_bool_3 with 90s (1) cores
% 78.42/13.57 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 78.42/13.57 % G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with pid 2721409 completed with status 0
% 78.42/13.57 % Result found by G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI
% 78.42/13.57 % Preprocessing class: FMLLSMLLSSSNFFN.
% 78.42/13.57 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 78.42/13.57 % Starting new_bool_3 with 897s (3) cores
% 78.42/13.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 78.42/13.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 78.42/13.57 % Search class: FGHSM-SMLM32-DFFFFFNN
% 78.42/13.57 % Scheduled 13 strats onto 3 cores with 897 seconds (897 total)
% 78.42/13.57 % Starting SubtermCWHack with 81s (1) cores
% 78.42/13.57 % Starting new_bool_3 with 90s (1) cores
% 78.42/13.57 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 78.42/13.57 % Preprocessing time : 0.143 s
% 78.42/13.57
% 78.42/13.57 % Proof found!
% 78.42/13.57 % SZS status Theorem
% 78.42/13.57 % SZS output start CNFRefutation
% See solution above
% 78.42/13.57 % Parsed axioms : 12454
% 78.42/13.57 % Removed by relevancy pruning/SinE : 10329
% 78.42/13.57 % Initial clauses : 6947
% 78.42/13.57 % Removed in clause preprocessing : 1825
% 78.42/13.57 % Initial clauses in saturation : 5122
% 78.42/13.57 % Processed clauses : 5164
% 78.42/13.57 % ...of these trivial : 128
% 78.42/13.57 % ...subsumed : 1125
% 78.42/13.57 % ...remaining for further processing : 3911
% 78.42/13.57 % Other redundant clauses eliminated : 1920
% 78.42/13.57 % Clauses deleted for lack of memory : 0
% 78.42/13.57 % Backward-subsumed : 24
% 78.42/13.57 % Backward-rewritten : 17
% 78.42/13.57 % Generated clauses : 109898
% 78.42/13.57 % ...of the previous two non-redundant : 104900
% 78.42/13.57 % ...aggressively subsumed : 0
% 78.42/13.57 % Contextual simplify-reflections : 80
% 78.42/13.57 % Paramodulations : 108564
% 78.42/13.57 % Factorizations : 63
% 78.42/13.57 % NegExts : 0
% 78.42/13.57 % Equation resolutions : 1951
% 78.42/13.57 % Disequality decompositions : 0
% 78.42/13.57 % Total rewrite steps : 24128
% 78.42/13.57 % ...of those cached : 21692
% 78.42/13.57 % Propositional unsat checks : 0
% 78.42/13.57 % Propositional check models : 0
% 78.42/13.57 % Propositional check unsatisfiable : 0
% 78.42/13.57 % Propositional clauses : 0
% 78.42/13.57 % Propositional clauses after purity: 0
% 78.42/13.57 % Propositional unsat core size : 0
% 78.42/13.57 % Propositional preprocessing time : 0.000
% 78.42/13.57 % Propositional encoding time : 0.000
% 78.42/13.57 % Propositional solver time : 0.000
% 78.42/13.57 % Success case prop preproc time : 0.000
% 78.42/13.57 % Success case prop encoding time : 0.000
% 78.42/13.57 % Success case prop solver time : 0.000
% 78.42/13.57 % Current number of processed clauses : 2783
% 78.42/13.57 % Positive orientable unit clauses : 301
% 78.42/13.57 % Positive unorientable unit clauses: 20
% 78.42/13.57 % Negative unit clauses : 82
% 78.42/13.57 % Non-unit-clauses : 2380
% 78.42/13.57 % Current number of unprocessed clauses: 104858
% 78.42/13.57 % ...number of literals in the above : 515784
% 78.42/13.57 % Current number of archived formulas : 0
% 78.42/13.57 % Current number of archived clauses : 42
% 78.42/13.57 % Clause-clause subsumption calls (NU) : 7140689
% 78.42/13.57 % Rec. Clause-clause subsumption calls : 333373
% 78.42/13.57 % Non-unit clause-clause subsumptions : 1117
% 78.42/13.57 % Unit Clause-clause subsumption calls : 9283
% 78.42/13.57 % Rewrite failures with RHS unbound : 0
% 78.42/13.57 % BW rewrite match attempts : 2548
% 78.42/13.57 % BW rewrite match successes : 79
% 78.42/13.57 % Condensation attempts : 0
% 78.42/13.57 % Condensation successes : 0
% 78.42/13.57 % Termbank termtop insertions : 4647178
% 78.42/13.57 % Search garbage collected termcells : 181306
% 78.42/13.57
% 78.42/13.57 % -------------------------------------------------
% 78.42/13.57 % User time : 11.241 s
% 78.42/13.57 % System time : 0.172 s
% 78.42/13.57 % Total time : 11.413 s
% 78.42/13.57 % Maximum resident set size: 44984 pages
% 78.42/13.57
% 78.42/13.57 % -------------------------------------------------
% 78.42/13.57 % User time : 32.899 s
% 78.42/13.57 % System time : 0.545 s
% 78.42/13.57 % Total time : 33.444 s
% 78.42/13.57 % Maximum resident set size: 31488 pages
% 78.42/13.57 % E exiting
%------------------------------------------------------------------------------