%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP077^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 08:06:40 AM UTC 2026
% Result : Theorem 61.60s 24.33s
% Output : Refutation 61.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 39 ( 4 ~; 1 |; 0 &; 34 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 43 ( 43 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_list_list_list_a_type,type,
set_list_list_list_a: $tType ).
thf(multis971982480list_a_type,type,
multis971982480list_a: $tType ).
thf(list_set_list_list_a_type,type,
list_set_list_list_a: $tType ).
thf(set_list_set_list_a_type,type,
set_list_set_list_a: $tType ).
thf(set_list_list_set_a_type,type,
set_list_list_set_a: $tType ).
thf(list_set_set_list_a_type,type,
list_set_set_list_a: $tType ).
thf(list_set_list_set_a_type,type,
list_set_list_set_a: $tType ).
thf(set_list_set_set_a_type,type,
set_list_set_set_a: $tType ).
thf(list_set_set_set_a_type,type,
list_set_set_set_a: $tType ).
thf(list_multiset_list_a_type,type,
list_multiset_list_a: $tType ).
thf(set_multiset_list_a_type,type,
set_multiset_list_a: $tType ).
thf(set_list_multiset_a_type,type,
set_list_multiset_a: $tType ).
thf(multiset_set_list_a_type,type,
multiset_set_list_a: $tType ).
thf(list_set_multiset_a_type,type,
list_set_multiset_a: $tType ).
thf(multiset_set_set_a_type,type,
multiset_set_set_a: $tType ).
thf(list_list_list_a_type,type,
list_list_list_a: $tType ).
thf(set_list_list_a_type,type,
set_list_list_a: $tType ).
thf(multiset_multiset_a_type,type,
multiset_multiset_a: $tType ).
thf(list_set_list_a_type,type,
list_set_list_a: $tType ).
thf(list_list_set_a_type,type,
list_list_set_a: $tType ).
thf(set_set_list_a_type,type,
set_set_list_a: $tType ).
thf(set_list_set_a_type,type,
set_list_set_a: $tType ).
thf(list_set_set_a_type,type,
list_set_set_a: $tType ).
thf(set_set_set_a_type,type,
set_set_set_a: $tType ).
thf(multiset_list_a_type,type,
multiset_list_a: $tType ).
thf(list_multiset_a_type,type,
list_multiset_a: $tType ).
thf(set_multiset_a_type,type,
set_multiset_a: $tType ).
thf(multiset_set_a_type,type,
multiset_set_a: $tType ).
thf(set_list_nat_type,type,
set_list_nat: $tType ).
thf(list_set_nat_type,type,
list_set_nat: $tType ).
thf(set_set_nat_type,type,
set_set_nat: $tType ).
thf(list_list_a_type,type,
list_list_a: $tType ).
thf(set_list_a_type,type,
set_list_a: $tType ).
thf(list_set_a_type,type,
list_set_a: $tType ).
thf(multiset_nat_type,type,
multiset_nat: $tType ).
thf(set_set_a_type,type,
set_set_a: $tType ).
thf(multiset_a_type,type,
multiset_a: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(list_a_type,type,
list_a: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(groups1792256535list_a_decl,type,
groups1792256535list_a: list_a > a ).
thf(comm_m543484931mset_a_decl,type,
comm_m543484931mset_a: multiset_a > a ).
thf(mset_a_decl,type,
mset_a: list_a > multiset_a ).
thf(a3_decl,type,
a3: a ).
thf(qs2_decl,type,
qs2: list_a ).
thf(qs_decl,type,
qs: list_a ).
thf(253,axiom,
( ( mset_a @ qs2 )
= ( mset_a @ qs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062mset_Aqs2_A_061_Amset_Aqs_092_060close_062) ).
thf(1254,plain,
( ( mset_a @ qs2 )
= ( mset_a @ qs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(1255,plain,
( ( mset_a @ qs )
= ( mset_a @ qs2 ) ),
inference(lifteq,[status(thm)],[1254]) ).
thf(250,axiom,
! [A: list_a] :
( ( comm_m543484931mset_a @ ( mset_a @ A ) )
= ( groups1792256535list_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_sum__mset__sum__list) ).
thf(1235,plain,
! [A: list_a] :
( ( comm_m543484931mset_a @ ( mset_a @ A ) )
= ( groups1792256535list_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1236,plain,
! [A: list_a] :
( ( comm_m543484931mset_a @ ( mset_a @ A ) )
= ( groups1792256535list_a @ A ) ),
inference(cnf,[status(esa)],[1235]) ).
thf(1237,plain,
! [A: list_a] :
( ( comm_m543484931mset_a @ ( mset_a @ A ) )
= ( groups1792256535list_a @ A ) ),
inference(lifteq,[status(thm)],[1236]) ).
thf(2320,plain,
! [A: list_a] :
( ( ( comm_m543484931mset_a @ ( mset_a @ qs2 ) )
= ( groups1792256535list_a @ A ) )
| ( ( mset_a @ qs )
!= ( mset_a @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1255,1237]) ).
thf(2321,plain,
( ( comm_m543484931mset_a @ ( mset_a @ qs2 ) )
= ( groups1792256535list_a @ qs ) ),
inference(pattern_uni,[status(thm)],[2320:[bind(A,$thf( qs ))]]) ).
thf(255,axiom,
( a3
= ( groups1792256535list_a @ qs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_a) ).
thf(1257,plain,
( a3
= ( groups1792256535list_a @ qs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1258,plain,
( ( groups1792256535list_a @ qs )
= a3 ),
inference(lifteq,[status(thm)],[1257]) ).
thf(2328,plain,
( ( groups1792256535list_a @ qs2 )
= a3 ),
inference(rewrite,[status(thm)],[2321,1237,1258]) ).
thf(1,conjecture,
( a3
= ( groups1792256535list_a @ qs2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( a3
!= ( groups1792256535list_a @ qs2 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(262,plain,
( a3
!= ( groups1792256535list_a @ qs2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(263,plain,
( ( groups1792256535list_a @ qs2 )
!= a3 ),
inference(lifteq,[status(thm)],[262]) ).
thf(2329,plain,
$false,
inference(simplifyReflect,[status(thm)],[2328,263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP077^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/0.21 % Computer : n007.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 19:45:56 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.41/1.24 % [INFO] Parsing done (427ms).
% 2.41/1.25 % [INFO] Running in sequential loop mode.
% 3.60/1.63 % [INFO] eprover registered as external prover.
% 3.60/1.64 % [INFO] Scanning for conjecture ...
% 4.02/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 353 axioms. Running axiom selection ...
% 4.26/1.98 % [INFO] Axiom selection finished. Selected 259 axioms (removed 94 axioms).
% 5.23/2.22 % [INFO] Problem is higher-order (TPTP THF).
% 5.23/2.24 % [INFO] Type checking passed.
% 5.23/2.24 % [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 ...
% 61.60/24.32 % [INFO] Killing All external provers ...
% 61.60/24.33 % Time passed: 23967ms (effective reasoning time: 23063ms)
% 61.60/24.33 % 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)>
% 61.60/24.33 % Axioms used in derivation (3): fact_0__092_060open_062mset_Aqs2_A_061_Amset_Aqs_092_060close_062, fact_24_sum__mset__sum__list, fact_2_a
% 61.60/24.33 % No. of inferences in proof: 18
% 61.60/24.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 23967 ms resp. 23063 ms w/o parsing
% 61.60/24.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 61.60/24.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------