%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP220_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 : n005.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 12:54:39 PM UTC 2026
% Result : Theorem 103.00s 16.85s
% Output : CNFRefutation 103.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 4 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
fun_nat_bool: $tType ).
tff(decl_sort2,type,
fun_nat_fun_nat_bool: $tType ).
tff(decl_sort3,type,
nat: $tType ).
tff(decl_sort4,type,
fun_nat_nat: $tType ).
tff(decl_sort5,type,
num: $tType ).
tff(decl_sort6,type,
fun_nat_fun_nat_nat: $tType ).
tff(decl_sort7,type,
vEBT_VEBT: $tType ).
tff(decl_sort8,type,
bool: $tType ).
tff(decl_sort9,type,
fun_num_nat: $tType ).
tff(decl_sort10,type,
fun_num_num: $tType ).
tff(decl_574,type,
one_one_nat: nat ).
tff(decl_724,type,
suc: fun_nat_nat ).
tff(decl_793,type,
bit0: fun_num_num ).
tff(decl_795,type,
one: num ).
tff(decl_804,type,
numeral_numeral_nat: fun_num_nat ).
tff(decl_955,type,
divide_divide_nat: fun_nat_fun_nat_nat ).
tff(decl_962,type,
dvd_dvd_nat: fun_nat_fun_nat_bool ).
tff(decl_1084,type,
vEBT_VEBT_membermima: vEBT_VEBT > fun_nat_bool ).
tff(decl_1092,type,
vEBT_vebt_buildup: nat > vEBT_VEBT ).
tff(decl_1153,type,
aa_nat_bool: ( nat * fun_nat_bool ) > bool ).
tff(decl_1156,type,
aa_nat_nat: ( nat * fun_nat_nat ) > nat ).
tff(decl_1170,type,
aa_nat_fun_nat_bool: ( nat * fun_nat_fun_nat_bool ) > fun_nat_bool ).
tff(decl_1172,type,
aa_nat_fun_nat_nat: ( nat * fun_nat_fun_nat_nat ) > fun_nat_nat ).
tff(decl_1189,type,
aa_num_nat: ( num * fun_num_nat ) > nat ).
tff(decl_1190,type,
aa_num_num: ( num * fun_num_num ) > num ).
tff(decl_1308,type,
pp: bool > $o ).
tff(decl_1309,type,
va: nat ).
tff(decl_1310,type,
y: nat ).
tff(conj_0,conjecture,
~ pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_vebt_buildup(aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(fact_1__C3_OIH_C_I1_J,axiom,
! [X1: nat,X2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
=> ( ( X1 = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) )
=> ~ pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_vebt_buildup(X1)),X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__C3_OIH_C_I1_J) ).
tff(fact_4_div2__Suc__Suc,axiom,
! [X3: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X3))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X3),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_div2__Suc__Suc) ).
tff(fact_525_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_525_Suc__1) ).
tff(fact_0_True,axiom,
pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_True) ).
tff(c_0_5,negated_conjecture,
~ ~ pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_vebt_buildup(aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),y)),
inference(assume_negation,[status(cth)],[conj_0]) ).
tff(c_0_6,plain,
! [X1: nat,X2: nat] :
( pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va))))
=> ( ( X1 = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) )
=> ~ pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_vebt_buildup(X1)),X2)) ) ),
inference(fof_simplification,[status(thm)],[fact_1__C3_OIH_C_I1_J]) ).
tff(c_0_7,plain,
! [X17026: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X17026))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X17026),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ),
inference(variable_rename,[status(thm)],[fact_4_div2__Suc__Suc]) ).
tff(c_0_8,negated_conjecture,
pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_vebt_buildup(aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),y)),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
tff(c_0_9,plain,
! [X16714: nat,X16715: nat] :
( ~ pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_vebt_buildup(X16714)),X16715))
| ( X16714 != aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va)))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
tcf(c_0_10,plain,
! [X1: nat] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X1))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X1),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
tcf(c_0_11,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_525_Suc__1]) ).
