%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : LCL414^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 11:34:08 AM UTC 2026
% Result : CounterSatisfiable 0.21s 0.48s
% Output : Saturation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL414^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 5 06:26:23 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.41 ---- Original DTF file ---
% 0.12/0.41 thf(spec,logic,$$dhol).
% 0.12/0.41 %------------------------------------------------------------------------------
% 0.12/0.41 % File : LCL414^7 : TPTP v9.3.1. Released v5.5.0.
% 0.12/0.41 % Domain : Logic Calculi
% 0.12/0.41 % Problem : Peter Andrews Problem THM147
% 0.12/0.41 % Version : [Ben12] axioms.
% 0.12/0.41 % English :
% 0.12/0.41
% 0.12/0.41 % Refs : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
% 0.12/0.41 % : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% 0.12/0.41 % Source : [Ben12]
% 0.12/0.41 % Names : s4-cumul-GLC414+1 [Ben12]
% 0.12/0.41
% 0.12/0.41 % Status : Theorem
% 0.12/0.41 % Rating : 1.00 v8.2.0, 0.92 v8.1.0, 1.00 v5.5.0
% 0.12/0.41 % Syntax : Number of formulae : 78 ( 35 unt; 39 typ; 32 def)
% 0.12/0.41 % Number of atoms : 156 ( 36 equ; 0 cnn)
% 0.12/0.41 % Maximal formula atoms : 48 ( 4 avg)
% 0.12/0.41 % Number of connectives : 235 ( 5 ~; 5 |; 9 &; 206 @)
% 0.12/0.41 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.12/0.41 % Maximal formula depth : 24 ( 2 avg)
% 0.12/0.41 % Number of types : 3 ( 1 usr)
% 0.12/0.41 % Number of type conns : 185 ( 185 >; 0 *; 0 +; 0 <<)
% 0.12/0.41 % Number of symbols : 40 ( 38 usr; 1 con; 0-3 aty)
% 0.12/0.41 % Number of variables : 105 ( 59 ^; 39 !; 7 ?; 105 :)
% 0.12/0.41 % SPC : TH0_THM_EQU_NAR_NDT
% 0.12/0.41
% 0.12/0.41 % Comments : Goedel translation of LCL414+1
% 0.12/0.41 %------------------------------------------------------------------------------
% 0.12/0.41 %----Include axioms for Modal logic S4 under cumulative domains
% 0.12/0.41 include('Axioms/LCL015^0.ax').
% 0.12/0.41 include('Axioms/LCL013^5.ax').
% 0.12/0.41 include('Axioms/LCL015^1.ax').
% 0.12/0.41 %------------------------------------------------------------------------------
% 0.12/0.41 thf(a_truth_type,type,
% 0.12/0.41 a_truth: mu > $i > $o ).
% 0.12/0.41
% 0.12/0.41 thf(not_type,type,
% 0.12/0.41 not: mu > mu ).
% 0.12/0.41
% 0.12/0.41 thf(existence_of_not_ax,axiom,
% 0.12/0.41 ! [V: $i,V1: mu] : ( exists_in_world @ ( not @ V1 ) @ V ) ).
% 0.12/0.41
% 0.12/0.41 thf(implies_type,type,
% 0.12/0.41 implies: mu > mu > mu ).
% 0.12/0.41
% 0.12/0.41 thf(existence_of_implies_ax,axiom,
% 0.12/0.41 ! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( implies @ V2 @ V1 ) @ V ) ).
% 0.12/0.41
% 0.12/0.41 thf(thm147,conjecture,
% 0.12/0.41 ( mvalid
% 0.12/0.41 @ ( mbox_s4
% 0.12/0.41 @ ( mnot
% 0.12/0.41 @ ( mand
% 0.12/0.41 @ ( mbox_s4
% 0.12/0.41 @ ( mforall_ind
% 0.12/0.41 @ ^ [P: mu] :
% 0.12/0.41 ( mbox_s4
% 0.12/0.41 @ ( mforall_ind
% 0.12/0.41 @ ^ [Q: mu] : ( mor @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( a_truth @ ( implies @ P @ Q ) ) ) ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( a_truth @ P ) ) ) ) @ ( mbox_s4 @ ( a_truth @ Q ) ) ) ) ) ) ) )
% 0.12/0.41 @ ( mand
% 0.12/0.41 @ ( mbox_s4
% 0.12/0.41 @ ( mforall_ind
% 0.12/0.41 @ ^ [P: mu] :
% 0.12/0.41 ( mbox_s4
% 0.12/0.41 @ ( mforall_ind
% 0.12/0.41 @ ^ [Q: mu] : ( mbox_s4 @ ( a_truth @ ( implies @ P @ ( implies @ Q @ P ) ) ) ) ) ) ) )
% 0.12/0.41 @ ( mand
% 0.12/0.41 @ ( mbox_s4
% 0.12/0.41 @ ( mforall_ind
% 0.12/0.41 @ ^ [P: mu] :
% 0.12/0.41 ( mbox_s4
% 0.12/0.41 @ ( mforall_ind
% 0.12/0.41 @ ^ [Q: mu] :
% 0.12/0.41 ( mbox_s4
% 0.12/0.41 @ ( mforall_ind
% 0.12/0.41 @ ^ [R: mu] : ( mbox_s4 @ ( a_truth @ ( implies @ ( implies @ P @ ( implies @ Q @ R ) ) @ ( implies @ ( implies @ P @ Q ) @ ( implies @ P @ R ) ) ) ) ) ) ) ) ) ) )
% 0.12/0.41 @ ( mand
% 0.12/0.41 @ ( mbox_s4
% 0.12/0.41 @ ( mforall_ind
% 0.12/0.41 @ ^ [P: mu] :
% 0.12/0.41 ( mbox_s4
% 0.12/0.41 @ ( mforall_ind
% 0.12/0.41 @ ^ [Q: mu] : ( mbox_s4 @ ( a_truth @ ( implies @ ( implies @ ( not @ P ) @ ( not @ Q ) ) @ ( implies @ Q @ P ) ) ) ) ) ) ) )
% 0.12/0.41 @ ( mexists_ind
% 0.12/0.41 @ ^ [A: mu] : ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( a_truth @ ( implies @ A @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.12/0.41
% 0.12/0.41 %------------------------------------------------------------------------------
% 0.12/0.41 ------------------------
% 0.12/0.41 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found.
% 0.12/0.42 ---- Embedded in THF ---
% 0.12/0.42 ------------------------
% 0.12/0.44 ---- Cleaned THF ---
% 0.12/0.45 ------------------------
% 0.21/0.48 % (371400)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_371381 for (2999ds/2Mi)
% 0.21/0.48 % (371400)First to succeed.
% 0.21/0.48 % SZS status Satisfiable for DTF2THF_371381
% 0.21/0.48 % (371400)# SZS output start Saturation.
% 0.21/0.48 % (371400)# SZS output end Saturation.
% 0.21/0.48 % (371400)------------------------------
% 0.21/0.48 % (371400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.21/0.48 % (371400)Termination reason: Satisfiable
% 0.21/0.48
% 0.21/0.48 % (371400)Memory used [KB]: 5373
% 0.21/0.48 % (371400)Time elapsed: 0.001 s
% 0.21/0.48 % (371400)------------------------------
% 0.21/0.48 % (371400)------------------------------
% 0.21/0.48 % (371396)Success in time 0.012 s
%------------------------------------------------------------------------------