%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV345-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 : Thu Sep 24 02:47:25 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.57s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 11 unt; 4 def)
% Number of atoms : 81 ( 18 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 87 ( 42 ~; 41 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 14 con; 0-3 aty)
% Number of variables : 102 ( 102 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2944,axiom,
! [V_evs,V_A_H,V_B_H,V_K,V_na_H,V_nb_H,V_X_H,V_A,V_B,V_na,V_nb,V_X] :
( V_na = V_na_H
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na_H,V_nb_H)))),V_X_H)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2945,axiom,
! [V_evs,V_A_H,V_B_H,V_K,V_na_H,V_nb_H,V_X_H,V_A,V_B,V_na,V_nb,V_X] :
( V_nb = V_nb_H
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na_H,V_nb_H)))),V_X_H)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2948,negated_conjecture,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2949,negated_conjecture,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2950,negated_conjecture,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(v_na,v_nb)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OKey(v_K))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2953,negated_conjecture,
v_nb != c_Message_Omsg_ONonce(v_NB),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6557,plain,
! [V_na_H,V_na] :
( V_na = V_na_H
| ! [V_evs,V_K] :
( ! [V_A,V_B,V_nb,V_X] : ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ! [V_A_H,V_B_H,V_nb_H,V_X_H] : ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na_H,V_nb_H)))),V_X_H)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) ),
inference(miniscoping,[status(thm)],[f2944]) ).
fof(f6558,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( X9 = X4
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X7,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X7),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X8),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X3),c_Message_Omsg_OMPair(X9,X10)))),X11)),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X1,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X3),c_Message_Omsg_OMPair(X4,X5)))),X6)),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(cnf_transformation,[status(thm)],[f6557]) ).
fof(f6559,plain,
! [V_nb_H,V_nb] :
( V_nb = V_nb_H
| ! [V_evs,V_K] :
( ! [V_A,V_B,V_na,V_X] : ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na,V_nb)))),V_X)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ! [V_A_H,V_B_H,V_na_H,V_X_H] : ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,V_A_H,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(V_A_H),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V_B_H),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(V_K),c_Message_Omsg_OMPair(V_na_H,V_nb_H)))),V_X_H)),c_List_Oset(V_evs,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) ),
inference(miniscoping,[status(thm)],[f2945]) ).
fof(f6560,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( X10 = X5
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X7,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X7),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X8),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X3),c_Message_Omsg_OMPair(X9,X10)))),X11)),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X1,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X2),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(X3),c_Message_Omsg_OMPair(X4,X5)))),X6)),c_List_Oset(X0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(X0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(cnf_transformation,[status(thm)],[f6559]) ).
fof(f6563,plain,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(cnf_transformation,[status(thm)],[f2948]) ).
fof(f6564,plain,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(cnf_transformation,[status(thm)],[f2949]) ).
fof(f6565,plain,
c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(v_na,v_nb)))),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OKey(v_K))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(cnf_transformation,[status(thm)],[f2950]) ).
fof(f6568,plain,
v_nb != c_Message_Omsg_ONonce(v_NB),
inference(cnf_transformation,[status(thm)],[f2953]) ).
fof(f7086,definition,
( sQ32_spl
<=> c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f7088,plain,
( sQ32_spl
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(component_clause,[status(thm)],[f7086]) ).
fof(f7102,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7088,f6563]) ).
fof(f7103,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f7102]) ).
fof(f7141,plain,
! [X0,X1,X2,X3,X4] :
( X2 = v_na
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(resolution,[status(thm)],[f6558,f6565]) ).
fof(f7145,definition,
! [X0,X1,X2,X3,X4] :
( sQ43_spl
<=> ( X2 = v_na
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f7146,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ43_spl
| X2 = v_na
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(component_clause,[status(thm)],[f7145]) ).
fof(f7148,plain,
( sQ43_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f7141,f7086,f7145]) ).
fof(f7158,plain,
! [X0,X1,X2,X3,X4] :
( X3 = v_nb
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(resolution,[status(thm)],[f6560,f6565]) ).
fof(f7162,definition,
! [X0,X1,X2,X3,X4] :
( sQ46_spl
<=> ( X3 = v_nb
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f7163,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ46_spl
| X3 = v_nb
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,X0,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(X0),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(X1),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(X2,X3)))),X4)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(component_clause,[status(thm)],[f7162]) ).
fof(f7165,plain,
( sQ46_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f7158,f7086,f7162]) ).
fof(f7422,plain,
( ~ sQ43_spl
| c_Message_Omsg_ONonce(v_NA) = v_na ),
inference(resolution,[status(thm)],[f7146,f6564]) ).
fof(f7426,plain,
( ~ sQ43_spl
| c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_Aa,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OKey(v_K),c_Message_Omsg_OMPair(v_na,c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(backward_demodulation,[status(thm)],[f7422,f6564]) ).
fof(f7528,definition,
( sQ59_spl
<=> v_na = v_na ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f7530,plain,
( sQ59_spl
| v_na != v_na ),
inference(component_clause,[status(thm)],[f7528]) ).
fof(f7535,plain,
( sQ59_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f7530]) ).
fof(f7536,plain,
sQ59_spl,
inference(contradiction_clause,[status(thm)],[f7535]) ).
fof(f7639,plain,
( ~ sQ43_spl
| ~ sQ46_spl
| c_Message_Omsg_ONonce(v_NB) = v_nb ),
inference(resolution,[status(thm)],[f7163,f7426]) ).
fof(f7641,plain,
( ~ sQ43_spl
| ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7639,f6568]) ).
fof(f7642,plain,
( ~ sQ43_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f7641]) ).
fof(f7643,plain,
$false,
inference(sat_refutation,[status(thm)],[f7103,f7148,f7165,f7536,f7642]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV345-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.33 % Computer : n013.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8046.5625MB
% 0.09/0.33 % OS : Linux 6.8.0-71-generic
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Mon Sep 21 08:41:36 UTC 2026
% 0.09/0.33 % CPUTime :
% 0.22/0.46 % Drodi V4.1.1
% 0.22/0.57 % Refutation found
% 0.22/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.22/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.60 % Elapsed time: 0.260834 seconds
% 0.22/0.60 % CPU time: 0.903195 seconds
% 0.22/0.60 % Total memory used: 237.082 MB
% 0.22/0.60 % Net memory used: 236.329 MB
%------------------------------------------------------------------------------