%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : LCL690^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 11:34:44 AM UTC 2026
% Result : CounterSatisfiable 0.14s 0.44s
% Output : Saturation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL690^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 4 20:23:49 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.38 ---- Original DTF file ---
% 0.14/0.38 thf(spec,logic,$$dhol).
% 0.14/0.38 %------------------------------------------------------------------------------
% 0.14/0.38 % File : LCL690^1 : TPTP v9.3.1. Released v3.7.0.
% 0.14/0.38 % Domain : Logical Calculi
% 0.14/0.38 % Problem : Prove K in the CS4 translation
% 0.14/0.38 % Version : [AM+01] axioms.
% 0.14/0.38 % English :
% 0.14/0.38
% 0.14/0.38 % Refs : [AM+01] Alechina et al. (2001), Categorical and Kripke Semanti
% 0.14/0.38 % : [Gar09] Garg (2009), Email to Geoff Sutcliffe
% 0.14/0.38 % Source : [Gar09]
% 0.14/0.38 % Names :
% 0.14/0.38
% 0.14/0.38 % Status : Theorem
% 0.14/0.38 % Rating : 0.25 v9.3.0, 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.44 v7.3.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.67 v3.7.0
% 0.14/0.38 % Syntax : Number of formulae : 61 ( 24 unt; 31 typ; 24 def)
% 0.14/0.38 % Number of atoms : 117 ( 24 equ; 0 cnn)
% 0.14/0.38 % Maximal formula atoms : 11 ( 3 avg)
% 0.14/0.38 % Number of connectives : 106 ( 3 ~; 1 |; 2 &; 99 @)
% 0.14/0.38 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.14/0.38 % Maximal formula depth : 10 ( 2 avg)
% 0.14/0.38 % Number of types : 3 ( 1 usr)
% 0.14/0.38 % Number of type conns : 130 ( 130 >; 0 *; 0 +; 0 <<)
% 0.14/0.38 % Number of symbols : 33 ( 30 usr; 3 con; 0-3 aty)
% 0.14/0.38 % Number of variables : 53 ( 38 ^; 11 !; 4 ?; 53 :)
% 0.14/0.38 % SPC : TH0_THM_EQU_NAR_NDT
% 0.14/0.38
% 0.14/0.38 % Comments :
% 0.14/0.38 %------------------------------------------------------------------------------
% 0.14/0.38 %----Include axioms of multi-modal logic
% 0.14/0.38 include('Axioms/LCL008^0.ax').
% 0.14/0.38 %----Include axioms translating constructive S4 (CS4) to bimodal classical
% 0.14/0.38 %----S4 (BS4)
% 0.14/0.38 include('Axioms/LCL009^0.ax').
% 0.14/0.38 %------------------------------------------------------------------------------
% 0.14/0.38 thf(cs4_k,conjecture,
% 0.14/0.38 ! [A: $i > $o,B: $i > $o] : ( cs4_valid @ ( cs4_impl @ ( cs4_box @ ( cs4_impl @ ( cs4_atom @ A ) @ ( cs4_atom @ B ) ) ) @ ( cs4_impl @ ( cs4_box @ ( cs4_atom @ A ) ) @ ( cs4_box @ ( cs4_atom @ B ) ) ) ) ) ).
% 0.14/0.38
% 0.14/0.38 %------------------------------------------------------------------------------
% 0.14/0.38 ------------------------
% 0.14/0.38 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found.
% 0.14/0.38 ---- Embedded in THF ---
% 0.14/0.39 ------------------------
% 0.14/0.40 ---- Cleaned THF ---
% 0.14/0.41 ------------------------
% 0.14/0.43 % (2749942)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_2749924 for (3000ds/27Mi)
% 0.14/0.43 % (2749942)Refutation not found, incomplete strategy
% 0.14/0.43 % (2749942)------------------------------
% 0.14/0.43 % (2749942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.14/0.43 % (2749942)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.43
% 0.14/0.43
% 0.14/0.43 % (2749942)Memory used [KB]: 5373
% 0.14/0.43 % (2749942)Time elapsed: 0.002 s
% 0.14/0.43 % (2749942)------------------------------
% 0.14/0.43 % (2749942)------------------------------
% 0.14/0.44 % (2749941)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_2749924 for (3000ds/4Mi)
% 0.14/0.44 % (2749940)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2749924 for (3000ds/183Mi)
% 0.14/0.44 % (2749941)First to succeed.
% 0.14/0.44 % (2749943)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2749924 for (3000ds/2Mi)
% 0.14/0.44 % (2749940)Also succeeded, but the first one will report.
% 0.14/0.44 % (2749944)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_2749924 for (3000ds/2Mi)
% 0.14/0.44 % (2749945)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_2749924 for (3000ds/275Mi)
% 0.14/0.44 % (2749946)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2749924 for (3000ds/18Mi)
% 0.14/0.44 % (2749944)Refutation not found, incomplete strategy
% 0.14/0.44 % (2749944)------------------------------
% 0.14/0.44 % (2749944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.14/0.44 % (2749944)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.44
% 0.14/0.44
% 0.14/0.44 % (2749944)Memory used [KB]: 5373
% 0.14/0.44 % (2749944)Time elapsed: 0.003 s
% 0.14/0.44 % (2749944)Instructions burned: 1 (million)
% 0.14/0.44 % (2749944)------------------------------
% 0.14/0.44 % (2749944)------------------------------
% 0.14/0.44 % (2749945)Refutation not found, incomplete strategy
% 0.14/0.44 % (2749945)------------------------------
% 0.14/0.44 % (2749945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.14/0.44 % (2749945)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.44
% 0.14/0.44
% 0.14/0.44 % (2749945)Memory used [KB]: 5373
% 0.14/0.44 % (2749945)Time elapsed: 0.003 s
% 0.14/0.44 % (2749945)Instructions burned: 1 (million)
% 0.14/0.44 % (2749945)------------------------------
% 0.14/0.44 % (2749945)------------------------------
% 0.14/0.44 % SZS status Satisfiable for DTF2THF_2749924
% 0.14/0.44 % (2749941)# SZS output start Saturation.
% 0.14/0.44 % (2749941)# SZS output end Saturation.
% 0.14/0.44 % (2749941)------------------------------
% 0.14/0.44 % (2749941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.14/0.44 % (2749941)Termination reason: Satisfiable
% 0.14/0.44
% 0.14/0.44 % (2749941)Memory used [KB]: 5373
% 0.14/0.44 % (2749941)Time elapsed: 0.003 s
% 0.14/0.44 % (2749941)------------------------------
% 0.14/0.44 % (2749941)------------------------------
% 0.14/0.44 % (2749939)Success in time 0.018 s
%------------------------------------------------------------------------------