%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : LCL632^1 : 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 : n028.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 11:34:27 AM UTC 2026
% Result : CounterSatisfiable 0.13s 0.44s
% Output : Saturation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL632^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n028.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 5 04:31:59 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.38 ---- Original DTF file ---
% 0.13/0.38 thf(spec,logic,$$dhol).
% 0.13/0.38 %------------------------------------------------------------------------------
% 0.13/0.38 % File : LCL632^1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.13/0.38 % Domain : Logical Calculi
% 0.13/0.38 % Problem : The muddy forehead puzzle
% 0.13/0.38 % Version : [Ben08] axioms.
% 0.13/0.38 % English :
% 0.13/0.38
% 0.13/0.38 % Refs : [Fit07] Fitting (2007), Modal Proof Theory
% 0.13/0.38 % : [Ben08] Benzmueller (2008), Email to G. Sutcliffe
% 0.13/0.38 % Source : [Ben08]
% 0.13/0.38 % Names : Fitting-HB-Knowledge-3b [Ben08]
% 0.13/0.38
% 0.13/0.38 % Status : Theorem
% 0.13/0.38 % Rating : 1.00 v7.3.0
% 0.13/0.38 % Syntax : Number of formulae : 56 ( 17 unt; 29 typ; 17 def)
% 0.13/0.38 % Number of atoms : 168 ( 17 equ; 0 cnn)
% 0.13/0.38 % Maximal formula atoms : 17 ( 6 avg)
% 0.13/0.38 % Number of connectives : 158 ( 3 ~; 1 |; 2 &; 151 @)
% 0.13/0.38 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.13/0.38 % Maximal formula depth : 16 ( 4 avg)
% 0.13/0.38 % Number of types : 3 ( 1 usr)
% 0.13/0.38 % Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% 0.13/0.38 % Number of symbols : 31 ( 28 usr; 3 con; 0-3 aty)
% 0.13/0.38 % Number of variables : 41 ( 30 ^; 7 !; 4 ?; 41 :)
% 0.13/0.38 % SPC : TH0_THM_EQU_NAR_NDT
% 0.13/0.38
% 0.13/0.38 % Comments :
% 0.13/0.38 % Bugfixes : v7.3.0 - Made relation R a constant.
% 0.13/0.38 %------------------------------------------------------------------------------
% 0.13/0.38 %----Include simple maths definitions and axioms
% 0.13/0.38 include('Axioms/LCL008^0.ax').
% 0.13/0.38 %------------------------------------------------------------------------------
% 0.13/0.38 %----Signature
% 0.13/0.38 thf(a,type,
% 0.13/0.38 a: $i > $i > $o ).
% 0.13/0.38
% 0.13/0.38 thf(b,type,
% 0.13/0.38 b: $i > $i > $o ).
% 0.13/0.38
% 0.13/0.38 thf(c,type,
% 0.13/0.38 c: $i > $i > $o ).
% 0.13/0.38
% 0.13/0.38 thf(mfa,type,
% 0.13/0.38 mfa: $i > $o ).
% 0.13/0.38
% 0.13/0.38 thf(mfb,type,
% 0.13/0.38 mfb: $i > $o ).
% 0.13/0.38
% 0.13/0.38 thf(mfc,type,
% 0.13/0.38 mfc: $i > $o ).
% 0.13/0.38
% 0.13/0.38 thf(ck,type,
% 0.13/0.38 ck: ( $i > $o ) > $i > $o ).
% 0.13/0.38
% 0.13/0.38 thf(s,type,
% 0.13/0.38 s: $i > $o ).
% 0.13/0.38
% 0.13/0.38 thf(r_type,type,
% 0.13/0.38 r: $i > $i > $o ).
% 0.13/0.38
% 0.13/0.38 %----Axioms
% 0.13/0.38 thf(knowledge_implies_truth,axiom,
% 0.13/0.38 ! [X: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X ) @ X ) ) ).
% 0.13/0.38
% 0.13/0.38 thf(positive_introspection,axiom,
% 0.13/0.38 ! [X: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X ) @ ( mbox @ r @ ( mbox @ r @ X ) ) ) ) ).
% 0.13/0.38
% 0.13/0.38 thf(negitive_introspection,axiom,
% 0.13/0.38 ! [X: $i > $o] : ( mvalid @ ( mimpl @ ( mnot @ ( mbox @ r @ X ) ) @ ( mbox @ r @ ( mnot @ ( mbox @ r @ X ) ) ) ) ) ).
% 0.13/0.38
% 0.13/0.38 thf(common_knowledge,definition,
% 0.13/0.38 ( ck
% 0.13/0.38 = ( ^ [X: $i > $o,W: $i] : ( mbox @ r @ X @ W ) ) ) ).
% 0.13/0.38
% 0.13/0.38 thf(what_a_knows_about_b,axiom,
% 0.13/0.38 mvalid @ ( ck @ ( mor @ ( mbox @ a @ mfb ) @ ( mbox @ a @ ( mnot @ mfb ) ) ) ) ).
% 0.13/0.38
% 0.13/0.38 thf(what_a_knows_about_c,axiom,
% 0.13/0.38 mvalid @ ( ck @ ( mor @ ( mbox @ a @ mfc ) @ ( mbox @ a @ ( mnot @ mfc ) ) ) ) ).
