%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV353-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 : Sun Sep 27 09:07:31 AM UTC 2026
% Result : Unsatisfiable 50.02s 17.67s
% Output : CNFRefutation 50.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 52 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 54 ( 28 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 15 con; 0-3 aty)
% Number of variables : 64 ( 30 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_8,axiom,
! [VAR_0] :
( v_NA != v_NAa
| VAR_0 != c_Message_Omsg_OKey(v_K) ),
file('theBenchmark.p',cls_conjecture_8) ).
cnf(c_653,plain,
( v_NA != v_NAa
| A != c_Message_Omsg_OKey(v_K) ),
inference(clausify,[status(thm)],[cls_conjecture_8]) ).
cnf(c_14614,plain,
( v_NA != v_NAa
| c_Message_Omsg_OKey(v_K) != A ),
inference(copy,[status(thm)],[c_653]) ).
cnf(c_14615,plain,
( v_NAa != v_NA
| c_Message_Omsg_OKey(v_K) != A ),
inference(copy,[status(thm)],[c_14614]) ).
cnf(c_654,plain,
v_NAa != v_NA,
inference(copy,[status(thm)],[c_14615]) ).
fof(cls_conjecture_6,axiom,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_655,plain,
~ c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
fof(cls_conjecture_5,axiom,
c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_656,plain,
c_in(c_Event_Oevent_OSays(v_B,c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OCrypt(c_Public_OshrK(v_B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_A),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NA),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_3,axiom,
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_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_658,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_NAa),c_Message_Omsg_ONonce(v_NB))))),v_X)),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_2,axiom,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_659,plain,
c_in(v_evso,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_Yahalom_OSays__unique__NB_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7,VAR_8,VAR_9,VAR_10,VAR_11,VAR_12] :
( VAR_5 = VAR_12
| c_in(VAR_6,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_0)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(VAR_7,VAR_8,c_Message_Omsg_OMPair(VAR_9,c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_10),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_11),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(VAR_12),VAR_6))))),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OGets(VAR_1,c_Message_Omsg_OMPair(VAR_2,c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_3),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_4),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(VAR_5),VAR_6))))),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(VAR_0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_Yahalom_OSays__unique__NB_0) ).
cnf(c_674,plain,
( F = V12
| c_in(V6,c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,A)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OSays(V7,V8,c_Message_Omsg_OMPair(V9,c_Message_Omsg_OCrypt(c_Public_OshrK(V10),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(V11),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(V12),V6))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OGets(B,c_Message_Omsg_OMPair(C,c_Message_Omsg_OCrypt(c_Public_OshrK(D),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(E),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(F),V6))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(clausify,[status(thm)],[cls_Yahalom_OSays__unique__NB_0]) ).
fof(cls_Yahalom_OSays__Server__imp__YM2_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_2),c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_2),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_1),c_Message_Omsg_OMPair(VAR_4,VAR_5))))),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,VAR_1,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(VAR_1),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(VAR_2),c_Message_Omsg_OMPair(VAR_3,c_Message_Omsg_OMPair(VAR_4,VAR_5)))),VAR_6)),c_List_Oset(VAR_0,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(VAR_0,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
file('theBenchmark.p',cls_Yahalom_OSays__Server__imp__YM2_0) ).
cnf(c_675,plain,
( c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(B),c_Message_Omsg_OMPair(E,F))))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,B,c_Message_Omsg_OMPair(c_Message_Omsg_OCrypt(c_Public_OshrK(B),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(C),c_Message_Omsg_OMPair(D,c_Message_Omsg_OMPair(E,F)))),V6)),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)
| ~ c_in(A,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(clausify,[status(thm)],[cls_Yahalom_OSays__Server__imp__YM2_0]) ).
cnf(c_14616,plain,
( E = v_NA
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(A,c_Message_Omsg_OMPair(B,c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(D),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(E),c_Message_Omsg_ONonce(v_NB)))))),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(resolve,[status(thm)],[c_674,c_656]) ).
cnf(c_14617,plain,
( v_NA = E
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(A,c_Message_Omsg_OMPair(B,c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(D),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(E),c_Message_Omsg_ONonce(v_NB)))))),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(copy,[status(thm)],[c_14616]) ).
cnf(c_14618,plain,
( v_NA = E
| c_in(c_Message_Omsg_ONonce(v_NB),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,v_evso)),tc_Message_Omsg)
| ~ c_in(c_Event_Oevent_OGets(A,c_Message_Omsg_OMPair(B,c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(D),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(E),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolve,[status(thm)],[c_659,c_14617]) ).
