%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN549+1 : TPTP v9.3.1. Released v2.2.0.
% 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 : 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 09:17:49 AM UTC 2026
% Result : Theorem 15.19s 4.54s
% Output : Refutation 15.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 0 equ; 0 cnn)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 117 ( 2 ~; 8 |; 22 &; 76 @)
% ( 2 <=>; 7 =>; 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 : 5 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 11 !; 19 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(reachable_decl,type,
reachable: $i > $i > $o ).
thf(initial_world_decl,type,
initial_world: $i ).
thf(p_decl,type,
p: $i > $o ).
thf(q_decl,type,
q: $i > $o ).
thf(1,conjecture,
? [A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ( ? [C: $i] :
( ( ? [D: $i] :
( ( D @ q )
& ( D @ ( C @ reachable ) ) )
| ( C @ p ) )
& ( C @ ( B @ reachable ) ) )
<=> ( ? [C: $i] :
( ( C @ q )
& ( C @ ( B @ reachable ) ) )
| ? [C: $i] :
( ( C @ p )
& ( C @ ( B @ reachable ) ) ) ) ) )
& ( A @ ( initial_world @ reachable ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ( ? [C: $i] :
( ( ? [D: $i] :
( ( D @ q )
& ( D @ ( C @ reachable ) ) )
| ( C @ p ) )
& ( C @ ( B @ reachable ) ) )
<=> ( ? [C: $i] :
( ( C @ q )
& ( C @ ( B @ reachable ) ) )
| ? [C: $i] :
( ( C @ p )
& ( C @ ( B @ reachable ) ) ) ) ) )
& ( A @ ( initial_world @ reachable ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ? [A: $i] :
( ! [B: $i] :
( ( B @ ( A @ reachable ) )
=> ( ( ( ? [C: $i] :
( ( C @ q )
& ( C @ ( B @ reachable ) ) )
| ? [C: $i] :
( ( C @ p )
& ( C @ ( B @ reachable ) ) ) )
=> ? [C: $i] :
( ( ? [D: $i] :
( ( D @ q )
& ( D @ ( C @ reachable ) ) )
| ( C @ p ) )
& ( C @ ( B @ reachable ) ) ) )
& ( ? [C: $i] :
( ( ? [D: $i] :
( ( D @ q )
& ( D @ ( C @ reachable ) ) )
| ( C @ p ) )
& ( C @ ( B @ reachable ) ) )
=> ( ? [C: $i] :
( ( C @ q )
& ( C @ ( B @ reachable ) ) )
| ? [C: $i] :
( ( C @ p )
& ( C @ ( B @ reachable ) ) ) ) ) ) )
& ( A @ ( initial_world @ reachable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] : ( A @ ( A @ reachable ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_reachable) ).
thf(22,plain,
! [A: $i] : ( A @ ( A @ reachable ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ reachable ) )
& ( B @ ( A @ reachable ) ) )
=> ( C @ ( A @ reachable ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_reachable) ).
thf(24,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ reachable ) )
& ( B @ ( A @ reachable ) ) )
=> ( C @ ( A @ reachable ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2328,plain,
$false,
inference(e,[status(thm)],[5,22,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN549+1 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.12/0.37 % Computer : n007.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 18:10:54 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 0.86/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.15 % [INFO] Parsing done (178ms).
% 1.24/1.17 % [INFO] Running in sequential loop mode.
% 1.79/1.57 % [INFO] eprover registered as external prover.
% 1.79/1.58 % [INFO] Scanning for conjecture ...
% 1.98/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.15/1.71 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.15/1.72 % [INFO] Problem is first-order (TPTP FOF).
% 2.15/1.73 % [INFO] Type checking passed.
% 2.15/1.73 % [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 ...
% 15.19/4.54 % External prover 'e' found a proof!
% 15.19/4.54 % [INFO] Killing All external provers ...
% 15.19/4.54 % Time passed: 4016ms (effective reasoning time: 3364ms)
% 15.19/4.54 % 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)>
% 15.19/4.54 % Axioms used in derivation (2): reflexivity_of_reachable, transitivity_of_reachable
% 15.19/4.54 % No. of inferences in proof: 8
% 15.19/4.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4016 ms resp. 3364 ms w/o parsing
% 15.19/4.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.19/4.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------