%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWC028-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 08:51:52 AM UTC 2026
% Result : Unsatisfiable 117.85s 44.43s
% Output : Refutation 117.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 68 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 158 ( 74 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 279 ( 82 ~; 74 |; 0 &; 123 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(ssList_decl,type,
ssList: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(nil_decl,type,
nil: $i ).
thf(neq_decl,type,
neq: $i > $i > $o ).
thf(rearsegP_decl,type,
rearsegP: $i > $i > $o ).
thf(11,negated_conjecture,
( ( nil @ ( sk3 @ neq ) )
| ( nil = sk4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
thf(211,plain,
( ( nil @ ( sk3 @ neq ) )
| ( nil = sk4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(216,plain,
( ( nil @ ( sk3 @ neq ) )
| ( nil = sk4 ) ),
inference(cnf,[status(esa)],[211]) ).
thf(217,plain,
( ( nil @ ( sk3 @ neq ) )
| ( nil = sk4 ) ),
inference(lifteq,[status(thm)],[216]) ).
thf(5,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
thf(200,plain,
sk2 = sk4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(227,plain,
sk4 = sk2,
inference(lifteq,[status(thm)],[200]) ).
thf(6,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
thf(204,plain,
sk1 = sk3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(222,plain,
sk3 = sk1,
inference(lifteq,[status(thm)],[204]) ).
thf(698,plain,
( ( nil @ ( sk1 @ neq ) )
| ( nil = sk2 ) ),
inference(rewrite,[status(thm)],[217,227,222]) ).
thf(72,axiom,
nil @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
thf(342,plain,
nil @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
thf(299,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(300,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[299]) ).
thf(301,plain,
! [B: $i,A: $i] :
( ~ ( A @ ssList )
| ~ ( B @ ssList )
| ~ ( B @ ( A @ neq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[300]) ).
thf(302,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[301]) ).
thf(11282,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ $true
| ~ ( A @ ( A @ neq ) ) ),
inference(paramod_ordered,[status(thm)],[342,302]) ).
thf(11283,plain,
! [A: $i] :
( ( ( nil @ ssList )
!= ( A @ ssList ) )
| ~ ( A @ ( A @ neq ) ) ),
inference(simp,[status(thm)],[11282]) ).
thf(11284,plain,
~ ( nil @ ( nil @ neq ) ),
inference(pattern_uni,[status(thm)],[11283:[bind(A,$thf( nil ))]]) ).
thf(11353,plain,
( ( ( nil @ ( nil @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ~ $true
| ( nil = sk2 ) ),
inference(paramod_ordered,[status(thm)],[698,11284]) ).
thf(11354,plain,
( ( ( nil @ ( nil @ neq ) )
!= ( nil @ ( sk1 @ neq ) ) )
| ( nil = sk2 ) ),
inference(simp,[status(thm)],[11353]) ).
thf(11430,plain,
( ( nil != nil )
| ( nil != sk1 )
| ( nil = sk2 ) ),
inference(simp,[status(thm)],[11354]) ).
thf(11436,plain,
( ( nil != sk1 )
| ( nil = sk2 ) ),
inference(simp,[status(thm)],[11430]) ).
thf(14,negated_conjecture,
( ( sk3 @ ( sk4 @ rearsegP ) )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
thf(202,plain,
( ( sk3 @ ( sk4 @ rearsegP ) )
| ( nil = sk3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(214,plain,
( ( sk3 @ ( sk4 @ rearsegP ) )
| ( nil = sk3 ) ),
inference(cnf,[status(esa)],[202]) ).
thf(215,plain,
( ( sk3 @ ( sk4 @ rearsegP ) )
| ( nil = sk3 ) ),
inference(lifteq,[status(thm)],[214]) ).
thf(652,plain,
( ( sk1 @ ( sk2 @ rearsegP ) )
| ( nil = sk1 ) ),
inference(rewrite,[status(thm)],[215,227,222]) ).
thf(2,negated_conjecture,
sk2 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
thf(207,plain,
sk2 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(74,axiom,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause58) ).
thf(346,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(347,plain,
! [A: $i] :
( ( nil @ ( A @ rearsegP ) )
| ~ ( A @ ssList ) ),
inference(cnf,[status(esa)],[346]) ).
thf(25236,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,347]) ).
thf(25237,plain,
! [A: $i] :
( ( ( sk2 @ ssList )
!= ( A @ ssList ) )
| ( nil @ ( A @ rearsegP ) ) ),
inference(simp,[status(thm)],[25236]) ).
thf(25238,plain,
nil @ ( sk2 @ rearsegP ),
inference(pattern_uni,[status(thm)],[25237:[bind(A,$thf( sk2 ))]]) ).
