%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL805_5 : TPTP v9.3.1. Released v6.0.0.
% 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 : Sun Sep 27 07:53:00 AM UTC 2026
% Result : Theorem 23.04s 13.83s
% Output : Refutation 23.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 17 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 275 ( 13 ~; 6 |; 2 &; 251 @)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 9 con; 0-5 aty)
% Number of variables : 33 ( 0 ^; 33 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(dB_type,type,
dB: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > TB > ( TA @ ( TC @ fun ) ) ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(it_decl,type,
it: bool @ ( dB @ fun ) ).
thf(lift_decl,type,
lift: dB @ ( nat @ fun ) @ ( dB @ fun ) ).
thf(subst_decl,type,
subst: dB @ ( nat @ fun ) @ ( dB @ fun ) @ ( dB @ fun ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( TA @ list ) ).
thf(listsp_decl,type,
listsp:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(map_decl,type,
map:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( TB @ list ) > ( TA @ list ) ) ).
thf(i_decl,type,
i: nat ).
thf(u_decl,type,
u: dB ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TB @ ( TA @ map ) ) ) )
= ( TB @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_map__is__Nil__conv) ).
thf(302,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TB @ ( TA @ map ) ) ) )
= ( TB @ nil ) ) )
& ( ( ( A @ ( B @ ( TB @ ( TA @ map ) ) ) )
= ( TB @ nil ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(303,plain,
! [TA: $tType,TB: $tType,B: TA @ ( TB @ fun ),A: TB @ list] :
( ( ( ( A @ ( B @ ( TA @ ( TB @ map ) ) ) )
= ( TA @ nil ) )
| ( A
!= ( TB @ nil ) ) )
& ( ( A
= ( TB @ nil ) )
| ( ( A @ ( B @ ( TA @ ( TB @ map ) ) ) )
!= ( TA @ nil ) ) ) ),
inference(cnf,[status(esa)],[302]) ).
thf(305,plain,
! [TA: $tType,TB: $tType,B: TA @ ( TB @ fun ),A: TB @ list] :
( ( ( A @ ( B @ ( TA @ ( TB @ map ) ) ) )
= ( TA @ nil ) )
| ( A
!= ( TB @ nil ) ) ),
inference(cnfConj,[status(thm)],[303]) ).
thf(307,plain,
! [TA: $tType,TB: $tType,B: TA @ ( TB @ fun ),A: TB @ list] :
( ( ( A @ ( B @ ( TA @ ( TB @ map ) ) ) )
= ( TA @ nil ) )
| ( A
!= ( TB @ nil ) ) ),
inference(lifteq,[status(thm)],[305]) ).
thf(308,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun )] :
( ( TB @ nil @ ( A @ ( TA @ ( TB @ map ) ) ) )
= ( TA @ nil ) ),
inference(simp,[status(thm)],[307]) ).
thf(1,conjecture,
dB @ nil @ ( i @ ( u @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( it @ ( dB @ listsp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( dB @ nil @ ( i @ ( u @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( it @ ( dB @ listsp ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(114,plain,
~ ( dB @ nil @ ( i @ ( u @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( it @ ( dB @ listsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(673,plain,
! [TB: $tType,A: dB @ ( TB @ fun )] :
( ( ( TB @ nil @ ( A @ ( dB @ ( TB @ map ) ) ) )
!= ( dB @ nil @ ( i @ ( u @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) ) )
| ~ ( dB @ nil @ ( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( it @ ( dB @ listsp ) ) ) ),
inference(paramod_ordered,[status(thm)],[308,114]) ).
thf(674,plain,
~ ( dB @ nil @ ( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) @ ( it @ ( dB @ listsp ) ) ),
inference(pattern_uni,[status(thm)],[673:[bind(A,$thf( i @ ( u @ ( subst @ ( dB @ ( nat @ fun ) @ ( dB @ ( dB @ combc ) ) ) ) @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( dB ))]]) ).
thf(679,plain,
! [TB: $tType,A: dB @ ( TB @ fun )] :
( ( ( TB @ nil @ ( A @ ( dB @ ( TB @ map ) ) ) )
!= ( dB @ nil @ ( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) @ ( dB @ ( dB @ map ) ) ) ) )
| ~ ( dB @ nil @ ( it @ ( dB @ listsp ) ) ) ),
inference(paramod_ordered,[status(thm)],[308,674]) ).
thf(680,plain,
~ ( dB @ nil @ ( it @ ( dB @ listsp ) ) ),
inference(pattern_uni,[status(thm)],[679:[bind(A,$thf( nat @ zero_zero @ ( lift @ ( dB @ ( nat @ ( dB @ combc ) ) ) ) )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( dB ))]]) ).
thf(107,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ listsp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_listsp_ONil) ).
thf(557,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ listsp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(558,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ listsp ) ) ),
inference(cnf,[status(esa)],[557]) ).
thf(693,plain,
~ $true,
inference(rewrite,[status(thm)],[680,558]) ).
thf(694,plain,
$false,
inference(simp,[status(thm)],[693]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL805_5 : TPTP v9.3.1. Released v6.0.0.
% 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
% 0.07/0.33 % Computer : n012.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Fri Sep 25 23:36:06 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.07/0.33 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
% 0.50/0.61 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.65/0.78 % [INFO] Parsing done (167ms).
% 0.65/0.79 % [INFO] Running in sequential loop mode.
% 1.38/1.00 % [INFO] eprover registered as external prover.
% 1.38/1.01 % [INFO] Scanning for conjecture ...
% 1.64/1.11 % [INFO] Found a conjecture (or negated_conjecture) and 111 axioms. Running axiom selection ...
% 1.86/1.18 % [INFO] Axiom selection finished. Selected 111 axioms (removed 0 axioms).
% 2.65/1.30 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.65/1.32 % [INFO] Type checking passed.
% 2.65/1.33 % [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 ...
% 23.04/13.83 % [INFO] Killing All external provers ...
% 23.04/13.83 % Time passed: 13422ms (effective reasoning time: 13032ms)
% 23.04/13.83 % 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)>
% 23.04/13.83 % Axioms used in derivation (2): fact_9_map__is__Nil__conv, fact_6_listsp_ONil
% 23.04/13.83 % No. of inferences in proof: 18
% 23.04/13.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 13422 ms resp. 13032 ms w/o parsing
% 23.04/13.85 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.04/13.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------