%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP222^1 : TPTP v9.3.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 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 : Wed Sep 30 08:07:15 AM UTC 2026
% Result : Theorem 13.80s 4.56s
% Output : Refutation 13.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 8 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 8 ( 7 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 17 ( 3 ~; 0 |; 0 &; 14 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 84 ( 84 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(produc3368934014287244435at_num_type,type,
produc3368934014287244435at_num: $tType ).
thf(produc4471711990508489141at_nat_type,type,
produc4471711990508489141at_nat: $tType ).
thf(set_fi4554929511873752355omplex_type,type,
set_fi4554929511873752355omplex: $tType ).
thf(list_P7413028617227757229T_VEBT_type,type,
list_P7413028617227757229T_VEBT: $tType ).
thf(produc2963631642982155120at_num_type,type,
produc2963631642982155120at_num: $tType ).
thf(produc7248412053542808358at_nat_type,type,
produc7248412053542808358at_nat: $tType ).
thf(set_fi7789364187291644575l_real_type,type,
set_fi7789364187291644575l_real: $tType ).
thf(filter6041513312241820739omplex_type,type,
filter6041513312241820739omplex: $tType ).
thf(list_P7037539587688870467BT_nat_type,type,
list_P7037539587688870467BT_nat: $tType ).
thf(list_P4547456442757143711BT_int_type,type,
list_P4547456442757143711BT_int: $tType ).
thf(list_P5647936690300460905T_VEBT_type,type,
list_P5647936690300460905T_VEBT: $tType ).
thf(produc8243902056947475879T_VEBT_type,type,
produc8243902056947475879T_VEBT: $tType ).
thf(set_Pr5085853215250843933omplex_type,type,
set_Pr5085853215250843933omplex: $tType ).
thf(produc8923325533196201883nteger_type,type,
produc8923325533196201883nteger: $tType ).
thf(produc7272778201969148633d_enat_type,type,
produc7272778201969148633d_enat: $tType ).
thf(list_P3126845725202233233VEBT_o_type,type,
list_P3126845725202233233VEBT_o: $tType ).
thf(list_P7495141550334521929T_VEBT_type,type,
list_P7495141550334521929T_VEBT: $tType ).
thf(filter2146258269922977983l_real_type,type,
filter2146258269922977983l_real: $tType ).
thf(list_P8526636022914148096eger_o_type,type,
list_P8526636022914148096eger_o: $tType ).
thf(set_Pr448751882837621926eger_o_type,type,
set_Pr448751882837621926eger_o: $tType ).
thf(option4927543243414619207at_nat_type,type,
option4927543243414619207at_nat: $tType ).
thf(filter1242075044329608583at_nat_type,type,
filter1242075044329608583at_nat: $tType ).
thf(set_Pr6218003697084177305l_real_type,type,
set_Pr6218003697084177305l_real: $tType ).
thf(list_P3744719386663036955um_num_type,type,
list_P3744719386663036955um_num: $tType ).
thf(produc9072475918466114483BT_nat_type,type,
produc9072475918466114483BT_nat: $tType ).
thf(produc4894624898956917775BT_int_type,type,
produc4894624898956917775BT_int: $tType ).
thf(set_Pr8218934625190621173um_num_type,type,
set_Pr8218934625190621173um_num: $tType ).
thf(set_Pr6200539531224447659at_num_type,type,
set_Pr6200539531224447659at_num: $tType ).
thf(set_Pr1261947904930325089at_nat_type,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(set_Pr958786334691620121nt_int_type,type,
set_Pr958786334691620121nt_int: $tType ).
thf(produc4411394909380815293omplex_type,type,
produc4411394909380815293omplex: $tType ).
thf(list_P7333126701944960589_nat_o_type,type,
list_P7333126701944960589_nat_o: $tType ).
thf(list_P6285523579766656935_o_nat_type,type,
list_P6285523579766656935_o_nat: $tType ).
thf(list_P3795440434834930179_o_int_type,type,
list_P3795440434834930179_o_int: $tType ).
thf(produc334124729049499915VEBT_o_type,type,
produc334124729049499915VEBT_o: $tType ).
thf(produc2504756804600209347T_VEBT_type,type,
produc2504756804600209347T_VEBT: $tType ).
thf(produc6271795597528267376eger_o_type,type,
produc6271795597528267376eger_o: $tType ).
thf(produc2422161461964618553l_real_type,type,
produc2422161461964618553l_real: $tType ).
thf(product_prod_num_num_type,type,
product_prod_num_num: $tType ).
thf(product_prod_nat_num_type,type,
product_prod_nat_num: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(product_prod_int_int_type,type,
product_prod_int_int: $tType ).
thf(list_P4002435161011370285od_o_o_type,type,
list_P4002435161011370285od_o_o: $tType ).
thf(list_VEBT_VEBT_type,type,
list_VEBT_VEBT: $tType ).