thf(25483,plain,
( ( nil != nil )
| ( sk1 @ ( sk2 @ rearsegP ) )
| ( sk1 @ ( sk2 @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[652,25238]) ).
thf(25484,plain,
( ( nil != nil )
| ( sk1 @ ( sk2 @ rearsegP ) ) ),
inference(simp,[status(thm)],[25483]) ).
thf(25485,plain,
sk1 @ ( sk2 @ rearsegP ),
inference(pattern_uni,[status(thm)],[25484:[]]) ).
thf(81,axiom,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause82) ).
thf(363,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(364,plain,
! [A: $i] :
( ( nil = A )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(cnf,[status(esa)],[363]) ).
thf(365,plain,
! [A: $i] :
( ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) )
| ( nil = A ) ),
inference(lifteq,[status(thm)],[364]) ).
thf(10,negated_conjecture,
( ( nil != sk2 )
| ( nil != sk1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
thf(201,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(220,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(cnf,[status(esa)],[201]) ).
thf(221,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(lifteq,[status(thm)],[220]) ).
thf(30440,plain,
! [A: $i] :
( ( nil != nil )
| ( nil != sk2 )
| ( A != sk1 )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(paramod_ordered,[status(thm)],[365,221]) ).
thf(30441,plain,
! [A: $i] :
( ( nil != sk2 )
| ( A != sk1 )
| ~ ( A @ ssList )
| ~ ( A @ ( nil @ rearsegP ) ) ),
inference(pattern_uni,[status(thm)],[30440:[]]) ).
thf(31800,plain,
( ( nil != sk2 )
| ~ ( sk1 @ ssList )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[30441]) ).
thf(1,negated_conjecture,
sk1 @ ssList,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
thf(203,plain,
sk1 @ ssList,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(36677,plain,
( ( nil != sk2 )
| ~ $true
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(rewrite,[status(thm)],[31800,203]) ).
thf(36678,plain,
( ( nil != sk2 )
| ~ ( sk1 @ ( nil @ rearsegP ) ) ),
inference(simp,[status(thm)],[36677]) ).
thf(36812,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( sk1 @ ( sk2 @ rearsegP ) ) )
| ( nil != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25485,36678]) ).
thf(36813,plain,
( ( ( sk1 @ ( nil @ rearsegP ) )
!= ( sk1 @ ( sk2 @ rearsegP ) ) )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[36812]) ).
thf(36828,plain,
( ( sk1 != sk1 )
| ( nil != sk2 )
| ( nil != sk2 ) ),
inference(simp,[status(thm)],[36813]) ).
thf(36866,plain,
nil != sk2,
inference(simp,[status(thm)],[36828]) ).
thf(36877,plain,
nil != sk1,
inference(simplifyReflect,[status(thm)],[11436,36866]) ).
thf(7,negated_conjecture,
( ( nil = sk1 )
| ( nil = sk2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
thf(209,plain,
( ( nil = sk1 )
| ( nil = sk2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(225,plain,
( ( nil = sk1 )
| ( nil = sk2 ) ),
inference(cnf,[status(esa)],[209]) ).
thf(226,plain,
( ( nil = sk1 )
| ( nil = sk2 ) ),
inference(lifteq,[status(thm)],[225]) ).
thf(36878,plain,
nil = sk1,
inference(simplifyReflect,[status(thm)],[226,36866]) ).
thf(37024,plain,
sk1 != sk1,
inference(rewrite,[status(thm)],[36877,36878]) ).
thf(37025,plain,
$false,
inference(simp,[status(thm)],[37024]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC028-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.18/5.45 % Computer : n007.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Sat Sep 26 12:03:31 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.32/6.24 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.45/6.62 % [INFO] Parsing done (379ms).
% 2.45/6.64 % [INFO] Running in sequential loop mode.
% 3.76/7.25 % [INFO] eprover registered as external prover.
% 3.76/7.26 % [INFO] Scanning for conjecture ...
% 4.16/7.48 % [INFO] Found a conjecture (or negated_conjecture) and 185 axioms. Running axiom selection ...
% 4.56/7.68 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 5.41/7.91 % [INFO] Problem is propositional (TPTP CNF).
% 5.41/7.94 % [INFO] Type checking passed.
% 5.41/7.95 % [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 ...
% 117.85/44.43 % [INFO] Killing All external provers ...
% 117.85/44.43 % Time passed: 38765ms (effective reasoning time: 37774ms)
% 117.85/44.43 % Axioms used in derivation (4): clause8, clause115, clause58, clause82
% 117.85/44.43 % No. of inferences in proof: 68
% 117.85/44.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 38765 ms resp. 37774 ms w/o parsing
% 117.85/44.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 117.85/44.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------