%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL098-1 : TPTP v9.3.1. Released v2.7.0.
% 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 : 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 06:56:28 AM UTC 2026
% Result : Unsatisfiable 3.30s 3.02s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 236 ( 24 ~; 22 |; 0 &; 190 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 34 ( 0 ^; 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_decl,type,
member: $i > $i > $o ).
thf(pair_decl,type,
pair: $i > $i > $i ).
thf(x_decl,type,
x: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(r_decl,type,
r: $i ).
thf(trancl_decl,type,
trancl: $i > $i ).
thf(z_decl,type,
z: $i ).
thf(sk1_decl,type,
sk1: $i > $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(y_decl,type,
y: $i ).
thf(trans_decl,type,
trans: $i > $o ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( r @ ( A @ ( z @ pair ) @ member ) )
| ~ ( r @ trancl @ ( A @ ( sk3 @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2c2) ).
thf(13,plain,
! [A: $i] :
( ~ ( r @ ( A @ ( z @ pair ) @ member ) )
| ~ ( r @ trancl @ ( A @ ( sk3 @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( r @ ( C @ ( B @ ( A @ sk1 ) ) @ ( C @ pair ) @ member ) )
| ~ ( r @ ( C @ ( A @ pair ) @ member ) )
| ~ ( r @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h2) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( r @ ( C @ ( B @ ( A @ sk1 ) ) @ ( C @ pair ) @ member ) )
| ~ ( r @ ( C @ ( A @ pair ) @ member ) )
| ~ ( r @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
r @ trancl @ ( y @ ( x @ pair ) @ member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h3) ).
thf(27,plain,
r @ trancl @ ( y @ ( x @ pair ) @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,negated_conjecture,
r @ ( sk3 @ ( x @ pair ) @ member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2c1) ).
thf(12,plain,
r @ ( sk3 @ ( x @ pair ) @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [A: $i] : ( A @ trancl @ trans ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_trancl) ).
thf(23,plain,
! [A: $i] : ( A @ trancl @ trans ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i] :
( ( r @ trancl @ ( A @ sk2 @ ( A @ pair ) @ member ) )
| ~ ( r @ ( A @ ( x @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h5) ).
thf(19,plain,
! [A: $i] :
( ( r @ trancl @ ( A @ sk2 @ ( A @ pair ) @ member ) )
| ~ ( r @ ( A @ ( x @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( r @ ( C @ ( B @ ( A @ sk1 ) ) @ ( B @ pair ) @ member ) )
| ~ ( r @ ( C @ ( A @ pair ) @ member ) )
| ~ ( r @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h1) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( r @ ( C @ ( B @ ( A @ sk1 ) ) @ ( B @ pair ) @ member ) )
| ~ ( r @ ( C @ ( A @ pair ) @ member ) )
| ~ ( r @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
r @ ( z @ ( y @ pair ) @ member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h4) ).
thf(24,plain,
r @ ( z @ ( y @ pair ) @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ pair ) @ member ) )
| ~ ( A @ ( D @ ( C @ pair ) @ member ) )
| ~ ( A @ ( C @ ( B @ pair ) @ member ) )
| ~ ( A @ trans ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transD) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ pair ) @ member ) )
| ~ ( A @ ( D @ ( C @ pair ) @ member ) )
| ~ ( A @ ( C @ ( B @ pair ) @ member ) )
| ~ ( A @ trans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ trancl @ ( B @ ( A @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r_into_trancl) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ trancl @ ( B @ ( A @ pair ) @ member ) )
| ~ ( C @ ( B @ ( A @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: $i] :
( ( r @ ( A @ sk2 @ ( y @ pair ) @ member ) )
| ~ ( r @ ( A @ ( x @ pair ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h6) ).
thf(21,plain,
! [A: $i] :
( ( r @ ( A @ sk2 @ ( y @ pair ) @ member ) )
| ~ ( r @ ( A @ ( x @ pair ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(30,plain,
$false,
inference(e,[status(thm)],[13,17,27,12,23,19,15,24,25,28,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL098-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.08 % 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
% 0.10/0.41 % Computer : n007.cluster.edu
% 0.10/0.41 % Model : x86_64 x86_64
% 0.10/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.41 % Memory : 8046.5625MB
% 0.10/0.41 % OS : Linux 6.8.0-71-generic
% 0.10/0.41 % CPULimit : 300
% 0.10/0.41 % WCLimit : 300
% 0.10/0.41 % DateTime : Sat Sep 26 23:12:09 UTC 2026
% 0.10/0.41 % CPUTime :
% 0.10/0.41 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
% 0.92/1.19 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.44 % [INFO] Parsing done (243ms).
% 1.25/1.46 % [INFO] Running in sequential loop mode.
% 1.89/1.97 % [INFO] eprover registered as external prover.
% 1.89/1.99 % [INFO] Scanning for conjecture ...
% 2.12/2.14 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 2.26/2.24 % [INFO] Axiom selection finished. Selected 9 axioms (removed 6 axioms).
% 2.26/2.27 % [INFO] Problem is propositional (TPTP CNF).
% 2.26/2.27 % [INFO] Type checking passed.
% 2.26/2.28 % [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 ...
% 3.30/3.02 % External prover 'e' found a proof!
% 3.30/3.02 % [INFO] Killing All external provers ...
% 3.30/3.02 % Time passed: 2447ms (effective reasoning time: 1549ms)
% 3.30/3.02 % Axioms used in derivation (9): diamond_strip_lemmaD_2h4, r_into_trancl, trans_trancl, diamond_strip_lemmaD_2h1, diamond_strip_lemmaD_2h5, diamond_strip_lemmaD_2h2, diamond_strip_lemmaD_2h3, diamond_strip_lemmaD_2h6, transD
% 3.30/3.02 % No. of inferences in proof: 23
% 3.30/3.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2447 ms resp. 1549 ms w/o parsing
% 3.67/3.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.67/3.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------