%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : LCL588^1 : 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 : n011.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 11:34:22 AM UTC 2026
% Result : CounterSatisfiable 0.02s 0.45s
% Output : Saturation 0.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL588^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.02/0.36 % Computer : n011.cluster.edu
% 0.02/0.36 % Model : x86_64 x86_64
% 0.02/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.36 % Memory : 8046.5625MB
% 0.02/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Fri Sep 4 13:56:43 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.02/0.39 ---- Original DTF file ---
% 0.02/0.39 thf(spec,logic,$$dhol).
% 0.02/0.39 %------------------------------------------------------------------------------
% 0.02/0.39 % File : LCL588^1 : TPTP v9.3.1. Released v3.6.0.
% 0.02/0.39 % Domain : Logical Calculi
% 0.02/0.39 % Problem : Popkorn problem 9
% 0.02/0.39 % Version : [BP09] axioms.
% 0.02/0.39 % English :
% 0.02/0.39
% 0.02/0.39 % Refs : [Pop95] Popkorn (1995), First Steps in Modal Logic
% 0.02/0.39 % : [BP09] Benzmueller & Paulson (2009), Exploring Properties of
% 0.02/0.39 % Source : [BP09]
% 0.02/0.39 % Names : K-i [BP09]
% 0.02/0.39
% 0.02/0.39 % Status : Theorem
% 0.02/0.39 % Rating : 0.17 v9.3.0, 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 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
% 0.02/0.39 % Syntax : Number of formulae : 39 ( 15 unt; 23 typ; 15 def)
% 0.02/0.39 % Number of atoms : 51 ( 15 equ; 0 cnn)
% 0.02/0.39 % Maximal formula atoms : 14 ( 3 avg)
% 0.02/0.39 % Number of connectives : 48 ( 3 ~; 1 |; 2 &; 41 @)
% 0.02/0.39 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.02/0.39 % Maximal formula depth : 8 ( 1 avg)
% 0.02/0.39 % Number of types : 3 ( 1 usr)
% 0.02/0.39 % Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% 0.02/0.39 % Number of symbols : 25 ( 22 usr; 3 con; 0-3 aty)
% 0.02/0.39 % Number of variables : 36 ( 28 ^; 4 !; 4 ?; 36 :)
% 0.02/0.39 % SPC : TH0_THM_EQU_NAR_NDT
% 0.02/0.39
% 0.02/0.39 % Comments :
% 0.02/0.39 %------------------------------------------------------------------------------
% 0.02/0.39 %----Include simple maths definitions and axioms
% 0.02/0.39 include('Axioms/LCL008^0.ax').
% 0.02/0.39 %------------------------------------------------------------------------------
% 0.02/0.39 %----Signature
% 0.02/0.39 thf(a,type,
% 0.02/0.39 a: $i > $o ).
% 0.02/0.39
% 0.02/0.39 thf(b,type,
% 0.02/0.39 b: $i > $o ).
% 0.02/0.39
% 0.02/0.39 thf(r,type,
% 0.02/0.39 r: $i > $i > $o ).
% 0.02/0.39
% 0.02/0.39 %----Conjecture
% 0.02/0.39 thf(thm,conjecture,
% 0.02/0.39 mvalid @ ( mimpl @ ( mimpl @ ( mdia @ r @ a ) @ ( mbox @ r @ b ) ) @ ( mbox @ r @ ( mimpl @ a @ b ) ) ) ).
% 0.02/0.39
% 0.02/0.39 %------------------------------------------------------------------------------
% 0.02/0.39 ------------------------
% 0.02/0.39 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found.
% 0.02/0.39 ---- Embedded in THF ---
% 0.02/0.40 ------------------------
% 0.02/0.42 ---- Cleaned THF ---
% 0.02/0.42 ------------------------
% 0.02/0.44 % (3937069)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_3937048 for (3000ds/275Mi)
% 0.02/0.44 % (3937069)Refutation not found, incomplete strategy
% 0.02/0.44 % (3937069)------------------------------
% 0.02/0.44 % (3937069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.02/0.44 % (3937069)Termination reason: Refutation not found, incomplete strategy
% 0.02/0.44
% 0.02/0.44
% 0.02/0.44 % (3937069)Memory used [KB]: 5373
% 0.02/0.44 % (3937069)Time elapsed: 0.002 s
% 0.02/0.44 % (3937069)Instructions burned: 1 (million)
% 0.02/0.44 % (3937069)------------------------------
% 0.02/0.44 % (3937069)------------------------------
% 0.02/0.45 % (3937064)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3937048 for (3000ds/183Mi)
% 0.02/0.45 % (3937067)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3937048 for (3000ds/2Mi)
% 0.02/0.45 % (3937065)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_3937048 for (3000ds/4Mi)
% 0.02/0.45 % (3937068)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_3937048 for (3000ds/2Mi)
% 0.02/0.45 % (3937066)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_3937048 for (3000ds/27Mi)
% 0.02/0.45 % (3937064)First to succeed.
% 0.02/0.45 % (3937067)Also succeeded, but the first one will report.
% 0.02/0.45 % (3937068)Refutation not found, incomplete strategy
% 0.02/0.45 % (3937068)------------------------------
% 0.02/0.45 % (3937068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.02/0.45 % (3937068)Termination reason: Refutation not found, incomplete strategy
% 0.02/0.45
% 0.02/0.45
% 0.02/0.45 % (3937068)Memory used [KB]: 5373
% 0.02/0.45 % (3937068)Time elapsed: 0.003 s
% 0.02/0.45 % (3937068)Instructions burned: 1 (million)
% 0.02/0.45 % (3937068)------------------------------
% 0.02/0.45 % (3937068)------------------------------
% 0.02/0.45 % (3937066)Refutation not found, incomplete strategy
% 0.02/0.45 % (3937066)------------------------------
% 0.02/0.45 % (3937066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.02/0.45 % (3937066)Termination reason: Refutation not found, incomplete strategy
% 0.02/0.45
% 0.02/0.45
% 0.02/0.45 % (3937066)Memory used [KB]: 5373
% 0.02/0.45 % (3937066)Time elapsed: 0.002 s
% 0.02/0.45 % (3937066)Instructions burned: 1 (million)
% 0.02/0.45 % (3937066)------------------------------
% 0.02/0.45 % (3937066)------------------------------
% 0.02/0.45 % SZS status Satisfiable for DTF2THF_3937048
% 0.02/0.45 % (3937064)# SZS output start Saturation.
% 0.02/0.45 % (3937064)# SZS output end Saturation.
% 0.02/0.45 % (3937064)------------------------------
% 0.02/0.45 % (3937064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.02/0.45 % (3937064)Termination reason: Satisfiable
% 0.02/0.45
% 0.02/0.45 % (3937064)Memory used [KB]: 5373
% 0.02/0.45 % (3937064)Time elapsed: 0.002 s
% 0.02/0.45 % (3937064)Instructions burned: 1 (million)
% 0.02/0.45 % (3937064)------------------------------
% 0.02/0.45 % (3937064)------------------------------
% 0.02/0.45 % (3937063)Success in time 0.017 s
%------------------------------------------------------------------------------