% 0.13/0.38
% 0.13/0.38 thf(what_b_knows_about_a,axiom,
% 0.13/0.38 mvalid @ ( ck @ ( mor @ ( mbox @ b @ mfa ) @ ( mbox @ b @ ( mnot @ mfa ) ) ) ) ).
% 0.13/0.38
% 0.13/0.38 thf(what_b_knows_about_c,axiom,
% 0.13/0.38 mvalid @ ( ck @ ( mor @ ( mbox @ b @ mfc ) @ ( mbox @ b @ ( mnot @ mfc ) ) ) ) ).
% 0.13/0.38
% 0.13/0.38 thf(what_c_knows_about_a,axiom,
% 0.13/0.38 mvalid @ ( ck @ ( mor @ ( mbox @ c @ mfa ) @ ( mbox @ c @ ( mnot @ mfa ) ) ) ) ).
% 0.13/0.38
% 0.13/0.38 thf(what_c_knows_about_b,axiom,
% 0.13/0.38 mvalid @ ( ck @ ( mor @ ( mbox @ c @ mfb ) @ ( mbox @ c @ ( mnot @ mfb ) ) ) ) ).
% 0.13/0.38
% 0.13/0.38 thf(someone_knows_its_forehead,definition,
% 0.13/0.38 ( s
% 0.13/0.38 = ( mor @ ( mbox @ a @ mfa ) @ ( mor @ ( mbox @ a @ ( mnot @ mfa ) ) @ ( mor @ ( mbox @ b @ mfb ) @ ( mor @ ( mbox @ b @ ( mnot @ mfb ) ) @ ( mor @ ( mbox @ c @ mfc ) @ ( mbox @ c @ ( mnot @ mfc ) ) ) ) ) ) ) ) ).
% 0.13/0.38
% 0.13/0.38 %----Conjecture
% 0.13/0.38 thf(thm,conjecture,
% 0.13/0.38 mvalid @ ( mimpl @ ( ck @ ( mnot @ ( mimpl @ ( ck @ ( mnot @ ( mimpl @ ( ck @ ( mor @ mfa @ ( mor @ mfb @ mfc ) ) ) @ s ) ) ) @ s ) ) ) @ s ) ).
% 0.13/0.38
% 0.13/0.38 %------------------------------------------------------------------------------
% 0.13/0.38 ------------------------
% 0.13/0.38 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found.
% 0.13/0.39 ---- Embedded in THF ---
% 0.13/0.39 ------------------------
% 0.13/0.41 ---- Cleaned THF ---
% 0.13/0.41 ------------------------
% 0.13/0.44 % (1531827)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_1531806 for (2999ds/275Mi)
% 0.13/0.44 % (1531827)Refutation not found, incomplete strategy
% 0.13/0.44 % (1531827)------------------------------
% 0.13/0.44 % (1531827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.13/0.44 % (1531827)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.44
% 0.13/0.44
% 0.13/0.44 % (1531827)Memory used [KB]: 5373
% 0.13/0.44 % (1531827)Time elapsed: 0.002 s
% 0.13/0.44 % (1531827)Instructions burned: 1 (million)
% 0.13/0.44 % (1531827)------------------------------
% 0.13/0.44 % (1531827)------------------------------
% 0.13/0.44 % (1531822)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1531806 for (2999ds/183Mi)
% 0.13/0.44 % (1531823)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_1531806 for (2999ds/4Mi)
% 0.13/0.44 % (1531824)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_1531806 for (2999ds/27Mi)
% 0.13/0.44 % (1531825)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1531806 for (2999ds/2Mi)
% 0.13/0.44 % (1531822)First to succeed.
% 0.13/0.44 % (1531824)Refutation not found, incomplete strategy
% 0.13/0.44 % (1531824)------------------------------
% 0.13/0.44 % (1531824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.13/0.44 % (1531824)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.44
% 0.13/0.44 % (1531823)Also succeeded, but the first one will report.
% 0.13/0.44
% 0.13/0.44 % (1531824)Memory used [KB]: 5373
% 0.13/0.44 % (1531824)Time elapsed: 0.003 s
% 0.13/0.44 % (1531824)------------------------------
% 0.13/0.44 % (1531824)------------------------------
% 0.13/0.44 % (1531828)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1531806 for (2999ds/18Mi)
% 0.13/0.44 % SZS status Satisfiable for DTF2THF_1531806
% 0.13/0.44 % (1531822)# SZS output start Saturation.
% 0.13/0.44 % (1531822)# SZS output end Saturation.
% 0.13/0.44 % (1531822)------------------------------
% 0.13/0.44 % (1531822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.13/0.44 % (1531822)Termination reason: Satisfiable
% 0.13/0.44
% 0.13/0.44 % (1531822)Memory used [KB]: 5373
% 0.13/0.44 % (1531822)Time elapsed: 0.002 s
% 0.13/0.44 % (1531822)Instructions burned: 1 (million)
% 0.13/0.44 % (1531822)------------------------------
% 0.13/0.44 % (1531822)------------------------------
% 0.13/0.44 % (1531821)Success in time 0.019 s
%------------------------------------------------------------------------------