%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : LCL881^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 11:35:07 AM UTC 2026
% Result : CounterSatisfiable 0.10s 0.45s
% Output : Saturation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL881^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n014.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 : Sun Sep 6 01:35:57 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 ---
% 0.10/0.40 thf(spec,logic,$$dhol).
% 0.10/0.40 %------------------------------------------------------------------------------
% 0.10/0.40 % File : LCL881^1 : TPTP v9.3.1. Released v5.2.0.
% 0.10/0.40 % Domain : Logic Calculi (Doxastic multimodal logic)
% 0.10/0.40 % Problem : Axiom 5s is dependent
% 0.10/0.40 % Version : [Ben11] axioms.
% 0.10/0.40 % English :
% 0.10/0.40
% 0.10/0.40 % Refs : [Ben11] Benzmueller (2011), Email to Geoff Sutcliffe
% 0.10/0.40 % : [Ben11] Benzmueller (2011), Combining and Automating Classical
% 0.10/0.40 % Source : [Ben11]
% 0.10/0.40 % Names : Ex_7_6 [Ben11]
% 0.10/0.40
% 0.10/0.40 % Status : Theorem
% 0.10/0.40 % Rating : 0.75 v9.3.0, 0.78 v9.1.0, 0.75 v9.0.0, 0.90 v8.2.0, 0.92 v8.1.0, 0.82 v7.5.0, 0.71 v7.4.0, 0.78 v7.2.0, 0.75 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.3.0, 1.00 v5.2.0
% 0.10/0.40 % Syntax : Number of formulae : 85 ( 31 unt; 35 typ; 31 def)
% 0.10/0.40 % Number of atoms : 347 ( 36 equ; 0 cnn)
% 0.10/0.40 % Maximal formula atoms : 99 ( 6 avg)
% 0.10/0.40 % Number of connectives : 413 ( 4 ~; 4 |; 16 &; 381 @)
% 0.10/0.40 % ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% 0.10/0.40 % Maximal formula depth : 17 ( 4 avg)
% 0.10/0.40 % Number of types : 3 ( 1 usr)
% 0.10/0.40 % Number of type conns : 201 ( 201 >; 0 *; 0 +; 0 <<)
% 0.10/0.40 % Number of symbols : 36 ( 34 usr; 1 con; 0-3 aty)
% 0.10/0.40 % Number of variables : 111 ( 76 ^; 29 !; 6 ?; 111 :)
% 0.10/0.40 % SPC : TH0_THM_EQU_NAR_NDT
% 0.10/0.40
% 0.10/0.40 % Comments :
% 0.10/0.40 %------------------------------------------------------------------------------
% 0.10/0.40 %----Include embedding of quantified multimodal logic in simple type theory
% 0.10/0.40 include('Axioms/LCL013^0.ax').
% 0.10/0.40 %------------------------------------------------------------------------------
% 0.10/0.40 thf(r1,type,
% 0.10/0.40 r1: $i > $i > $o ).
% 0.10/0.40
% 0.10/0.40 thf(r2,type,
% 0.10/0.40 r2: $i > $i > $o ).