thf(set_list_nat_type,type,
set_list_nat: $tType ).
thf(product_prod_o_nat_type,type,
product_prod_o_nat: $tType ).
thf(product_prod_o_int_type,type,
product_prod_o_int: $tType ).
thf(list_set_nat_type,type,
list_set_nat: $tType ).
thf(list_Code_integer_type,type,
list_Code_integer: $tType ).
thf(set_VEBT_VEBT_type,type,
set_VEBT_VEBT: $tType ).
thf(set_set_nat_type,type,
set_set_nat: $tType ).
thf(set_set_int_type,type,
set_set_int: $tType ).
thf(set_Code_integer_type,type,
set_Code_integer: $tType ).
thf(set_Product_unit_type,type,
set_Product_unit: $tType ).
thf(set_Extended_enat_type,type,
set_Extended_enat: $tType ).
thf(list_complex_type,type,
list_complex: $tType ).
thf(product_prod_o_o_type,type,
product_prod_o_o: $tType ).
thf(set_complex_type,type,
set_complex: $tType ).
thf(filter_real_type,type,
filter_real: $tType ).
thf(set_set_o_type,type,
set_set_o: $tType ).
thf(option_num_type,type,
option_num: $tType ).
thf(filter_nat_type,type,
filter_nat: $tType ).
thf(set_char_type,type,
set_char: $tType ).
thf(list_real_type,type,
list_real: $tType ).
thf(set_real_type,type,
set_real: $tType ).
thf(list_num_type,type,
list_num: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(list_int_type,type,
list_int: $tType ).
thf(vEBT_VEBT_type,type,
vEBT_VEBT: $tType ).
thf(set_rat_type,type,
set_rat: $tType ).
thf(set_num_type,type,
set_num: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(set_int_type,type,
set_int: $tType ).
thf(code_integer_type,type,
code_integer: $tType ).
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(list_o_type,type,
list_o: $tType ).
thf(complex_type,type,
complex: $tType ).
thf(set_o_type,type,
set_o: $tType ).
thf(char_type,type,
char: $tType ).
thf(real_type,type,
real: $tType ).
thf(rat_type,type,
rat: $tType ).
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(extend5688581933313929465d_enat_decl,type,
extend5688581933313929465d_enat: extended_enat ).
thf(vEBT_VEBT_elim_dead_decl,type,
vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
thf(summarya_decl,type,
summarya: vEBT_VEBT ).
thf(45,axiom,
( ( vEBT_VEBT_elim_dead @ summarya @ extend5688581933313929465d_enat )
= summarya ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__C2_OIH_C_I2_J) ).
thf(318,plain,
( ( vEBT_VEBT_elim_dead @ summarya @ extend5688581933313929465d_enat )
= summarya ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(319,plain,
( ( vEBT_VEBT_elim_dead @ summarya @ extend5688581933313929465d_enat )
= summarya ),
inference(lifteq,[status(thm)],[318]) ).
thf(1,conjecture,
( ( vEBT_VEBT_elim_dead @ summarya @ extend5688581933313929465d_enat )
= summarya ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( vEBT_VEBT_elim_dead @ summarya @ extend5688581933313929465d_enat )
!= summarya ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(67,plain,
( ( vEBT_VEBT_elim_dead @ summarya @ extend5688581933313929465d_enat )
!= summarya ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(68,plain,
( ( vEBT_VEBT_elim_dead @ summarya @ extend5688581933313929465d_enat )
!= summarya ),
inference(lifteq,[status(thm)],[67]) ).
thf(393,plain,
$false,
inference(simplifyReflect,[status(thm)],[319,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP222^1 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n018.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 20:22:11 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.83/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 6.15/2.16 % [INFO] Parsing done (1388ms).
% 6.15/2.18 % [INFO] Running in sequential loop mode.
% 6.88/2.54 % [INFO] eprover registered as external prover.
% 6.88/2.55 % [INFO] Scanning for conjecture ...
% 8.16/3.02 % [INFO] Found a conjecture (or negated_conjecture) and 10251 axioms. Running axiom selection ...
% 9.10/3.17 % [INFO] Axiom selection finished. Selected 64 axioms (removed 10187 axioms).
% 9.36/3.25 % [INFO] Problem is higher-order (TPTP THF).
% 9.36/3.27 % [INFO] Type checking passed.
% 9.36/3.27 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 13.80/4.55 % [INFO] Killing All external provers ...
% 13.80/4.55 % Time passed: 4209ms (effective reasoning time: 2364ms)
% 13.80/4.55 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 13.80/4.56 % Axioms used in derivation (1): fact_1__C2_OIH_C_I2_J
% 13.80/4.56 % No. of inferences in proof: 8
% 13.80/4.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4209 ms resp. 2364 ms w/o parsing
% 13.80/4.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.80/4.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------