%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : LCL583^1 : 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 : n010.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 0.12s 0.43s
% Output : Saturation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL583^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n010.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 6 02:03:39 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.38 ---- Original DTF file ---
% 0.12/0.38 thf(spec,logic,$$dhol).
% 0.12/0.38 %------------------------------------------------------------------------------
% 0.12/0.38 % File : LCL583^1 : TPTP v9.3.1. Released v3.6.0.
% 0.12/0.38 % Domain : Logical Calculi
% 0.12/0.38 % Problem : Popkorn problem 4
% 0.12/0.38 % Version : [BP09] axioms.
% 0.12/0.38 % English :
% 0.12/0.38
% 0.12/0.38 % Refs : [Pop95] Popkorn (1995), First Steps in Modal Logic
% 0.12/0.38 % : [BP09] Benzmueller & Paulson (2009), Exploring Properties of
% 0.12/0.38 % Source : [BP09]
% 0.12/0.38 % Names : K-d [BP09]
% 0.12/0.38
% 0.12/0.38 % Status : Theorem
% 0.12/0.38 % 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
% 0.12/0.38 % Syntax : Number of formulae : 39 ( 15 unt; 23 typ; 15 def)
% 0.12/0.38 % Number of atoms : 47 ( 15 equ; 0 cnn)
% 0.12/0.38 % Maximal formula atoms : 10 ( 2 avg)
% 0.12/0.38 % Number of connectives : 44 ( 3 ~; 1 |; 2 &; 37 @)
% 0.12/0.38 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.12/0.38 % Maximal formula depth : 7 ( 1 avg)
% 0.12/0.38 % Number of types : 3 ( 1 usr)
% 0.12/0.38 % Number of type conns : 84 ( 84 >; 0 *; 0 +; 0 <<)
% 0.12/0.38 % Number of symbols : 25 ( 22 usr; 3 con; 0-3 aty)
% 0.12/0.38 % Number of variables : 36 ( 28 ^; 4 !; 4 ?; 36 :)
% 0.12/0.38 % SPC : TH0_THM_EQU_NAR_NDT
% 0.12/0.38
% 0.12/0.38 % Comments :
% 0.12/0.38 %------------------------------------------------------------------------------
% 0.12/0.38 %----Include simple maths definitions and axioms
% 0.12/0.38 include('Axioms/LCL008^0.ax').
% 0.12/0.38 %------------------------------------------------------------------------------
% 0.12/0.38 %----Signature
% 0.12/0.38 thf(a,type,
% 0.12/0.38 a: $i > $o ).
% 0.12/0.38
% 0.12/0.38 thf(r,type,
% 0.12/0.38 r: $i > $i > $o ).
% 0.12/0.38
% 0.12/0.38 thf(s,type,
% 0.12/0.38 s: $i > $i > $o ).
% 0.12/0.38
% 0.12/0.38 %----Conjecture
% 0.12/0.38 thf(thm,conjecture,
% 0.12/0.38 mvalid @ ( mbox @ s @ ( mimpl @ ( mbox @ r @ a ) @ ( mbox @ r @ a ) ) ) ).
% 0.12/0.38
% 0.12/0.38 %------------------------------------------------------------------------------
% 0.12/0.38 ------------------------
% 0.12/0.38 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found.
% 0.12/0.39 ---- Embedded in THF ---
% 0.12/0.39 ------------------------
% 0.12/0.40 ---- Cleaned THF ---
% 0.12/0.41 ------------------------
% 0.12/0.43 % (1413467)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_1413450 for (2999ds/4Mi)
% 0.12/0.43 % (1413467)First to succeed.
% 0.12/0.43 % SZS status Satisfiable for DTF2THF_1413450
% 0.12/0.43 % (1413467)# SZS output start Saturation.
% 0.12/0.43 % (1413467)# SZS output end Saturation.
% 0.12/0.43 % (1413467)------------------------------
% 0.12/0.43 % (1413467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.12/0.43 % (1413467)Termination reason: Satisfiable
% 0.12/0.43
% 0.12/0.43 % (1413467)Memory used [KB]: 5373
% 0.12/0.43 % (1413467)Time elapsed: 0.002 s
% 0.12/0.43 % (1413467)Instructions burned: 1 (million)
% 0.12/0.43 % (1413467)------------------------------
% 0.12/0.43 % (1413467)------------------------------
% 0.12/0.43 % (1413465)Success in time 0.012 s
%------------------------------------------------------------------------------