% 0.10/0.40
% 0.10/0.40 thf(r3,type,
% 0.10/0.40 r3: $i > $i > $o ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_D_for_r1,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r1 @ Phi ) @ ( mdia @ r1 @ Phi ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_D_for_r2,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mdia @ r2 @ Phi ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_D_for_r3,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mdia @ r3 @ Phi ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_I_for_r2_r1,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mbox @ r1 @ Phi ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_I_for_r3_r1,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r1 @ Phi ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_I_for_r3_r2,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r2 @ Phi ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_4s_for_r1_r1,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r1 @ Phi ) @ ( mbox @ r1 @ ( mbox @ r1 @ Phi ) ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_4s_for_r1_r2,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r1 @ Phi ) @ ( mbox @ r2 @ ( mbox @ r1 @ Phi ) ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_4s_for_r1_r3,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r1 @ Phi ) @ ( mbox @ r3 @ ( mbox @ r1 @ Phi ) ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_4s_for_r2_r1,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mbox @ r1 @ ( mbox @ r2 @ Phi ) ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_4s_for_r2_r2,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mbox @ r2 @ ( mbox @ r2 @ Phi ) ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_4s_for_r2_r3,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r2 @ Phi ) @ ( mbox @ r3 @ ( mbox @ r2 @ Phi ) ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_4s_for_r3_r1,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r1 @ ( mbox @ r3 @ Phi ) ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_4s_for_r3_r2,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r2 @ ( mbox @ r3 @ Phi ) ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_4s_for_r3_r3,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mbox @ r3 @ Phi ) @ ( mbox @ r3 @ ( mbox @ r3 @ Phi ) ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_5_for_r1,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r1 @ Phi ) ) @ ( mbox @ r1 @ ( mnot @ ( mbox @ r1 @ Phi ) ) ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_5_for_r2,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r2 @ Phi ) ) @ ( mbox @ r2 @ ( mnot @ ( mbox @ r2 @ Phi ) ) ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(axiom_5_for_r3,axiom,
% 0.10/0.40 ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r3 @ Phi ) ) @ ( mbox @ r3 @ ( mnot @ ( mbox @ r3 @ Phi ) ) ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 thf(conj,conjecture,
% 0.10/0.40 ( ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r1 @ Phi ) ) @ ( mbox @ r1 @ ( mnot @ ( mbox @ r1 @ Phi ) ) ) ) ) )
% 0.10/0.40 & ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r1 @ Phi ) ) @ ( mbox @ r2 @ ( mnot @ ( mbox @ r1 @ Phi ) ) ) ) ) )
% 0.10/0.40 & ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r1 @ Phi ) ) @ ( mbox @ r3 @ ( mnot @ ( mbox @ r1 @ Phi ) ) ) ) ) )
% 0.10/0.40 & ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r2 @ Phi ) ) @ ( mbox @ r1 @ ( mnot @ ( mbox @ r2 @ Phi ) ) ) ) ) )
% 0.10/0.40 & ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r2 @ Phi ) ) @ ( mbox @ r2 @ ( mnot @ ( mbox @ r2 @ Phi ) ) ) ) ) )
% 0.10/0.40 & ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r2 @ Phi ) ) @ ( mbox @ r3 @ ( mnot @ ( mbox @ r2 @ Phi ) ) ) ) ) )
% 0.10/0.40 & ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r3 @ Phi ) ) @ ( mbox @ r1 @ ( mnot @ ( mbox @ r3 @ Phi ) ) ) ) ) )
% 0.10/0.40 & ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r3 @ Phi ) ) @ ( mbox @ r2 @ ( mnot @ ( mbox @ r3 @ Phi ) ) ) ) ) )
% 0.10/0.40 & ( mvalid
% 0.10/0.40 @ ( mforall_prop
% 0.10/0.40 @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ r3 @ Phi ) ) @ ( mbox @ r3 @ ( mnot @ ( mbox @ r3 @ Phi ) ) ) ) ) ) ) ).
% 0.10/0.40
% 0.10/0.40 %------------------------------------------------------------------------------
% 0.10/0.40 ------------------------
% 0.10/0.40 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found.
% 0.10/0.40 ---- Embedded in THF ---
% 0.10/0.40 ------------------------
% 0.10/0.42 ---- Cleaned THF ---
% 0.10/0.42 ------------------------
% 0.10/0.45 % (3796818)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3796799 for (3000ds/2Mi)
% 0.10/0.45 % (3796818)First to succeed.
% 0.10/0.45 % SZS status Satisfiable for DTF2THF_3796799
% 0.10/0.45 % (3796818)# SZS output start Saturation.
% 0.10/0.45 % (3796818)# SZS output end Saturation.
% 0.10/0.45 % (3796818)------------------------------
% 0.10/0.45 % (3796818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.10/0.45 % (3796818)Termination reason: Satisfiable
% 0.10/0.45
% 0.10/0.45 % (3796818)Memory used [KB]: 5373
% 0.10/0.45 % (3796818)Time elapsed: 0.002 s
% 0.10/0.45 % (3796818)Instructions burned: 1 (million)
% 0.10/0.45 % (3796818)------------------------------
% 0.10/0.45 % (3796818)------------------------------
% 0.10/0.45 % (3796814)Success in time 0.011 s
%------------------------------------------------------------------------------