%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT130^1 : 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 : n010.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 07:48:02 AM UTC 2026
% Result : Theorem 51.00s 20.55s
% Output : Refutation 51.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 11 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 192 ( 8 ~; 2 |; 0 &; 182 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(coindu526335360e_lSup_decl,type,
coindu526335360e_lSup:
!>[TA: $tType] : ( ( set @ ( coindu1593790203_llist @ TA ) ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu1046438764le_lhd_decl,type,
coindu1046438764le_lhd:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > TA ) ).
thf(coindu1047225960le_ltl_decl,type,
coindu1047225960le_ltl:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(ya_decl,type,
ya: set @ ( coindu1593790203_llist @ a ) ).
thf(less_eq_decl,type,
less_eq: a > a > $o ).
thf(xs_decl,type,
xs: coindu1593790203_llist @ a ).
thf(182,axiom,
( ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) )
= ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062lhd_A_Iltl_A_IlSup_AY_J_J_A_061_Alhd_A_Iltl_Axs_J_092_060close_062) ).
thf(930,plain,
( ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) )
= ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(931,plain,
( ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) )
= ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ),
inference(lifteq,[status(thm)],[930]) ).
thf(188,axiom,
less_eq @ ( coindu1046438764le_lhd @ a @ xs ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062lhd_Axs_A_092_060le_062_Alhd_A_Iltl_Axs_J_092_060close_062) ).
thf(955,plain,
less_eq @ ( coindu1046438764le_lhd @ a @ xs ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(149,axiom,
( ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) )
= ( coindu1046438764le_lhd @ a @ xs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062lhd_A_IlSup_AY_J_A_061_Alhd_Axs_092_060close_062) ).
thf(792,plain,
( ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) )
= ( coindu1046438764le_lhd @ a @ xs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(793,plain,
( ( coindu1046438764le_lhd @ a @ xs )
= ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ),
inference(lifteq,[status(thm)],[792]) ).
thf(1540,plain,
less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ),
inference(rewrite,[status(thm)],[955,793]) ).
thf(1,conjecture,
less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(241,plain,
~ ( less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1550,plain,
( ~ $true
| ( ( less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) )
!= ( less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1540,241]) ).
thf(1551,plain,
( ( less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) )
!= ( less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ) ),
inference(simp,[status(thm)],[1550]) ).
thf(1557,plain,
( ( ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) )
!= ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) )
| ( ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) )
!= ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ) ),
inference(simp,[status(thm)],[1551]) ).
thf(1560,plain,
( ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) )
!= ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ),
inference(simp,[status(thm)],[1557]) ).
thf(1604,plain,
$false,
inference(simplifyReflect,[status(thm)],[931,1560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT130^1 : 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
% 0.11/0.19 % Computer : n010.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 17:59:03 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 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
% 0.87/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.03/1.19 % [INFO] Parsing done (415ms).
% 2.36/1.20 % [INFO] Running in sequential loop mode.
% 3.04/1.59 % [INFO] eprover registered as external prover.
% 3.04/1.59 % [INFO] Scanning for conjecture ...
% 3.39/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 263 axioms. Running axiom selection ...
% 3.83/1.90 % [INFO] Axiom selection finished. Selected 238 axioms (removed 25 axioms).
% 4.65/2.21 % [INFO] Problem is higher-order (TPTP THF).
% 4.65/2.24 % [INFO] Type checking passed.
% 4.65/2.25 % [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 ...
% 51.00/20.55 % [INFO] Killing All external provers ...
% 51.00/20.55 % Time passed: 20220ms (effective reasoning time: 19336ms)
% 51.00/20.55 % 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)>
% 51.00/20.55 % Axioms used in derivation (3): fact_5__092_060open_062lhd_A_Iltl_A_IlSup_AY_J_J_A_061_Alhd_A_Iltl_Axs_J_092_060close_062, fact_1__092_060open_062lhd_Axs_A_092_060le_062_Alhd_A_Iltl_Axs_J_092_060close_062, fact_4__092_060open_062lhd_A_IlSup_AY_J_A_061_Alhd_Axs_092_060close_062
% 51.00/20.55 % No. of inferences in proof: 17
% 51.00/20.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 20220 ms resp. 19336 ms w/o parsing
% 51.00/20.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 51.00/20.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------