%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT319^1 : 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 : n002.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 07:48:14 AM UTC 2026
% Result : Theorem 3.68s 2.25s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 19 unt; 0 typ; 2 def)
% Number of atoms : 25 ( 24 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 239 ( 10 ~; 2 |; 0 &; 227 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 49 ( 0 ^; 47 !; 0 ?; 49 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf('const/lists/APPEND_decl',type,
'const/lists/APPEND':
!>[TA: $tType] : ( ( 'type/ind_types/list' @ TA ) > ( 'type/ind_types/list' @ TA ) > ( 'type/ind_types/list' @ TA ) ) ).
thf('const/ind_types/NIL_decl',type,
'const/ind_types/NIL':
!>[TA: $tType] : ( 'type/ind_types/list' @ TA ) ).
thf('const/ind_types/CONS_decl',type,
'const/ind_types/CONS':
!>[TA: $tType] : ( TA > ( 'type/ind_types/list' @ TA ) > ( 'type/ind_types/list' @ TA ) ) ).
thf(sk1_decl,type,
sk1: skt1 ).
thf(sk2_decl,type,
sk2: 'type/ind_types/list' @ skt1 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1] :
~ ! [B: 'type/ind_types/list' @ skt1] :
( ( 'const/lists/APPEND' @ skt1 @ ( 'const/ind_types/CONS' @ skt1 @ A @ ( 'const/ind_types/NIL' @ skt1 ) ) @ B )
= ( 'const/ind_types/CONS' @ skt1 @ A @ B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: 'type/ind_types/list' @ skt1] :
( ( 'const/lists/APPEND' @ skt1 @ ( 'const/ind_types/CONS' @ skt1 @ sk1 @ ( 'const/ind_types/NIL' @ skt1 ) ) @ A )
!= ( 'const/ind_types/CONS' @ skt1 @ sk1 @ A ) ) ) ) ).
thf(3,axiom,
! [TA: $tType,A: 'type/ind_types/list' @ TA] :
( ( 'const/lists/APPEND' @ TA @ ( 'const/ind_types/NIL' @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/APPEND_0') ).
thf(8,plain,
! [TA: $tType,A: 'type/ind_types/list' @ TA] :
( ( 'const/lists/APPEND' @ TA @ ( 'const/ind_types/NIL' @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
! [TA: $tType,A: 'type/ind_types/list' @ TA] :
( ( 'const/lists/APPEND' @ TA @ ( 'const/ind_types/NIL' @ TA ) @ A )
= A ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
! [TA: $tType,A: 'type/ind_types/list' @ TA] :
( ( 'const/lists/APPEND' @ TA @ ( 'const/ind_types/NIL' @ TA ) @ A )
= A ),
inference(lifteq,[status(thm)],[9]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: 'type/ind_types/list' @ TA,C: 'type/ind_types/list' @ TA] :
( ( 'const/lists/APPEND' @ TA @ ( 'const/ind_types/CONS' @ TA @ A @ B ) @ C )
= ( 'const/ind_types/CONS' @ TA @ A @ ( 'const/lists/APPEND' @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/APPEND_1') ).
thf(11,plain,
! [TA: $tType,A: TA,B: 'type/ind_types/list' @ TA,C: 'type/ind_types/list' @ TA] :
( ( 'const/lists/APPEND' @ TA @ ( 'const/ind_types/CONS' @ TA @ A @ B ) @ C )
= ( 'const/ind_types/CONS' @ TA @ A @ ( 'const/lists/APPEND' @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
! [TA: $tType,C: 'type/ind_types/list' @ TA,B: 'type/ind_types/list' @ TA,A: TA] :
( ( 'const/lists/APPEND' @ TA @ ( 'const/ind_types/CONS' @ TA @ A @ B ) @ C )
= ( 'const/ind_types/CONS' @ TA @ A @ ( 'const/lists/APPEND' @ TA @ B @ C ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [TA: $tType,C: 'type/ind_types/list' @ TA,B: 'type/ind_types/list' @ TA,A: TA] :
( ( 'const/ind_types/CONS' @ TA @ A @ ( 'const/lists/APPEND' @ TA @ B @ C ) )
= ( 'const/lists/APPEND' @ TA @ ( 'const/ind_types/CONS' @ TA @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(15,plain,
! [TB: $tType,D: 'type/ind_types/list' @ TB,C: 'type/ind_types/list' @ TB,B: TB,A: 'type/ind_types/list' @ TB] :
( ( ( 'const/ind_types/CONS' @ TB @ B @ A )
= ( 'const/lists/APPEND' @ TB @ ( 'const/ind_types/CONS' @ TB @ B @ C ) @ D ) )
| ( ( 'const/lists/APPEND' @ TB @ ( 'const/ind_types/NIL' @ TB ) @ A )
!= ( 'const/lists/APPEND' @ TB @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10,13]) ).
