%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT282^1 : 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 : n026.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 3.16s 2.08s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 12 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 119 ( 7 ~; 1 |; 0 &; 111 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf('const/lists/ZIP_decl',type,
'const/lists/ZIP':
!>[TA: $tType,TB: $tType] : ( ( 'type/ind_types/list' @ TB ) > ( 'type/ind_types/list' @ TA ) > ( 'type/ind_types/list' @ ( 'type/pair/prod' @ TB @ TA ) ) ) ).
thf('const/ind_types/NIL_decl',type,
'const/ind_types/NIL':
!>[TA: $tType] : ( 'type/ind_types/list' @ TA ) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: 'type/ind_types/list' @ TA] :
( ( 'const/lists/ZIP' @ TB @ TA @ ( 'const/ind_types/NIL' @ TB ) @ A )
= ( 'const/ind_types/NIL' @ ( 'type/pair/prod' @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ZIP_DEF_0') ).
thf(7,plain,
! [TA: $tType,TB: $tType,A: 'type/ind_types/list' @ TA] :
( ( 'const/lists/ZIP' @ TB @ TA @ ( 'const/ind_types/NIL' @ TB ) @ A )
= ( 'const/ind_types/NIL' @ ( 'type/pair/prod' @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [TA: $tType,TB: $tType,A: 'type/ind_types/list' @ TB] :
( ( 'const/lists/ZIP' @ TA @ TB @ ( 'const/ind_types/NIL' @ TA ) @ A )
= ( 'const/ind_types/NIL' @ ( 'type/pair/prod' @ TA @ TB ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
! [TA: $tType,TB: $tType,A: 'type/ind_types/list' @ TB] :
( ( 'const/lists/ZIP' @ TA @ TB @ ( 'const/ind_types/NIL' @ TA ) @ A )
= ( 'const/ind_types/NIL' @ ( 'type/pair/prod' @ TA @ TB ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType] :
( ( 'const/lists/ZIP' @ TB @ TA @ ( 'const/ind_types/NIL' @ TB ) @ ( 'const/ind_types/NIL' @ TA ) )
= ( 'const/ind_types/NIL' @ ( 'type/pair/prod' @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ZIP_0') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType] :
( ( 'const/lists/ZIP' @ TB @ TA @ ( 'const/ind_types/NIL' @ TB ) @ ( 'const/ind_types/NIL' @ TA ) )
= ( 'const/ind_types/NIL' @ ( 'type/pair/prod' @ TB @ TA ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [TA: $tType,TB: $tType] :
( ( 'const/lists/ZIP' @ TB @ TA @ ( 'const/ind_types/NIL' @ TB ) @ ( 'const/ind_types/NIL' @ TA ) )
= ( 'const/ind_types/NIL' @ ( 'type/pair/prod' @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( 'const/lists/ZIP' @ skt1 @ skt2 @ ( 'const/ind_types/NIL' @ skt1 ) @ ( 'const/ind_types/NIL' @ skt2 ) )
!= ( 'const/ind_types/NIL' @ ( 'type/pair/prod' @ skt1 @ skt2 ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
( ( 'const/lists/ZIP' @ skt1 @ skt2 @ ( 'const/ind_types/NIL' @ skt1 ) @ ( 'const/ind_types/NIL' @ skt2 ) )
!= ( 'const/ind_types/NIL' @ ( 'type/pair/prod' @ skt1 @ skt2 ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(10,plain,
! [A: 'type/ind_types/list' @ skt2] :
( ( ( 'const/ind_types/NIL' @ ( 'type/pair/prod' @ skt1 @ skt2 ) )
!= ( 'const/ind_types/NIL' @ ( 'type/pair/prod' @ skt1 @ skt2 ) ) )
| ( ( 'const/lists/ZIP' @ skt1 @ skt2 @ ( 'const/ind_types/NIL' @ skt1 ) @ A )
!= ( 'const/lists/ZIP' @ skt1 @ skt2 @ ( 'const/ind_types/NIL' @ skt1 ) @ ( 'const/ind_types/NIL' @ skt2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,6]) ).
thf(11,plain,
! [A: 'type/ind_types/list' @ skt2] :
( ( 'const/lists/ZIP' @ skt1 @ skt2 @ ( 'const/ind_types/NIL' @ skt1 ) @ A )
!= ( 'const/lists/ZIP' @ skt1 @ skt2 @ ( 'const/ind_types/NIL' @ skt1 ) @ ( 'const/ind_types/NIL' @ skt2 ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(12,plain,
$false,
inference(pattern_uni,[status(thm)],[11:[bind(A,$thf( 'const/ind_types/NIL' @ skt2 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT282^1 : 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
% 0.10/0.20 % Computer : n026.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 18:22:42 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.90/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.98 % [INFO] Parsing done (196ms).
% 1.21/1.00 % [INFO] Running in sequential loop mode.
% 1.77/1.39 % [INFO] eprover registered as external prover.
% 1.77/1.40 % [INFO] Scanning for conjecture ...
% 1.95/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.11/1.52 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.11/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.11/1.53 % [INFO] Type checking passed.
% 2.11/1.54 % [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 ...
% 3.16/2.07 % [INFO] Killing All external provers ...
% 3.16/2.07 % Time passed: 1735ms (effective reasoning time: 1068ms)
% 3.16/2.07 % 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)>
% 3.16/2.08 % Axioms used in derivation (1): thm/lists/ZIP_DEF_0
% 3.16/2.08 % No. of inferences in proof: 12
% 3.16/2.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1735 ms resp. 1068 ms w/o parsing
% 3.16/2.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.16/2.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------