%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT178^1 : 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 : 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 : Wed Sep 30 07:48:05 AM UTC 2026
% Result : Theorem 17.65s 5.10s
% Output : Refutation 17.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 14 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 75 ( 10 ~; 2 |; 0 &; 63 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(coinductive_LNil_decl,type,
coinductive_LNil:
!>[TA: $tType] : ( coinductive_llist @ TA ) ).
thf(lList2281150353e_lrev_decl,type,
lList2281150353e_lrev:
!>[TA: $tType] : ( ( coinductive_llist @ TA ) > ( coinductive_llist @ TA ) ) ).
thf(p_decl,type,
p: ( coinductive_llist @ a ) > $o ).
thf(la_decl,type,
la: coinductive_llist @ a ).
thf(229,axiom,
! [TA: $tType] :
( ( lList2281150353e_lrev @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_lrev__LNil) ).
thf(1094,plain,
! [TA: $tType] :
( ( lList2281150353e_lrev @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1095,plain,
! [TA: $tType] :
( ( lList2281150353e_lrev @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(cnf,[status(esa)],[1094]) ).
thf(1096,plain,
! [TA: $tType] :
( ( lList2281150353e_lrev @ TA @ ( coinductive_LNil @ TA ) )
= ( coinductive_LNil @ TA ) ),
inference(lifteq,[status(thm)],[1095]) ).
thf(230,axiom,
p @ ( coinductive_LNil @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_init) ).
thf(1097,plain,
p @ ( coinductive_LNil @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(1,conjecture,
p @ ( lList2281150353e_lrev @ a @ la ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( p @ ( lList2281150353e_lrev @ a @ la ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(234,plain,
~ ( p @ ( lList2281150353e_lrev @ a @ la ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1125,plain,
( ~ $true
| ( ( p @ ( lList2281150353e_lrev @ a @ la ) )
!= ( p @ ( coinductive_LNil @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[1097,234]) ).
thf(1126,plain,
( ( p @ ( lList2281150353e_lrev @ a @ la ) )
!= ( p @ ( coinductive_LNil @ a ) ) ),
inference(simp,[status(thm)],[1125]) ).
thf(1129,plain,
( ( lList2281150353e_lrev @ a @ la )
!= ( coinductive_LNil @ a ) ),
inference(simp,[status(thm)],[1126]) ).
thf(233,axiom,
( la
= ( coinductive_LNil @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_LNil__fin_Ohyps) ).
thf(1103,plain,
( la
= ( coinductive_LNil @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1104,plain,
( la
= ( coinductive_LNil @ a ) ),
inference(lifteq,[status(thm)],[1103]) ).
thf(1137,plain,
( ( lList2281150353e_lrev @ a @ ( coinductive_LNil @ a ) )
!= ( coinductive_LNil @ a ) ),
inference(rewrite,[status(thm)],[1129,1104]) ).
thf(1385,plain,
( ( ( coinductive_LNil @ a )
!= ( coinductive_LNil @ a ) )
| ( ( lList2281150353e_lrev @ a @ ( coinductive_LNil @ a ) )
!= ( lList2281150353e_lrev @ a @ ( coinductive_LNil @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[1096,1137]) ).
thf(1386,plain,
( ( lList2281150353e_lrev @ a @ ( coinductive_LNil @ a ) )
!= ( lList2281150353e_lrev @ a @ ( coinductive_LNil @ a ) ) ),
inference(simp,[status(thm)],[1385]) ).
thf(1387,plain,
$false,
inference(pattern_uni,[status(thm)],[1386:[]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : DAT178^1 : TPTP v9.3.1. Released v7.0.0.
% 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
% 0.06/0.12 % Computer : n012.cluster.edu
% 0.06/0.12 % Model : x86_64 x86_64
% 0.06/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.12 % Memory : 8046.5625MB
% 0.06/0.12 % OS : Linux 6.8.0-71-generic
% 0.06/0.12 % CPULimit : 300
% 0.06/0.12 % WCLimit : 300
% 0.06/0.12 % DateTime : Tue Sep 29 18:05:48 UTC 2026
% 0.06/0.12 % CPUTime :
% 0.06/0.12 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
% 0.40/0.41 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.62 % [INFO] Parsing done (209ms).
% 1.23/0.63 % [INFO] Running in sequential loop mode.
% 1.76/0.82 % [INFO] eprover registered as external prover.
% 1.76/0.82 % [INFO] Scanning for conjecture ...
% 1.99/0.90 % [INFO] Found a conjecture (or negated_conjecture) and 272 axioms. Running axiom selection ...
% 1.99/0.98 % [INFO] Axiom selection finished. Selected 231 axioms (removed 41 axioms).
% 2.68/1.14 % [INFO] Problem is higher-order (TPTP THF).
% 2.68/1.16 % [INFO] Type checking passed.
% 2.68/1.16 % [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 ...
% 17.65/5.09 % [INFO] Killing All external provers ...
% 17.65/5.10 % Time passed: 4900ms (effective reasoning time: 4466ms)
% 17.65/5.10 % 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)>
% 17.65/5.10 % Axioms used in derivation (3): fact_3_lrev__LNil, fact_0_init, fact_1_LNil__fin_Ohyps
% 17.65/5.10 % No. of inferences in proof: 19
% 17.65/5.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4900 ms resp. 4466 ms w/o parsing
% 17.65/5.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.65/5.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------