%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : LCL873^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 0.19s 0.47s
% Output : Saturation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL873^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 5 04:34:20 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.41 ---- Original DTF file ---
% 0.11/0.41 thf(spec,logic,$$dhol).
% 0.11/0.41 %------------------------------------------------------------------------------
% 0.11/0.41 % File : LCL873^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.11/0.41 % Domain : Logical Calculi (Modal logic)
% 0.11/0.41 % Problem : Commutativity implies orthogonality in 2-D modal logic S5
% 0.11/0.41 % Version : [Ben10] axioms.
% 0.11/0.41 % English :
% 0.11/0.41
% 0.11/0.41 % Refs : [Seg73] Segerberg (1973), Two-Dimensional Modal Logic
% 0.11/0.41 % : [Ben10a] Benzmueller (2010), Email to Geoff Sutcliffe
% 0.11/0.41 % : [Ben10b] Benzmueller (2010), Simple Type Theory as a Framework
% 0.11/0.41 % Source : [Ben10a]
% 0.11/0.41 % Source : [Ben10], problem 35
% 0.11/0.41 % Names : Problem 35 [Ben10b]
% 0.11/0.41
% 0.11/0.41 % Status : Theorem
% 0.11/0.41 % Rating : 0.25 v9.3.0, 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.0.0
% 0.11/0.41 % Syntax : Number of formulae : 72 ( 31 unt; 34 typ; 31 def)
% 0.11/0.41 % Number of atoms : 136 ( 36 equ; 0 cnn)
% 0.11/0.41 % Maximal formula atoms : 32 ( 3 avg)
% 0.11/0.41 % Number of connectives : 168 ( 4 ~; 4 |; 9 &; 143 @)
% 0.11/0.41 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.11/0.41 % Maximal formula depth : 14 ( 2 avg)
% 0.11/0.41 % Number of types : 3 ( 1 usr)
% 0.11/0.41 % Number of type conns : 176 ( 176 >; 0 *; 0 +; 0 <<)
% 0.11/0.41 % Number of symbols : 35 ( 33 usr; 1 con; 0-3 aty)
% 0.11/0.41 % Number of variables : 88 ( 53 ^; 29 !; 6 ?; 88 :)
% 0.11/0.41 % SPC : TH0_THM_EQU_NAR_NDT
% 0.11/0.41
% 0.11/0.41 % Comments : Such a logic was discussed by Segerberg [Seg73] and the
% 0.11/0.41 % Bugfixes : v5.0.0 - Bugfix to LCL013^0.ax
% 0.11/0.41 % implication was only discovered later.
% 0.11/0.41 %------------------------------------------------------------------------------
% 0.11/0.41 %----Include the definitions for quantified multimodal logic
% 0.11/0.41 include('Axioms/LCL013^0.ax').
% 0.11/0.41 %------------------------------------------------------------------------------
% 0.11/0.41 thf(ra,type,
% 0.11/0.41 ra: $i > $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(rb,type,
% 0.11/0.41 rb: $i > $i > $o ).
% 0.11/0.41
% 0.11/0.41 thf(ax1,axiom,
% 0.11/0.41 mreflexive @ ra ).
% 0.11/0.41
% 0.11/0.41 thf(ax2,axiom,
% 0.11/0.41 mreflexive @ rb ).
% 0.11/0.41
% 0.11/0.41 thf(ax3,axiom,
% 0.11/0.41 mtransitive @ ra ).
% 0.11/0.41
% 0.11/0.41 thf(ax4,axiom,
% 0.11/0.41 mtransitive @ rb ).
% 0.11/0.41
% 0.11/0.41 thf(ax5,axiom,
% 0.11/0.41 meuclidean @ ra ).
% 0.11/0.41
% 0.11/0.41 thf(ax6,axiom,
% 0.11/0.41 meuclidean @ rb ).