tcf(c_0_12,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va)))),
inference(split_conjunct,[status(thm)],[fact_0_True]) ).
tcf(c_0_13,negated_conjecture,
pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_vebt_buildup(aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),y)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_14,plain,
! [X1: nat,X2: nat] :
( ~ pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_vebt_buildup(X1)),X2))
| ( X1 != aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) )
| ~ pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(suc,aa_nat_nat(suc,va)))) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_15,plain,
! [X1: nat] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,X1))),aa_nat_nat(suc,one_one_nat)) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X1),aa_nat_nat(suc,one_one_nat))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
tcf(c_0_16,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(dvd_dvd_nat,aa_nat_nat(suc,one_one_nat)),aa_nat_nat(suc,aa_nat_nat(suc,va)))),
inference(rw,[status(thm)],[c_0_12,c_0_11]) ).
tcf(c_0_17,negated_conjecture,
pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_vebt_buildup(aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,va))),aa_nat_nat(suc,one_one_nat)))),y)),
inference(rw,[status(thm)],[c_0_13,c_0_11]) ).
tcf(c_0_18,plain,
! [X1: nat] : ~ pp(aa_nat_bool(vEBT_VEBT_membermima(vEBT_vebt_buildup(aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,va),aa_nat_nat(suc,one_one_nat))))),X1)),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_11]),c_0_15]),c_0_11]),c_0_16])])]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP220_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n005.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 20 22:10:03 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.46 Running first-order theorem proving
% 0.13/0.46 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
% 103.00/16.85 % Version: 3.5.1
% 103.00/16.85 % Preprocessing class: FMLLSMLLSSSNFFN.
% 103.00/16.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 103.00/16.85 % Starting new_bool_3 with 900s (3) cores
% 103.00/16.85 % Starting new_bool_1 with 900s (3) cores
% 103.00/16.85 % Starting sh5l with 300s (1) cores
% 103.00/16.85 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 103.00/16.85 % new_bool_1 with pid 1856897 completed with status 0
% 103.00/16.85 % Result found by new_bool_1
% 103.00/16.85 % Preprocessing class: FMLLSMLLSSSNFFN.
% 103.00/16.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 103.00/16.85 % Starting new_bool_3 with 900s (3) cores
% 103.00/16.85 % Starting new_bool_1 with 900s (3) cores
% 103.00/16.85 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 103.00/16.85 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 103.00/16.85 % Search class: FGHSM-SMLM32-DFFFFFNN
% 103.00/16.85 % Scheduled 13 strats onto 3 cores with 899 seconds (899 total)
% 103.00/16.85 % Starting SubtermCWHack with 81s (1) cores
% 103.00/16.85 % Starting new_bool_1 with 90s (1) cores
% 103.00/16.85 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 103.00/16.85 % G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with pid 1856903 completed with status 0
% 103.00/16.85 % Result found by G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI
% 103.00/16.85 % Preprocessing class: FMLLSMLLSSSNFFN.
% 103.00/16.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 103.00/16.85 % Starting new_bool_3 with 900s (3) cores
% 103.00/16.85 % Starting new_bool_1 with 900s (3) cores
% 103.00/16.85 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 103.00/16.85 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 103.00/16.85 % Search class: FGHSM-SMLM32-DFFFFFNN
% 103.00/16.85 % Scheduled 13 strats onto 3 cores with 899 seconds (899 total)
% 103.00/16.85 % Starting SubtermCWHack with 81s (1) cores
% 103.00/16.85 % Starting new_bool_1 with 90s (1) cores
% 103.00/16.85 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 68s (1) cores
% 103.00/16.85 % Preprocessing time : 0.382 s
% 103.00/16.85
% 103.00/16.85 % Proof found!
