%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : LCL581^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n028.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 : Mon Sep 7 11:34:21 AM UTC 2026
% Result : CounterSatisfiable 0.18s 0.47s
% Output : Saturation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL581^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n028.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 : Fri Sep 4 16:22:28 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.40 ---- Original DTF file ---
% 0.14/0.40 thf(spec,logic,$$dhol).
% 0.14/0.40 %------------------------------------------------------------------------------
% 0.14/0.40 % File : LCL581^1 : TPTP v9.3.1. Released v3.6.0.
% 0.14/0.40 % Domain : Logical Calculi
% 0.14/0.40 % Problem : Popkorn problem 2
% 0.14/0.40 % Version : [BP09] axioms.
% 0.14/0.40 % English :
% 0.14/0.40
% 0.14/0.40 % Refs : [Pop95] Popkorn (1995), First Steps in Modal Logic
% 0.14/0.40 % : [BP09] Benzmueller & Paulson (2009), Exploring Properties of
% 0.14/0.40 % Source : [BP09]
% 0.14/0.40 % Names : K-b [BP09]
% 0.14/0.40
% 0.14/0.40 % Status : Theorem
% 0.14/0.40 % Rating : 0.08 v9.3.0, 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0, 0.33 v3.7.0
% 0.14/0.40 % Syntax : Number of formulae : 38 ( 15 unt; 22 typ; 15 def)
% 0.14/0.40 % Number of atoms : 45 ( 15 equ; 0 cnn)
% 0.14/0.40 % Maximal formula atoms : 8 ( 2 avg)
% 0.14/0.40 % Number of connectives : 42 ( 3 ~; 1 |; 2 &; 35 @)
% 0.14/0.40 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.14/0.40 % Maximal formula depth : 6 ( 1 avg)
% 0.14/0.40 % Number of types : 3 ( 1 usr)
% 0.14/0.40 % Number of type conns : 82 ( 82 >; 0 *; 0 +; 0 <<)
% 0.14/0.40 % Number of symbols : 24 ( 21 usr; 3 con; 0-3 aty)
% 0.14/0.40 % Number of variables : 36 ( 28 ^; 4 !; 4 ?; 36 :)
% 0.14/0.40 % SPC : TH0_THM_EQU_NAR_NDT
% 0.14/0.40
% 0.14/0.40 % Comments :
% 0.14/0.40 %------------------------------------------------------------------------------
% 0.14/0.40 %----Include simple maths definitions and axioms
% 0.14/0.40 include('Axioms/LCL008^0.ax').
% 0.14/0.40 %------------------------------------------------------------------------------
% 0.14/0.40 %----Signature
% 0.14/0.40 thf(a,type,
% 0.14/0.40 a: $i > $o ).
% 0.14/0.40
% 0.14/0.40 thf(r,type,
% 0.14/0.40 r: $i > $i > $o ).
% 0.14/0.40
% 0.14/0.40 %----Conjecture
% 0.14/0.40 thf(thm,conjecture,
% 0.14/0.40 mvalid @ ( mimpl @ ( mbox @ r @ a ) @ ( mbox @ r @ a ) ) ).
% 0.14/0.40
% 0.14/0.40 %------------------------------------------------------------------------------
% 0.14/0.40 ------------------------
% 0.14/0.40 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found.
% 0.14/0.40 ---- Embedded in THF ---
% 0.14/0.41 ------------------------
% 0.14/0.43 ---- Cleaned THF ---
% 0.14/0.43 ------------------------
% 0.18/0.47 % (989005)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_988989 for (3000ds/183Mi)
% 0.18/0.47 % (989006)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_988989 for (3000ds/4Mi)
% 0.18/0.47 % (989007)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_988989 for (3000ds/27Mi)
% 0.18/0.47 % (989006)First to succeed.
% 0.18/0.47 % (989007)Refutation not found, incomplete strategy
% 0.18/0.47 % (989007)------------------------------
% 0.18/0.47 % (989007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.18/0.47 % (989007)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 % (989007)Memory used [KB]: 5373
% 0.18/0.47 % (989007)Time elapsed: 0.002 s
% 0.18/0.47 % (989007)------------------------------
% 0.18/0.47 % (989007)------------------------------
% 0.18/0.47 % (989009)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_988989 for (3000ds/2Mi)
% 0.18/0.47 % (989005)Also succeeded, but the first one will report.
% 0.18/0.47 % (989009)Refutation not found, incomplete strategy
% 0.18/0.47 % (989009)------------------------------
% 0.18/0.47 % (989009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.18/0.47 % (989009)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 % (989009)Memory used [KB]: 5373
% 0.18/0.47 % (989009)Time elapsed: 0.002 s
% 0.18/0.47 % (989009)------------------------------
% 0.18/0.47 % (989009)------------------------------
% 0.18/0.47 % (989008)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_988989 for (3000ds/2Mi)
% 0.18/0.47 % (989008)Also succeeded, but the first one will report.
% 0.18/0.47 % SZS status Satisfiable for DTF2THF_988989
% 0.18/0.47 % (989006)# SZS output start Saturation.
% 0.18/0.47 % (989006)# SZS output end Saturation.
% 0.18/0.47 % (989006)------------------------------
% 0.18/0.47 % (989006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.18/0.47 % (989006)Termination reason: Satisfiable
% 0.18/0.47
% 0.18/0.47 % (989006)Memory used [KB]: 5373
% 0.18/0.47 % (989006)Time elapsed: 0.003 s
% 0.18/0.47 % (989006)------------------------------
% 0.18/0.47 % (989006)------------------------------
% 0.18/0.47 % (989004)Success in time 0.018 s
%------------------------------------------------------------------------------