%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP226^1 : 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 : n019.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 08:07:17 AM UTC 2026
% Result : Theorem 13.79s 4.33s
% Output : Refutation 14.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 34 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 23 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 165 ( 16 ~; 0 |; 0 &; 133 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 73 ( 72 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 14 ^; 44 !; 2 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr8693737435421807431at_nat_type,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(produc5835291356934675326atural_type,type,
produc5835291356934675326atural: $tType ).
thf(produc859450856879609959at_nat_type,type,
produc859450856879609959at_nat: $tType ).
thf(list_P7413028617227757229T_VEBT_type,type,
list_P7413028617227757229T_VEBT: $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(produc7822875418678951345atural_type,type,
produc7822875418678951345atural: $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(option4927543243414619207at_nat_type,type,
option4927543243414619207at_nat: $tType ).
thf(list_P3744719386663036955um_num_type,type,
list_P3744719386663036955um_num: $tType ).
thf(list_P1726324292696863441at_num_type,type,
list_P1726324292696863441at_num: $tType ).
thf(produc9072475918466114483BT_nat_type,type,
produc9072475918466114483BT_nat: $tType ).
thf(produc4894624898956917775BT_int_type,type,
produc4894624898956917775BT_int: $tType ).
thf(set_Pr1261947904930325089at_nat_type,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(set_Pr958786334691620121nt_int_type,type,
set_Pr958786334691620121nt_int: $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(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(set_VEBT_VEBT_type,type,
set_VEBT_VEBT: $tType ).
thf(set_set_nat_type,type,
set_set_nat: $tType ).
thf(set_Code_integer_type,type,
set_Code_integer: $tType ).
thf(set_Product_unit_type,type,
set_Product_unit: $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(option_num_type,type,
option_num: $tType ).
thf(filter_nat_type,type,
filter_nat: $tType ).
thf(filter_int_type,type,
filter_int: $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_natural_type,type,
code_natural: $tType ).
thf(code_integer_type,type,
code_integer: $tType ).
thf(product_unit_type,type,
product_unit: $tType ).
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(list_o_type,type,
list_o: $tType ).
thf(complex_type,type,
complex: $tType ).
thf(literal_type,type,
literal: $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(uminus_uminus_nat_o_decl,type,
uminus_uminus_nat_o: ( nat > $o ) > nat > $o ).
thf(uminus5710092332889474511et_nat_decl,type,
uminus5710092332889474511et_nat: set_nat > set_nat ).
thf(collect_nat_decl,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(vEBT_V8194947554948674370ptions_decl,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(vEBT_invar_vebt_decl,type,
vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
thf(vEBT_set_vebt_decl,type,
vEBT_set_vebt: vEBT_VEBT > set_nat ).
thf(vEBT_VEBT_minNull_decl,type,
vEBT_VEBT_minNull: vEBT_VEBT > $o ).
thf(vEBT_vebt_member_decl,type,
vEBT_vebt_member: vEBT_VEBT > nat > $o ).
thf(member_nat_decl,type,
member_nat: nat > set_nat > $o ).
thf(n_decl,type,
n: nat ).
thf(t_decl,type,
t: vEBT_VEBT ).
thf(x_decl,type,
x: nat ).
thf(17,axiom,
! [A: nat,B: set_nat] :
( ~ ( member_nat @ A @ B )
=> ( member_nat @ A @ ( uminus5710092332889474511et_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7888_ComplI) ).
thf(56,plain,
! [A: nat,B: set_nat] :
( ~ ( member_nat @ A @ B )
=> ( member_nat @ A @ ( uminus5710092332889474511et_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
! [A: vEBT_VEBT,B: nat] :
( ( vEBT_VEBT_minNull @ A )
=> ~ ( vEBT_vebt_member @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_min__Null__member) ).
thf(42,plain,
! [A: vEBT_VEBT,B: nat] :
( ( vEBT_VEBT_minNull @ A )
=> ~ ( vEBT_vebt_member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_nat @ A )
= ( collect_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Collect__cong) ).
thf(33,plain,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_nat @ A )
= ( collect_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_mem__Collect__eq) ).
thf(53,plain,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Collect__mem__eq) ).
thf(45,plain,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
( uminus5710092332889474511et_nat
= ( ^ [A: set_nat] :
( collect_nat
@ ^ [B: nat] :
~ ( member_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8150_Compl__eq) ).
thf(27,plain,
( uminus5710092332889474511et_nat
= ( ^ [A: set_nat] :
( collect_nat
@ ^ [B: nat] :
~ ( member_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
vEBT_invar_vebt @ t @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(39,plain,
vEBT_invar_vebt @ t @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
( uminus5710092332889474511et_nat
= ( ^ [A: set_nat] :
( collect_nat
@ ( uminus_uminus_nat_o
@ ^ [B: nat] : ( member_nat @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8161_uminus__set__def) ).
