%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT280^1 : 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 : n017.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 07:48:12 AM UTC 2026
% Result : Theorem 3.69s 2.19s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 17 ( 16 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 127 ( 9 ~; 1 |; 0 &; 117 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-7 aty)
% Number of variables : 47 ( 0 ^; 45 !; 0 ?; 47 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(skt3_type,type,
skt3: $tType ).
thf('const/lists/ITLIST2_decl',type,
'const/lists/ITLIST2':
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA > TA ) > ( 'type/ind_types/list' @ TC ) > ( 'type/ind_types/list' @ TB ) > TA > TA ) ).
thf('const/ind_types/NIL_decl',type,
'const/ind_types/NIL':
!>[TA: $tType] : ( 'type/ind_types/list' @ TA ) ).
thf(sk1_decl,type,
sk1: skt1 > skt2 > skt3 > skt3 ).
thf(sk2_decl,type,
sk2: skt3 ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > skt2 > skt3 > skt3] :
~ ! [B: skt3] :
( ( 'const/lists/ITLIST2' @ skt1 @ skt2 @ skt3 @ A @ ( 'const/ind_types/NIL' @ skt1 ) @ ( 'const/ind_types/NIL' @ skt2 ) @ B )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt3] :
( ( 'const/lists/ITLIST2' @ skt1 @ skt2 @ skt3 @ sk1 @ ( 'const/ind_types/NIL' @ skt1 ) @ ( 'const/ind_types/NIL' @ skt2 ) @ A )
!= A ) ) ) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > TA > TA,B: 'type/ind_types/list' @ TB,C: TA] :
( ( 'const/lists/ITLIST2' @ TC @ TB @ TA @ A @ ( 'const/ind_types/NIL' @ TC ) @ B @ C )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ITLIST2_DEF_0') ).
thf(7,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > TA > TA,B: 'type/ind_types/list' @ TB,C: TA] :
( ( 'const/lists/ITLIST2' @ TC @ TB @ TA @ A @ ( 'const/ind_types/NIL' @ TC ) @ B @ C )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TC,B: 'type/ind_types/list' @ TB,A: TA > TB > TC > TC] :
( ( 'const/lists/ITLIST2' @ TA @ TB @ TC @ A @ ( 'const/ind_types/NIL' @ TA ) @ B @ C )
= C ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TC,B: 'type/ind_types/list' @ TB,A: TA > TB > TC > TC] :
( ( 'const/lists/ITLIST2' @ TA @ TB @ TC @ A @ ( 'const/ind_types/NIL' @ TA ) @ B @ C )
= C ),
inference(lifteq,[status(thm)],[8]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > TA > TA,B: TA] :
( ( 'const/lists/ITLIST2' @ TC @ TB @ TA @ A @ ( 'const/ind_types/NIL' @ TC ) @ ( 'const/ind_types/NIL' @ TB ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ITLIST2_0') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > TA > TA,B: TA] :
( ( 'const/lists/ITLIST2' @ TC @ TB @ TA @ A @ ( 'const/ind_types/NIL' @ TC ) @ ( 'const/ind_types/NIL' @ TB ) @ B )
= B ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > TA > TA,B: TA] :
( ( 'const/lists/ITLIST2' @ TC @ TB @ TA @ A @ ( 'const/ind_types/NIL' @ TC ) @ ( 'const/ind_types/NIL' @ TB ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( 'const/lists/ITLIST2' @ skt1 @ skt2 @ skt3 @ sk1 @ ( 'const/ind_types/NIL' @ skt1 ) @ ( 'const/ind_types/NIL' @ skt2 ) @ sk2 )
!= sk2 ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
( ( 'const/lists/ITLIST2' @ skt1 @ skt2 @ skt3 @ sk1 @ ( 'const/ind_types/NIL' @ skt1 ) @ ( 'const/ind_types/NIL' @ skt2 ) @ sk2 )
!= sk2 ),
inference(lifteq,[status(thm)],[5]) ).
thf(10,plain,
! [TA: $tType,TB: $tType,C: skt3,B: 'type/ind_types/list' @ TB,A: TA > TB > skt3 > skt3] :
( ( C != sk2 )
| ( ( 'const/lists/ITLIST2' @ TA @ TB @ skt3 @ A @ ( 'const/ind_types/NIL' @ TA ) @ B @ C )
!= ( 'const/lists/ITLIST2' @ skt1 @ skt2 @ skt3 @ sk1 @ ( 'const/ind_types/NIL' @ skt1 ) @ ( 'const/ind_types/NIL' @ skt2 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[9,6]) ).
thf(11,plain,
sk2 != sk2,
inference(pattern_uni,[status(thm)],[10:[bind(A,$thf( sk1 )),bind(B,$thf( 'const/ind_types/NIL' @ skt2 )),bind(C,$thf( sk2 )),bind_type(TA,$thf( skt1 )),bind_type(TB,$thf( skt2 ))]]) ).
thf(12,plain,
$false,
inference(simp,[status(thm)],[11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT280^1 : TPTP v9.3.1. Released v7.0.0.
% 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
% 0.10/0.23 % Computer : n017.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 18:14:52 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
% 1.03/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.02 % [INFO] Parsing done (198ms).
% 1.45/1.03 % [INFO] Running in sequential loop mode.
% 2.01/1.43 % [INFO] eprover registered as external prover.
% 2.01/1.44 % [INFO] Scanning for conjecture ...
% 2.21/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.21/1.58 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.21/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.59 % [INFO] Type checking passed.
% 2.38/1.60 % [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 ...
% 3.69/2.18 % [INFO] Killing All external provers ...
% 3.69/2.19 % Time passed: 1807ms (effective reasoning time: 1148ms)
% 3.69/2.19 % 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)>
% 3.69/2.19 % Axioms used in derivation (1): thm/lists/ITLIST2_DEF_0
% 3.69/2.19 % No. of inferences in proof: 12
% 3.69/2.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1807 ms resp. 1148 ms w/o parsing
% 3.84/2.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.84/2.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------