%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : LCL872^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 11:35:06 AM UTC 2026
% Result : CounterSatisfiable 0.18s 0.48s
% Output : Saturation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL872^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 4 15:12:53 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.39 ---- Original DTF file ---
% 0.10/0.39 thf(spec,logic,$$dhol).
% 0.10/0.39 %------------------------------------------------------------------------------
% 0.10/0.39 % File : LCL872^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.10/0.39 % Domain : Logical Calculi (Modal logic)
% 0.10/0.39 % Problem : Correspondence between box and diamond and a confluence property
% 0.10/0.39 % Version : [Ben10] axioms.
% 0.10/0.39 % English :
% 0.10/0.39
% 0.10/0.39 % Refs : [Ben10a] Benzmueller (2010), Email to Geoff Sutcliffe
% 0.10/0.39 % : [Ben10b] Benzmueller (2010), Simple Type Theory as a Framework
% 0.10/0.39 % Source : [Ben10a]
% 0.10/0.39 % Names : Problem 34 [Ben10b]
% 0.10/0.39
% 0.10/0.39 % Status : Theorem
% 0.10/0.39 % Rating : 0.42 v9.3.0, 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.22 v7.3.0, 0.33 v7.2.0, 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, 0.80 v5.2.0
% 0.10/0.39 % Syntax : Number of formulae : 70 ( 32 unt; 37 typ; 32 def)
% 0.10/0.39 % Number of atoms : 110 ( 37 equ; 0 cnn)
% 0.10/0.39 % Maximal formula atoms : 16 ( 3 avg)
% 0.10/0.39 % Number of connectives : 151 ( 4 ~; 4 |; 10 &; 123 @)
% 0.10/0.39 % ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% 0.10/0.39 % Maximal formula depth : 10 ( 1 avg)
% 0.10/0.39 % Number of types : 3 ( 1 usr)
% 0.10/0.39 % Number of type conns : 197 ( 197 >; 0 *; 0 +; 0 <<)
% 0.10/0.39 % Number of symbols : 38 ( 36 usr; 1 con; 0-4 aty)
% 0.10/0.39 % Number of variables : 93 ( 54 ^; 32 !; 7 ?; 93 :)
% 0.10/0.39 % SPC : TH0_THM_EQU_NAR_NDT
% 0.10/0.39
% 0.10/0.39 % Comments :
% 0.10/0.39 % Bugfixes : v5.0.0 - Bugfix to LCL013^0.ax
% 0.10/0.39 % : v5.2.0 - Added missing types
% 0.10/0.39 %------------------------------------------------------------------------------
% 0.10/0.39 %----Include the definitions for quantified multimodal logic
% 0.10/0.39 include('Axioms/LCL013^0.ax').
% 0.10/0.39 %------------------------------------------------------------------------------
% 0.10/0.39 %----Constants for accesibility relations
% 0.10/0.39 thf(i,type,
% 0.10/0.39 i: $i > $i > $o ).
% 0.10/0.39
% 0.10/0.39 thf(j,type,
% 0.10/0.39 j: $i > $i > $o ).
% 0.10/0.39
% 0.10/0.39 thf(k,type,
% 0.10/0.39 k: $i > $i > $o ).
% 0.10/0.39
% 0.10/0.39 thf(l,type,
% 0.10/0.39 l: $i > $i > $o ).
% 0.10/0.39
% 0.10/0.39 %----Definition of confluence property
% 0.10/0.39 thf(confluences_type,type,
% 0.10/0.39 confluence: ( $i > $i > $o ) > ( $i > $i > $o ) > ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
% 0.10/0.39
% 0.10/0.39 thf(confluence,definition,
% 0.10/0.39 ( confluence
% 0.10/0.39 = ( ^ [I: $i > $i > $o,J: $i > $i > $o,K: $i > $i > $o,L: $i > $i > $o] :
% 0.10/0.39 ! [A: $i,B: $i,C: $i] :
% 0.10/0.39 ( ( ( I @ A @ B )
% 0.10/0.39 & ( K @ A @ C ) )
% 0.10/0.39 => ? [D: $i] :
% 0.10/0.39 ( ( J @ B @ D )
% 0.10/0.39 & ( L @ C @ D ) ) ) ) ) ).