thf(31,plain,
( uminus5710092332889474511et_nat
= ( ^ [A: set_nat] :
( collect_nat
@ ( uminus_uminus_nat_o
@ ^ [B: nat] : ( member_nat @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( vEBT_invar_vebt @ A @ B )
=> ( ( vEBT_V8194947554948674370ptions @ A @ C )
=> ( vEBT_vebt_member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_valid__member__both__member__options) ).
thf(20,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( vEBT_invar_vebt @ A @ B )
=> ( ( vEBT_V8194947554948674370ptions @ A @ C )
=> ( vEBT_vebt_member @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ A )
=> ? [B: nat] : ( vEBT_V8194947554948674370ptions @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_not__min__Null__member) ).
thf(29,plain,
! [A: vEBT_VEBT] :
( ~ ( vEBT_VEBT_minNull @ A )
=> ? [B: nat] : ( vEBT_V8194947554948674370ptions @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [A: nat,B: set_nat] :
( ( member_nat @ A @ ( uminus5710092332889474511et_nat @ B ) )
= ( ~ ( member_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7893_Compl__iff) ).
thf(48,plain,
! [A: nat,B: set_nat] :
( ( member_nat @ A @ ( uminus5710092332889474511et_nat @ B ) )
= ( ~ ( member_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,conjecture,
( ( vEBT_vebt_member @ t @ x )
= ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
( ( vEBT_vebt_member @ t @ x )
!= ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(18,plain,
( ( vEBT_vebt_member @ t @ x )
!= ( member_nat @ x @ ( vEBT_set_vebt @ t ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: nat,B: set_nat] :
( ( member_nat @ A @ ( uminus5710092332889474511et_nat @ B ) )
=> ~ ( member_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7939_ComplD) ).
thf(40,plain,
! [A: nat,B: set_nat] :
( ( member_nat @ A @ ( uminus5710092332889474511et_nat @ B ) )
=> ~ ( member_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( vEBT_invar_vebt @ A @ B )
=> ( ( vEBT_V8194947554948674370ptions @ A @ C )
= ( vEBT_vebt_member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_both__member__options__equiv__member) ).
thf(23,plain,
! [A: vEBT_VEBT,B: nat,C: nat] :
( ( vEBT_invar_vebt @ A @ B )
=> ( ( vEBT_V8194947554948674370ptions @ A @ C )
= ( vEBT_vebt_member @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: nat > $o] :
( ( collect_nat
@ ^ [B: nat] :
~ ( A @ B ) )
= ( uminus5710092332889474511et_nat @ ( collect_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8155_Collect__neg__eq) ).
thf(36,plain,
! [A: nat > $o] :
( ( collect_nat
@ ^ [B: nat] :
~ ( A @ B ) )
= ( uminus5710092332889474511et_nat @ ( collect_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
( vEBT_set_vebt
= ( ^ [A: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8231_set__vebt__def) ).
thf(51,plain,
( vEBT_set_vebt
= ( ^ [A: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(59,plain,
$false,
inference(e,[status(thm)],[56,42,33,53,45,27,39,31,20,29,48,18,40,23,36,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP226^1 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.08 % 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 : n019.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 20:21:32 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
% 0.85/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 7.32/2.44 % [INFO] Parsing done (1653ms).
% 7.32/2.46 % [INFO] Running in sequential loop mode.
% 8.45/2.82 % [INFO] eprover registered as external prover.
% 8.45/2.83 % [INFO] Scanning for conjecture ...
% 10.30/3.36 % [INFO] Found a conjecture (or negated_conjecture) and 10193 axioms. Running axiom selection ...
% 11.11/3.52 % [INFO] Axiom selection finished. Selected 15 axioms (removed 10178 axioms).
% 11.11/3.55 % [INFO] Problem is higher-order (TPTP THF).
% 11.11/3.56 % [INFO] Type checking passed.
% 11.11/3.56 % [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 ...
% 13.79/4.33 % External prover 'e' found a proof!
% 13.79/4.33 % [INFO] Killing All external provers ...
% 13.79/4.33 % Time passed: 3982ms (effective reasoning time: 1866ms)
% 13.79/4.33 % 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)>
% 13.79/4.33 % Axioms used in derivation (15): fact_4_both__member__options__equiv__member, fact_7939_ComplD, fact_48_mem__Collect__eq, fact_7893_Compl__iff, fact_8231_set__vebt__def, fact_7888_ComplI, fact_54_Collect__mem__eq, fact_0_min__Null__member, fact_59_Collect__cong, fact_8150_Compl__eq, fact_12_not__min__Null__member, fact_5_valid__member__both__member__options, fact_8161_uminus__set__def, conj_0, fact_8155_Collect__neg__eq
% 13.79/4.33 % No. of inferences in proof: 34
% 13.79/4.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3982 ms resp. 1866 ms w/o parsing
% 13.79/4.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.22/4.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------