%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW409-1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n009.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 09:10:07 AM UTC 2026
% Result : Unsatisfiable 4.53s 2.14s
% Output : Refutation 4.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 17
% Syntax : Number of formulae : 35 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 24 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 326 ( 28 ~; 20 |; 0 &; 278 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 76 ( 0 ^; 76 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(heap_decl,type,
heap: $i > $o ).
thf(sep_decl,type,
sep: $i > $i > $i ).
thf(lseg_decl,type,
lseg: $i > $i > $i ).
thf(x2_decl,type,
x2: $i ).
thf(nil_decl,type,
nil: $i ).
thf(emp_decl,type,
emp: $i ).
thf(x1_decl,type,
x1: $i ).
thf(x3_decl,type,
x3: $i ).
thf(next_decl,type,
next: $i > $i > $i ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ lseg ) @ sep ) @ ( C @ ( A @ lseg ) @ sep ) @ heap )
| ( C = D )
| ~ ( E @ ( D @ ( C @ lseg ) @ sep ) @ ( C @ ( B @ lseg ) @ sep ) @ ( B @ ( A @ lseg ) @ sep ) @ heap ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_5) ).
thf(25,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ lseg ) @ sep ) @ ( C @ ( A @ lseg ) @ sep ) @ heap )
| ( C = D )
| ~ ( E @ ( D @ ( C @ lseg ) @ sep ) @ ( C @ ( B @ lseg ) @ sep ) @ ( B @ ( A @ lseg ) @ sep ) @ heap ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
nil != x1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_1) ).
thf(52,plain,
nil != x1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,axiom,
x2 != x3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_4) ).
thf(41,plain,
x2 != x3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ next ) @ sep ) @ ( C @ ( A @ lseg ) @ sep ) @ heap )
| ~ ( E @ ( D @ ( C @ next ) @ sep ) @ ( C @ ( B @ lseg ) @ sep ) @ ( B @ ( A @ lseg ) @ sep ) @ heap ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_4) ).
thf(34,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ next ) @ sep ) @ ( C @ ( A @ lseg ) @ sep ) @ heap )
| ~ ( E @ ( D @ ( C @ next ) @ sep ) @ ( C @ ( B @ lseg ) @ sep ) @ ( B @ ( A @ lseg ) @ sep ) @ heap ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ lseg ) @ sep ) @ heap )
| ( A = B )
| ~ ( D @ ( C @ ( B @ lseg ) @ sep ) @ ( B @ ( A @ next ) @ sep ) @ heap ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_2) ).
thf(44,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ lseg ) @ sep ) @ heap )
| ( A = B )
| ~ ( D @ ( C @ ( B @ lseg ) @ sep ) @ ( B @ ( A @ next ) @ sep ) @ heap ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
~ ( emp @ ( nil @ ( x2 @ lseg ) @ sep ) @ heap ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_1) ).
thf(18,plain,
~ ( emp @ ( nil @ ( x2 @ lseg ) @ sep ) @ heap ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( nil @ ( A @ lseg ) @ sep ) @ heap )
| ~ ( C @ ( nil @ ( B @ lseg ) @ sep ) @ ( B @ ( A @ lseg ) @ sep ) @ heap ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unfolding_3) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( nil @ ( A @ lseg ) @ sep ) @ heap )
| ~ ( C @ ( nil @ ( B @ lseg ) @ sep ) @ ( B @ ( A @ lseg ) @ sep ) @ heap ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( D @ ( C @ ( A @ next ) @ sep ) @ ( B @ ( A @ next ) @ sep ) @ heap ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_3) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( D @ ( C @ ( A @ next ) @ sep ) @ ( B @ ( A @ next ) @ sep ) @ heap ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( A = B )
| ~ ( D @ ( C @ ( A @ lseg ) @ sep ) @ ( B @ ( A @ lseg ) @ sep ) @ heap ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_5) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( A = B )
| ~ ( D @ ( C @ ( A @ lseg ) @ sep ) @ ( B @ ( A @ lseg ) @ sep ) @ heap ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(2,axiom,
x1 != x3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_3) ).
thf(20,plain,
x1 != x3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( nil @ next ) @ sep ) @ heap ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_1) ).
thf(29,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( nil @ next ) @ sep ) @ heap ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
emp @ ( x3 @ ( x1 @ next ) @ sep ) @ ( nil @ ( x3 @ lseg ) @ sep ) @ ( x1 @ ( x2 @ lseg ) @ sep ) @ heap,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_5) ).
thf(28,plain,
emp @ ( x3 @ ( x1 @ next ) @ sep ) @ ( nil @ ( x3 @ lseg ) @ sep ) @ ( x1 @ ( x2 @ lseg ) @ sep ) @ heap,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
nil != x2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_2) ).
thf(38,plain,
nil != x2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ lseg ) @ sep ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',normalization) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ lseg ) @ sep ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( D @ ( C @ ( A @ lseg ) @ sep ) @ ( B @ ( A @ next ) @ sep ) @ heap ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_4) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( D @ ( C @ ( A @ lseg ) @ sep ) @ ( B @ ( A @ next ) @ sep ) @ heap ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( A = nil )
| ~ ( B @ ( A @ ( nil @ lseg ) @ sep ) @ heap ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellformedness_2) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( A = nil )
| ~ ( B @ ( A @ ( nil @ lseg ) @ sep ) @ heap ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ sep ) @ ( A @ sep ) )
= ( C @ ( A @ sep ) @ ( B @ sep ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_commutative) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ sep ) @ ( A @ sep ) )
= ( C @ ( A @ sep ) @ ( B @ sep ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(135,plain,
$false,
inference(e,[status(thm)],[25,52,41,34,44,18,58,36,47,20,29,28,38,50,31,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW409-1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % 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
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 15:49:59 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 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
% 0.61/0.67 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.77/0.78 % [INFO] Parsing done (101ms).
% 0.77/0.78 % [INFO] Running in sequential loop mode.
% 1.23/0.97 % [INFO] eprover registered as external prover.
% 1.23/0.97 % [INFO] Scanning for conjecture ...
% 1.23/1.02 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 1.55/1.06 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 1.55/1.10 % [INFO] Problem is propositional (TPTP CNF).
% 1.55/1.10 % [INFO] Type checking passed.
% 1.55/1.11 % [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 ...
% 4.53/2.13 % External prover 'e' found a proof!
% 4.53/2.13 % [INFO] Killing All external provers ...
% 4.53/2.13 % Time passed: 1667ms (effective reasoning time: 1348ms)
% 4.53/2.14 % Axioms used in derivation (16): premise_5, premise_2, wellformedness_2, wellformedness_3, wellformedness_4, premise_3, unfolding_2, premise_1, premise_4, wellformedness_1, wellformedness_5, associative_commutative, unfolding_5, normalization, unfolding_3, unfolding_4
% 4.53/2.14 % No. of inferences in proof: 35
% 4.53/2.14 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1667 ms resp. 1348 ms w/o parsing
% 4.53/2.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.53/2.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------