% 0.11/0.41
% 0.11/0.41 thf(conj,conjecture,
% 0.11/0.41 ( ( mvalid
% 0.11/0.41 @ ( mforall_prop
% 0.11/0.41 @ ^ [A: $i > $o] :
% 0.11/0.41 ( mforall_prop
% 0.11/0.41 @ ^ [B: $i > $o] : ( mimplies @ ( mbox @ ra @ ( mor @ ( mbox @ ra @ A ) @ ( mbox @ rb @ B ) ) ) @ ( mor @ ( mbox @ ra @ A ) @ ( mbox @ ra @ B ) ) ) ) ) )
% 0.11/0.41 & ( mvalid
% 0.11/0.41 @ ( mforall_prop
% 0.11/0.41 @ ^ [A: $i > $o] :
% 0.11/0.41 ( mforall_prop
% 0.11/0.41 @ ^ [B: $i > $o] : ( mimplies @ ( mbox @ rb @ ( mor @ ( mbox @ ra @ A ) @ ( mbox @ rb @ B ) ) ) @ ( mor @ ( mbox @ rb @ A ) @ ( mbox @ rb @ B ) ) ) ) ) ) ) ).
% 0.11/0.41
% 0.11/0.41 %------------------------------------------------------------------------------
% 0.11/0.41 ------------------------
% 0.11/0.41 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found.
% 0.11/0.42 ---- Embedded in THF ---
% 0.11/0.42 ------------------------
% 0.11/0.44 ---- Cleaned THF ---
% 0.11/0.44 ------------------------
% 0.19/0.47 % (2501039)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2501023 for (3000ds/183Mi)
% 0.19/0.47 % (2501040)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_2501023 for (3000ds/4Mi)
% 0.19/0.47 % (2501041)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_2501023 for (3000ds/27Mi)
% 0.19/0.47 % (2501042)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2501023 for (3000ds/2Mi)
% 0.19/0.47 % (2501043)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_2501023 for (3000ds/2Mi)
% 0.19/0.47 % (2501039)First to succeed.
% 0.19/0.47 % (2501041)Refutation not found, incomplete strategy
% 0.19/0.47 % (2501041)------------------------------
% 0.19/0.47 % (2501041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.19/0.47 % (2501041)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 % (2501041)Memory used [KB]: 5373
% 0.19/0.47 % (2501041)Time elapsed: 0.002 s
% 0.19/0.47 % (2501041)------------------------------
% 0.19/0.47 % (2501041)------------------------------
% 0.19/0.47 % (2501045)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2501023 for (3000ds/18Mi)
% 0.19/0.47 % (2501042)Also succeeded, but the first one will report.
% 0.19/0.47 % (2501043)Refutation not found, incomplete strategy
% 0.19/0.47 % (2501043)------------------------------
% 0.19/0.47 % (2501043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.19/0.47 % (2501043)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 % (2501043)Memory used [KB]: 5373
% 0.19/0.47 % (2501043)Time elapsed: 0.002 s
% 0.19/0.47 % (2501043)------------------------------
% 0.19/0.47 % (2501043)------------------------------
% 0.19/0.47 % (2501044)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_2501023 for (3000ds/275Mi)
% 0.19/0.47 % (2501044)Refutation not found, incomplete strategy
% 0.19/0.47 % (2501044)------------------------------
% 0.19/0.47 % (2501044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.19/0.47 % (2501044)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 % (2501044)Memory used [KB]: 5373
% 0.19/0.47 % (2501044)Time elapsed: 0.002 s
% 0.19/0.47 % (2501044)------------------------------
% 0.19/0.47 % (2501044)------------------------------
% 0.19/0.47 % SZS status Satisfiable for DTF2THF_2501023
% 0.19/0.47 % (2501039)# SZS output start Saturation.
% 0.19/0.47 % (2501039)# SZS output end Saturation.
% 0.19/0.47 % (2501039)------------------------------
% 0.19/0.47 % (2501039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.19/0.47 % (2501039)Termination reason: Satisfiable
% 0.19/0.47
% 0.19/0.47 % (2501039)Memory used [KB]: 5373
% 0.19/0.47 % (2501039)Time elapsed: 0.003 s
% 0.19/0.47 % (2501039)Instructions burned: 1 (million)
% 0.19/0.47 % (2501039)------------------------------
% 0.19/0.47 % (2501039)------------------------------
% 0.19/0.47 % (2501038)Success in time 0.016 s
%------------------------------------------------------------------------------