thf(16,plain,
! [TB: $tType,B: TB,A: 'type/ind_types/list' @ TB] :
( ( 'const/ind_types/CONS' @ TB @ B @ A )
= ( 'const/lists/APPEND' @ TB @ ( 'const/ind_types/CONS' @ TB @ B @ ( 'const/ind_types/NIL' @ TB ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( 'const/ind_types/NIL' @ TB )),bind(D,$thf( A ))]]) ).
thf(20,plain,
! [TA: $tType,B: TA,A: 'type/ind_types/list' @ TA] :
( ( 'const/ind_types/CONS' @ TA @ B @ A )
= ( 'const/lists/APPEND' @ TA @ ( 'const/ind_types/CONS' @ TA @ B @ ( 'const/ind_types/NIL' @ TA ) ) @ A ) ),
inference(simp,[status(thm)],[16]) ).
thf(1,conjecture,
! [TA: $tType,A: TA,B: 'type/ind_types/list' @ TA] :
( ( 'const/lists/APPEND' @ TA @ ( 'const/ind_types/CONS' @ TA @ A @ ( 'const/ind_types/NIL' @ TA ) ) @ B )
= ( 'const/ind_types/CONS' @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/APPEND_SING_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA,B: 'type/ind_types/list' @ TA] :
( ( 'const/lists/APPEND' @ TA @ ( 'const/ind_types/CONS' @ TA @ A @ ( 'const/ind_types/NIL' @ TA ) ) @ B )
= ( 'const/ind_types/CONS' @ TA @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA,B: 'type/ind_types/list' @ TA] :
( ( 'const/lists/APPEND' @ TA @ ( 'const/ind_types/CONS' @ TA @ A @ ( 'const/ind_types/NIL' @ TA ) ) @ B )
= ( 'const/ind_types/CONS' @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( 'const/lists/APPEND' @ skt1 @ ( 'const/ind_types/CONS' @ skt1 @ sk1 @ ( 'const/ind_types/NIL' @ skt1 ) ) @ sk2 )
!= ( 'const/ind_types/CONS' @ skt1 @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
( ( 'const/ind_types/CONS' @ skt1 @ sk1 @ sk2 )
!= ( 'const/lists/APPEND' @ skt1 @ ( 'const/ind_types/CONS' @ skt1 @ sk1 @ ( 'const/ind_types/NIL' @ skt1 ) ) @ sk2 ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(25,plain,
! [B: skt1,A: 'type/ind_types/list' @ skt1] :
( ( ( 'const/lists/APPEND' @ skt1 @ ( 'const/ind_types/CONS' @ skt1 @ B @ ( 'const/ind_types/NIL' @ skt1 ) ) @ A )
!= ( 'const/lists/APPEND' @ skt1 @ ( 'const/ind_types/CONS' @ skt1 @ sk1 @ ( 'const/ind_types/NIL' @ skt1 ) ) @ sk2 ) )
| ( ( 'const/ind_types/CONS' @ skt1 @ B @ A )
!= ( 'const/ind_types/CONS' @ skt1 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[20,7]) ).
thf(26,plain,
( ( 'const/lists/APPEND' @ skt1 @ ( 'const/ind_types/CONS' @ skt1 @ sk1 @ ( 'const/ind_types/NIL' @ skt1 ) ) @ sk2 )
!= ( 'const/lists/APPEND' @ skt1 @ ( 'const/ind_types/CONS' @ skt1 @ sk1 @ ( 'const/ind_types/NIL' @ skt1 ) ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(44,plain,
$false,
inference(simp,[status(thm)],[26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT319^1 : TPTP v9.3.1. Released v7.0.0.
% 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
% 0.10/0.23 % Computer : n002.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 18:29:52 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 0.97/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.14/0.99 % [INFO] Parsing done (180ms).
% 1.14/1.00 % [INFO] Running in sequential loop mode.
% 1.73/1.39 % [INFO] eprover registered as external prover.
% 1.91/1.40 % [INFO] Scanning for conjecture ...
% 1.91/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.07/1.53 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.07/1.54 % [INFO] Problem is higher-order (TPTP THF).
% 2.07/1.55 % [INFO] Type checking passed.
% 2.07/1.55 % [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 ...
% 3.68/2.24 % [INFO] Killing All external provers ...
% 3.68/2.25 % Time passed: 1871ms (effective reasoning time: 1236ms)
% 3.68/2.25 % 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)>
% 3.68/2.25 % Axioms used in derivation (2): thm/lists/APPEND_0, thm/lists/APPEND_1
% 3.68/2.25 % No. of inferences in proof: 19
% 3.68/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1871 ms resp. 1236 ms w/o parsing
% 3.68/2.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.68/2.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------