% 0.10/0.39
% 0.10/0.39 %----Correspondence between axiom and confluence property
% 0.10/0.39 thf(conj,conjecture,
% 0.10/0.39 ( ( mvalid
% 0.10/0.39 @ ( mforall_prop
% 0.10/0.39 @ ^ [P: $i > $o] : ( mimplies @ ( mdia @ i @ ( mbox @ j @ P ) ) @ ( mbox @ k @ ( mdia @ l @ P ) ) ) ) )
% 0.10/0.39 <=> ( confluence @ i @ j @ k @ l ) ) ).
% 0.10/0.39
% 0.10/0.39 %------------------------------------------------------------------------------
% 0.10/0.39 ------------------------
% 0.10/0.41 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found.
% 0.10/0.41 ---- Embedded in THF ---
% 0.10/0.41 ------------------------
% 0.10/0.43 ---- Cleaned THF ---
% 0.10/0.43 ------------------------
% 0.18/0.47 % (1014406)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_1014378 for (3000ds/2Mi)
% 0.18/0.47 % (1014406)Refutation not found, incomplete strategy
% 0.18/0.47 % (1014406)------------------------------
% 0.18/0.47 % (1014406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.18/0.47 % (1014406)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 % (1014406)Memory used [KB]: 5373
% 0.18/0.47 % (1014406)Time elapsed: 0.002 s
% 0.18/0.47 % (1014406)Instructions burned: 1 (million)
% 0.18/0.47 % (1014406)------------------------------
% 0.18/0.47 % (1014406)------------------------------
% 0.18/0.48 % (1014402)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1014378 for (3000ds/183Mi)
% 0.18/0.48 % (1014403)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_1014378 for (3000ds/4Mi)
% 0.18/0.48 % (1014404)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_1014378 for (3000ds/27Mi)
% 0.18/0.48 % (1014405)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1014378 for (3000ds/2Mi)
% 0.18/0.48 % (1014402)First to succeed.
% 0.18/0.48 % (1014403)Also succeeded, but the first one will report.
% 0.18/0.48 % (1014404)Refutation not found, incomplete strategy
% 0.18/0.48 % (1014404)------------------------------
% 0.18/0.48 % (1014404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.18/0.48 % (1014404)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.48
% 0.18/0.48
% 0.18/0.48 % (1014404)Memory used [KB]: 5373
% 0.18/0.48 % (1014407)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_1014378 for (3000ds/275Mi)
% 0.18/0.48 % (1014404)Time elapsed: 0.003 s
% 0.18/0.48 % (1014404)Instructions burned: 1 (million)
% 0.18/0.48 % (1014404)------------------------------
% 0.18/0.48 % (1014404)------------------------------
% 0.18/0.48 % (1014408)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1014378 for (3000ds/18Mi)
% 0.18/0.48 % (1014407)Refutation not found, incomplete strategy
% 0.18/0.48 % (1014407)------------------------------
% 0.18/0.48 % (1014407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.18/0.48 % (1014407)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.48
% 0.18/0.48
% 0.18/0.48 % (1014407)Memory used [KB]: 5373
% 0.18/0.48 % (1014407)Time elapsed: 0.003 s
% 0.18/0.48 % (1014407)------------------------------
% 0.18/0.48 % (1014407)------------------------------
% 0.18/0.48 % SZS status Satisfiable for DTF2THF_1014378
% 0.18/0.48 % (1014402)# SZS output start Saturation.
% 0.18/0.48 % (1014402)# SZS output end Saturation.
% 0.18/0.48 % (1014402)------------------------------
% 0.18/0.48 % (1014402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.18/0.48 % (1014402)Termination reason: Satisfiable
% 0.18/0.48
% 0.18/0.48 % (1014402)Memory used [KB]: 5373
% 0.18/0.48 % (1014402)Time elapsed: 0.003 s
% 0.18/0.48 % (1014402)Instructions burned: 1 (million)
% 0.18/0.48 % (1014402)------------------------------
% 0.18/0.48 % (1014402)------------------------------
% 0.18/0.48 % (1014401)Success in time 0.018 s
%------------------------------------------------------------------------------