%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : LCL626^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 11:34:26 AM UTC 2026
% Result : CounterSatisfiable 0.21s 0.50s
% Output : Saturation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL626^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.05 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.39 % Computer : n014.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 4 23:03:42 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.42 ---- Original DTF file ---
% 0.13/0.43 thf(spec,logic,$$dhol).
% 0.13/0.43 %------------------------------------------------------------------------------
% 0.13/0.43 % File : LCL626^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.13/0.43 % Domain : Logical Calculi
% 0.13/0.43 % Problem : Loeb axiom is valid in this frame
% 0.13/0.43 % Version : [Ben08] axioms.
% 0.13/0.43 % English : In a frame that is transitive and upwards well-founded, the Loeb
% 0.13/0.43 % axiom is valid.
% 0.13/0.43
% 0.13/0.43 % Refs : [Fit07] Fitting (2007), Modal Proof Theory
% 0.13/0.43 % : [Ben08] Benzmueller (2008), Email to G. Sutcliffe
% 0.13/0.43 % Source : [Ben08]
% 0.13/0.43 % Names : Fitting-HB-14 [Ben08]
% 0.13/0.43
% 0.13/0.43 % Status : Theorem
% 0.13/0.43 % 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 v7.3.0
% 0.13/0.43 % Syntax : Number of formulae : 80 ( 36 unt; 42 typ; 36 def)
% 0.13/0.43 % Number of atoms : 102 ( 40 equ; 0 cnn)
% 0.13/0.43 % Maximal formula atoms : 10 ( 2 avg)
% 0.13/0.43 % Number of connectives : 137 ( 6 ~; 3 |; 15 &; 103 @)
% 0.13/0.43 % ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% 0.13/0.43 % Maximal formula depth : 8 ( 1 avg)
% 0.13/0.43 % Number of types : 3 ( 1 usr)
% 0.13/0.43 % Number of type conns : 224 ( 224 >; 0 *; 0 +; 0 <<)
% 0.13/0.43 % Number of symbols : 44 ( 41 usr; 3 con; 0-4 aty)
% 0.13/0.43 % Number of variables : 109 ( 76 ^; 23 !; 10 ?; 109 :)
% 0.13/0.43 % SPC : TH0_THM_EQU_NAR_NDT
% 0.13/0.43
% 0.13/0.43 % Comments :
% 0.13/0.43 % Bugfixes : v7.3.0 - Made relation R a constant.
% 0.13/0.43 %------------------------------------------------------------------------------
% 0.13/0.43 %----Include simple maths definitions and axioms
% 0.13/0.43 include('Axioms/LCL008^0.ax').
% 0.13/0.43 include('Axioms/SET008^2.ax').
% 0.13/0.43 %------------------------------------------------------------------------------
% 0.13/0.43 %----Axioms
% 0.13/0.43 thf(r_type,type,
% 0.13/0.43 r: $i > $i > $o ).
% 0.13/0.43
% 0.13/0.43 thf(upwf_trans,axiom,
% 0.13/0.43 ( ( transitive @ r )
% 0.13/0.43 & ( upwards_well_founded @ r ) ) ).
% 0.13/0.43
% 0.13/0.43 %----Conjecture
% 0.13/0.43 thf(k4,conjecture,
% 0.13/0.43 ! [X: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X ) @ ( mbox @ r @ ( mbox @ r @ ( mbox @ r @ X ) ) ) ) ) ).
% 0.13/0.43
% 0.13/0.43 %------------------------------------------------------------------------------
% 0.13/0.43 ------------------------
% 0.13/0.43 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found.
% 0.13/0.43 ---- Embedded in THF ---
% 0.13/0.43 ------------------------
% 0.13/0.46 ---- Cleaned THF ---
% 0.13/0.46 ------------------------
% 0.21/0.50 % (2600020)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_2600002 for (2999ds/27Mi)
% 0.21/0.50 % (2600021)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2600002 for (2999ds/2Mi)
% 0.21/0.50 % (2600018)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2600002 for (2999ds/183Mi)
% 0.21/0.50 % (2600019)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_2600002 for (2999ds/4Mi)
% 0.21/0.50 % (2600022)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_2600002 for (2999ds/2Mi)
% 0.21/0.50 % (2600023)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_2600002 for (2999ds/275Mi)
% 0.21/0.50 % (2600024)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2600002 for (2999ds/18Mi)
% 0.21/0.50 % (2600020)Refutation not found, incomplete strategy
% 0.21/0.50 % (2600020)------------------------------
% 0.21/0.50 % (2600020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.21/0.50 % (2600022)Refutation not found, incomplete strategy
% 0.21/0.50 % (2600022)------------------------------
% 0.21/0.50 % (2600022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.21/0.50 % (2600020)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.50
% 0.21/0.50 % (2600022)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.50
% 0.21/0.50
% 0.21/0.50 % (2600019)First to succeed.
% 0.21/0.50 % (2600023)Refutation not found, incomplete strategy
% 0.21/0.50 % (2600023)------------------------------
% 0.21/0.50 % (2600023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.21/0.50 % (2600020)Memory used [KB]: 5373
% 0.21/0.50 % (2600023)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.50
% 0.21/0.50 % (2600020)Time elapsed: 0.003 s
% 0.21/0.50
% 0.21/0.50
% 0.21/0.50 % (2600020)Instructions burned: 1 (million)
% 0.21/0.50 % (2600022)Memory used [KB]: 5373
% 0.21/0.50 % (2600023)Memory used [KB]: 5373
% 0.21/0.50 % (2600022)Time elapsed: 0.003 s
% 0.21/0.50 % (2600020)------------------------------
% 0.21/0.50 % (2600020)------------------------------
% 0.21/0.50 % (2600023)Time elapsed: 0.002 s
% 0.21/0.50 % (2600022)------------------------------
% 0.21/0.50 % (2600022)------------------------------
% 0.21/0.50 % (2600023)------------------------------
% 0.21/0.50 % (2600023)------------------------------
% 0.21/0.50 % (2600018)Also succeeded, but the first one will report.
% 0.21/0.50 % (2600021)Also succeeded, but the first one will report.
% 0.21/0.50 % SZS status Satisfiable for DTF2THF_2600002
% 0.21/0.50 % (2600019)# SZS output start Saturation.
% 0.21/0.50 % (2600019)# SZS output end Saturation.
% 0.21/0.50 % (2600019)------------------------------
% 0.21/0.50 % (2600019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.21/0.50 % (2600019)Termination reason: Satisfiable
% 0.21/0.50
% 0.21/0.50 % (2600019)Memory used [KB]: 5373
% 0.21/0.50 % (2600019)Time elapsed: 0.002 s
% 0.21/0.50 % (2600019)Instructions burned: 1 (million)
% 0.21/0.50 % (2600019)------------------------------
% 0.21/0.50 % (2600019)------------------------------
% 0.21/0.50 % (2600017)Success in time 0.02 s
%------------------------------------------------------------------------------