%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : LCL584^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 0.11s 0.45s
% Output : Saturation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL584^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 6 02:10:35 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 ---- Original DTF file ---
% 0.11/0.38 thf(spec,logic,$$dhol).
% 0.11/0.38 %------------------------------------------------------------------------------
% 0.11/0.38 % File : LCL584^1 : TPTP v9.3.1. Released v3.6.0.
% 0.11/0.38 % Domain : Logical Calculi
% 0.11/0.38 % Problem : Popkorn problem 5
% 0.11/0.38 % Version : [BP09] axioms.
% 0.11/0.38 % English :
% 0.11/0.38
% 0.11/0.38 % Refs : [Pop95] Popkorn (1995), First Steps in Modal Logic
% 0.11/0.38 % : [BP09] Benzmueller & Paulson (2009), Exploring Properties of
% 0.11/0.38 % Source : [BP09]
% 0.11/0.38 % Names : K-e [BP09]
% 0.11/0.38
% 0.11/0.38 % Status : Theorem
% 0.11/0.38 % 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
% 0.11/0.38 % Syntax : Number of formulae : 40 ( 15 unt; 24 typ; 15 def)
% 0.11/0.38 % Number of atoms : 51 ( 15 equ; 0 cnn)
% 0.11/0.38 % Maximal formula atoms : 14 ( 3 avg)
% 0.11/0.38 % Number of connectives : 48 ( 3 ~; 1 |; 2 &; 41 @)
% 0.11/0.38 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.11/0.38 % Maximal formula depth : 7 ( 1 avg)
% 0.11/0.38 % Number of types : 3 ( 1 usr)
% 0.11/0.38 % Number of type conns : 85 ( 85 >; 0 *; 0 +; 0 <<)
% 0.11/0.38 % Number of symbols : 26 ( 23 usr; 3 con; 0-3 aty)
% 0.11/0.38 % Number of variables : 36 ( 28 ^; 4 !; 4 ?; 36 :)
% 0.11/0.38 % SPC : TH0_THM_EQU_NAR_NDT
% 0.11/0.38
% 0.11/0.38 % Comments :
% 0.11/0.38 %------------------------------------------------------------------------------
% 0.11/0.38 %----Include simple maths definitions and axioms
% 0.11/0.38 include('Axioms/LCL008^0.ax').
% 0.11/0.38 %------------------------------------------------------------------------------
% 0.11/0.38 %----Signature
% 0.11/0.38 thf(a,type,
% 0.11/0.38 a: $i > $o ).
% 0.11/0.38
% 0.11/0.38 thf(b,type,
% 0.11/0.38 b: $i > $o ).
% 0.11/0.38
% 0.11/0.38 thf(r,type,
% 0.11/0.38 r: $i > $i > $o ).
% 0.11/0.38
% 0.11/0.38 thf(s,type,
% 0.11/0.38 s: $i > $i > $o ).
% 0.11/0.38
% 0.11/0.38 %----Conjecture
% 0.11/0.38 thf(thm,conjecture,
% 0.11/0.38 mvalid @ ( miff @ ( mbox @ r @ ( mand @ a @ b ) ) @ ( mand @ ( mbox @ r @ a ) @ ( mbox @ r @ b ) ) ) ).
% 0.11/0.38
% 0.11/0.38 %------------------------------------------------------------------------------
% 0.11/0.38 ------------------------
% 0.11/0.38 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found.
% 0.11/0.39 ---- Embedded in THF ---
% 0.11/0.39 ------------------------
% 0.11/0.41 ---- Cleaned THF ---
% 0.11/0.41 ------------------------
% 0.11/0.44 % (1703280)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_1703259 for (3000ds/275Mi)
% 0.11/0.44 % (1703280)Refutation not found, incomplete strategy
% 0.11/0.44 % (1703280)------------------------------
% 0.11/0.44 % (1703280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.11/0.44 % (1703280)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.44
% 0.11/0.44
% 0.11/0.44 % (1703280)Memory used [KB]: 5373
% 0.11/0.44 % (1703280)Time elapsed: 0.001 s
% 0.11/0.44 % (1703280)------------------------------
% 0.11/0.44 % (1703280)------------------------------
% 0.11/0.44 % (1703275)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1703259 for (3000ds/183Mi)
% 0.11/0.44 % (1703277)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_1703259 for (3000ds/27Mi)
% 0.11/0.44 % (1703276)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_1703259 for (3000ds/4Mi)
% 0.11/0.44 % (1703278)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1703259 for (3000ds/2Mi)
% 0.11/0.44 % (1703275)First to succeed.
% 0.11/0.44 % (1703279)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_1703259 for (3000ds/2Mi)
% 0.11/0.44 % (1703277)Refutation not found, incomplete strategy
% 0.11/0.44 % (1703277)------------------------------
% 0.11/0.44 % (1703277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.11/0.44 % (1703277)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.44
% 0.11/0.44
% 0.11/0.44 % (1703277)Memory used [KB]: 5373
% 0.11/0.44 % (1703277)Time elapsed: 0.002 s
% 0.11/0.44 % (1703277)------------------------------
% 0.11/0.44 % (1703277)------------------------------
% 0.11/0.45 % (1703276)Also succeeded, but the first one will report.
% 0.11/0.45 % (1703279)Refutation not found, incomplete strategy
% 0.11/0.45 % (1703279)------------------------------
% 0.11/0.45 % (1703279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.11/0.45 % (1703279)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.45
% 0.11/0.45
% 0.11/0.45 % (1703279)Memory used [KB]: 5373
% 0.11/0.45 % (1703279)Time elapsed: 0.002 s
% 0.11/0.45 % (1703279)------------------------------
% 0.11/0.45 % (1703279)------------------------------
% 0.11/0.45 % (1703281)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1703259 for (3000ds/18Mi)
% 0.11/0.45 % SZS status Satisfiable for DTF2THF_1703259
% 0.11/0.45 % (1703275)# SZS output start Saturation.
% 0.11/0.45 % (1703275)# SZS output end Saturation.
% 0.11/0.45 % (1703275)------------------------------
% 0.11/0.45 % (1703275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.11/0.45 % (1703275)Termination reason: Satisfiable
% 0.11/0.45
% 0.11/0.45 % (1703275)Memory used [KB]: 5373
% 0.11/0.45 % (1703275)Time elapsed: 0.003 s
% 0.11/0.45 % (1703275)------------------------------
% 0.11/0.45 % (1703275)------------------------------
% 0.11/0.45 % (1703274)Success in time 0.016 s
%------------------------------------------------------------------------------