% 103.00/16.85 % SZS status Theorem
% 103.00/16.85 % SZS output start CNFRefutation
% See solution above
% 103.00/16.85 % Parsed axioms : 11990
% 103.00/16.85 % Removed by relevancy pruning/SinE : 8404
% 103.00/16.85 % Initial clauses : 8940
% 103.00/16.85 % Removed in clause preprocessing : 1545
% 103.00/16.85 % Initial clauses in saturation : 7395
% 103.00/16.85 % Processed clauses : 7514
% 103.00/16.85 % ...of these trivial : 328
% 103.00/16.85 % ...subsumed : 1181
% 103.00/16.85 % ...remaining for further processing : 6004
% 103.00/16.85 % Other redundant clauses eliminated : 2250
% 103.00/16.85 % Clauses deleted for lack of memory : 0
% 103.00/16.85 % Backward-subsumed : 61
% 103.00/16.85 % Backward-rewritten : 98
% 103.00/16.85 % Generated clauses : 233899
% 103.00/16.85 % ...of the previous two non-redundant : 220924
% 103.00/16.85 % ...aggressively subsumed : 0
% 103.00/16.85 % Contextual simplify-reflections : 59
% 103.00/16.85 % Paramodulations : 232192
% 103.00/16.85 % Factorizations : 49
% 103.00/16.85 % NegExts : 0
% 103.00/16.85 % Equation resolutions : 2333
% 103.00/16.85 % Disequality decompositions : 0
% 103.00/16.85 % Total rewrite steps : 62869
% 103.00/16.85 % ...of those cached : 54817
% 103.00/16.85 % Propositional unsat checks : 0
% 103.00/16.85 % Propositional check models : 0
% 103.00/16.85 % Propositional check unsatisfiable : 0
% 103.00/16.85 % Propositional clauses : 0
% 103.00/16.85 % Propositional clauses after purity: 0
% 103.00/16.85 % Propositional unsat core size : 0
% 103.00/16.85 % Propositional preprocessing time : 0.000
% 103.00/16.85 % Propositional encoding time : 0.000
% 103.00/16.85 % Propositional solver time : 0.000
% 103.00/16.85 % Success case prop preproc time : 0.000
% 103.00/16.85 % Success case prop encoding time : 0.000
% 103.00/16.85 % Success case prop solver time : 0.000
% 103.00/16.85 % Current number of processed clauses : 4610
% 103.00/16.85 % Positive orientable unit clauses : 611
% 103.00/16.85 % Positive unorientable unit clauses: 53
% 103.00/16.85 % Negative unit clauses : 146
% 103.00/16.85 % Non-unit-clauses : 3800
% 103.00/16.85 % Current number of unprocessed clauses: 220764
% 103.00/16.85 % ...number of literals in the above : 1061169
% 103.00/16.85 % Current number of archived formulas : 0
% 103.00/16.85 % Current number of archived clauses : 159
% 103.00/16.85 % Clause-clause subsumption calls (NU) : 13041960
% 103.00/16.85 % Rec. Clause-clause subsumption calls : 821162
% 103.00/16.85 % Non-unit clause-clause subsumptions : 1061
% 103.00/16.85 % Unit Clause-clause subsumption calls : 41710
% 103.00/16.85 % Rewrite failures with RHS unbound : 0
% 103.00/16.85 % BW rewrite match attempts : 8586
% 103.00/16.85 % BW rewrite match successes : 316
% 103.00/16.85 % Condensation attempts : 0
% 103.00/16.85 % Condensation successes : 0
% 103.00/16.85 % Termbank termtop insertions : 9072215
% 103.00/16.85 % Search garbage collected termcells : 169444
% 103.00/16.85
% 103.00/16.85 % -------------------------------------------------
% 103.00/16.85 % User time : 15.172 s
% 103.00/16.85 % System time : 0.242 s
% 103.00/16.85 % Total time : 15.414 s
% 103.00/16.85 % Maximum resident set size: 47376 pages
% 103.00/16.85
% 103.00/16.85 % -------------------------------------------------
% 103.00/16.85 % User time : 43.440 s
% 103.00/16.85 % System time : 0.644 s
% 103.00/16.85 % Total time : 44.084 s
% 103.00/16.85 % Maximum resident set size: 28672 pages
% 103.00/16.85 % E exiting
%------------------------------------------------------------------------------