%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT187^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n012.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 07:48:06 AM UTC 2026
% Result : Theorem 49.43s 21.91s
% Output : Refutation 49.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 102 ( 18 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 363 ( 34 ~; 13 |; 3 &; 313 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-3 aty)
% Number of variables : 23 ( 0 ^; 18 !; 4 ?; 23 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(coinductive_lappend_decl,type,
coinductive_lappend:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(lList2435255213lllsts_decl,type,
lList2435255213lllsts:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( coinductive_llist @ TA ) ) ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(p_decl,type,
p: set @ ( coinductive_llist @ a ) ).
thf(r_decl,type,
r: coinductive_llist @ a ).
thf(t_decl,type,
t: coinductive_llist @ a ).
thf(u_decl,type,
u: coinductive_llist @ a ).
thf(sk60_decl,type,
sk60: coinductive_llist @ a ).
thf(sk60_def,definition,
( sk60
= ( @+[A: coinductive_llist @ a] :
( t
= ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ A ) ) ) ) ) ).
thf(244,axiom,
~ ! [A: coinductive_llist @ a] :
( t
!= ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_At_A_061_Ar_A_064_064_Au_A_064_064_Av_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(1054,plain,
~ ! [A: coinductive_llist @ a] :
( t
!= ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1055,plain,
~ ! [A: coinductive_llist @ a] :
( t
!= ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ A ) ) ),
inference(polarity_switch,[status(thm)],[1054]) ).
thf(1056,plain,
~ ~ ? [A: coinductive_llist @ a] :
( t
= ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ A ) ) ),
inference(miniscope,[status(thm)],[1055]) ).
thf(1057,plain,
( t
= ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ sk60 ) ) ),
inference(cnf,[status(esa)],[1056]) ).
thf(1058,plain,
( t
= ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ sk60 ) ) ),
inference(lifteq,[status(thm)],[1057]) ).
thf(205,axiom,
member @ ( coinductive_llist @ a ) @ t @ p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tP) ).
thf(923,plain,
member @ ( coinductive_llist @ a ) @ t @ p,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1,conjecture,
? [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
& ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
& ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(281,plain,
~ ? [A: coinductive_llist @ a] :
( ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
& ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(282,plain,
! [A: coinductive_llist @ a] :
( ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ~ ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p ) ),
inference(cnf,[status(esa)],[281]) ).
thf(1169,plain,
! [A: coinductive_llist @ a] :
( ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ( ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p )
!= ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[282]) ).
thf(1170,plain,
! [A: coinductive_llist @ a] :
( ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ( ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p )
!= ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) ) ) ),
inference(simp,[status(thm)],[1169]) ).
thf(1967,plain,
! [A: coinductive_llist @ a] :
( ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ( ( member @ ( coinductive_llist @ a ) @ t @ p )
!= ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p ) ) ),
inference(paramod_ordered,[status(thm)],[923,1170]) ).
thf(1968,plain,
! [A: coinductive_llist @ a] :
( ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ( ( member @ ( coinductive_llist @ a ) @ t @ p )
!= ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ r @ A ) @ p ) ) ),
inference(simp,[status(thm)],[1967]) ).
thf(1989,plain,
! [A: coinductive_llist @ a] :
( ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ( t
!= ( coinductive_lappend @ a @ r @ A ) )
| ( p != p ) ),
inference(simp,[status(thm)],[1968]) ).
thf(2004,plain,
! [A: coinductive_llist @ a] :
( ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ( t
!= ( coinductive_lappend @ a @ r @ A ) ) ),
inference(simp,[status(thm)],[1989]) ).
thf(3344,plain,
! [A: coinductive_llist @ a] :
( ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ( t != t )
| ( ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ sk60 ) )
!= ( coinductive_lappend @ a @ r @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1058,2004]) ).
thf(3345,plain,
! [A: coinductive_llist @ a] :
( ~ ( member @ ( coinductive_llist @ a ) @ A @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) )
| ( ( coinductive_lappend @ a @ r @ ( coinductive_lappend @ a @ u @ sk60 ) )
!= ( coinductive_lappend @ a @ r @ A ) ) ),
inference(simp,[status(thm)],[3344]) ).
thf(3346,plain,
~ ( member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ u @ sk60 ) @ ( lList2435255213lllsts @ a @ ( top_top @ ( set @ a ) ) ) ),
inference(pattern_uni,[status(thm)],[3345:[bind(A,$thf( coinductive_lappend @ a @ u @ sk60 ))]]) ).
thf(160,axiom,
! [TA: $tType,A: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_alllsts__UNIV) ).
thf(752,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(753,plain,
! [TA: $tType,A: coinductive_llist @ TA] : ( member @ ( coinductive_llist @ TA ) @ A @ ( lList2435255213lllsts @ TA @ ( top_top @ ( set @ TA ) ) ) ),
inference(cnf,[status(esa)],[752]) ).
thf(3862,plain,
~ $true,
inference(rewrite,[status(thm)],[3346,753]) ).
thf(3863,plain,
$false,
inference(simp,[status(thm)],[3862]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : DAT187^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % 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
% 0.08/0.13 % Computer : n012.cluster.edu
% 0.08/0.13 % Model : x86_64 x86_64
% 0.08/0.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.13 % Memory : 8046.5625MB
% 0.08/0.13 % OS : Linux 6.8.0-71-generic
% 0.08/0.13 % CPULimit : 300
% 0.08/0.13 % WCLimit : 300
% 0.08/0.13 % DateTime : Tue Sep 29 18:06:03 UTC 2026
% 0.08/0.14 % CPUTime :
% 0.08/0.14 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
% 0.56/0.46 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.07/0.69 % [INFO] Parsing done (229ms).
% 1.45/0.70 % [INFO] Running in sequential loop mode.
% 2.08/0.92 % [INFO] eprover registered as external prover.
% 2.08/0.92 % [INFO] Scanning for conjecture ...
% 2.44/1.02 % [INFO] Found a conjecture (or negated_conjecture) and 279 axioms. Running axiom selection ...
% 2.44/1.11 % [INFO] Axiom selection finished. Selected 278 axioms (removed 1 axioms).
% 3.11/1.29 % [INFO] Problem is higher-order (TPTP THF).
% 3.45/1.31 % [INFO] Type checking passed.
% 3.45/1.31 % [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 ...
% 49.43/21.90 % [INFO] Killing All external provers ...
% 49.43/21.90 % Time passed: 21679ms (effective reasoning time: 21196ms)
% 49.43/21.90 % 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)>
% 49.43/21.90 % Axioms used in derivation (3): fact_4__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_At_A_061_Ar_A_064_064_Au_A_064_064_Av_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_0_tP, fact_5_alllsts__UNIV
% 49.43/21.90 % No. of inferences in proof: 26
% 49.43/21.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21679 ms resp. 21196 ms w/o parsing
% 49.43/21.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 49.43/21.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------