cnf(c_4372,plain,
( v_NA = E
| ~ c_in(c_Event_Oevent_OGets(A,c_Message_Omsg_OMPair(B,c_Message_Omsg_OCrypt(c_Public_OshrK(C),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(D),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(E),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent) ),
inference(resolve,[status(thm)],[c_655,c_14618]) ).
cnf(c_14619,plain,
( c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB)))))),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(resolve,[status(thm)],[c_675,c_658]) ).
cnf(c_4374,plain,
c_in(c_Event_Oevent_OGets(c_Message_Oagent_OServer,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Ba),c_Message_Omsg_OCrypt(c_Public_OshrK(v_Ba),c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_Aa),c_Message_Omsg_OMPair(c_Message_Omsg_ONonce(v_NAa),c_Message_Omsg_ONonce(v_NB)))))),c_List_Oset(v_evso,tc_Event_Oevent),tc_Event_Oevent),
inference(resolve,[status(thm)],[c_659,c_14619]) ).
cnf(c_14620,plain,
v_NA = v_NAa,
inference(resolve,[status(thm)],[c_4374,c_4372]) ).
cnf(c_14621,plain,
v_NAa = v_NA,
inference(copy,[status(thm)],[c_14620]) ).
cnf(c_14613,plain,
$false,
inference(resolve,[status(thm)],[c_654,c_14621]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV353-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/10.33 % Computer : n012.cluster.edu
% 0.07/10.33 % Model : x86_64 x86_64
% 0.07/10.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/10.33 % Memory : 8046.5625MB
% 0.07/10.33 % OS : Linux 6.8.0-71-generic
% 0.07/10.33 % CPULimit : 300
% 0.07/10.33 % WCLimit : 300
% 0.07/10.33 % DateTime : Sat Sep 26 13:36:31 UTC 2026
% 0.07/10.33 % CPUTime :
% 0.07/10.33 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/10.33 % Process 744227 was started by sandbox2 on n012,
% 0.07/10.33 % Sat Sep 26 13:36:31 2026
% 0.07/10.33 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/10.40
% 0.09/10.40 % From the command line: assign(max_seconds, 300).
% 50.02/17.67
% 50.02/17.67 % given #500 (I,wt=24): 940 -c_less(A,B,tc_nat) | c_in(c_Pair(A,B,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) # tptp_name(cls_Wellfounded__Relations_Oless__than__iff_1) # clausal_fof(1). [assumption].
% 50.02/17.67
% 50.02/17.67 % given #1000 (I,wt=19): 1607 -class_Numeral_Onumber__ring(A) | -class_Ring__and__Field_Oordered__idom(A) | c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,A),A) # tptp_name(cls_Numeral_Obin__rel__simps__11_0) # clausal_fof(1). [assumption].
% 50.02/17.67
% 50.02/17.67 % given #1500 (I,wt=33): 2366 c_append(A,c_List_Olist_OCons(B,c_List_Olist_ONil,C),C) != c_append(D,c_List_Olist_OCons(E,c_List_Olist_ONil,C),C) | A = D # tptp_name(cls_List_Oappend1__eq__conv_0) # clausal_fof(1). [assumption].
% 50.02/17.67
% 50.02/17.67 % given #2000 (I,wt=9): 3044 -class_Ring__and__Field_Oordered__idom(A) | class_OrderedGroup_Ocancel__ab__semigroup__add(A) # tptp_name(clsrel_Ring__and__Field_Oordered__idom_25) # clausal_fof(1). [assumption].
% 50.02/17.67
% 50.02/17.67 % given #2500 (I,wt=55): 3560 -c_in(c_Pair(A,c_List_Olist_OCons(B,C,D),tc_List_Olist(D),tc_List_Olist(D)),c_List_Olistrel(E,D),tc_prod(tc_List_Olist(D),tc_List_Olist(D))) | c_in(c_Pair(c_Main_Olistrel__Cons2__2(E,A,B,C,D),C,tc_List_Olist(D),tc_List_Olist(D)),c_List_Olistrel(E,D),tc_prod(tc_List_Olist(D),tc_List_Olist(D))) # tptp_name(cls_List_Olistrel__Cons2_1) # clausal_fof(1). [assumption].
% 50.02/17.67
% 50.02/17.67 % given #3000 (I,wt=26): 4091 -class_OrderedGroup_Omonoid__mult(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_uminus(c_1,A),A) | c_less(c_1,c_uminus(B,A),A). [resolve(66,b,49,a)].
% 50.02/17.67
% 50.02/17.67 % SZS status Unsatisfiable for theBenchmark
% 50.02/17.67
% 50.02/17.67 % Proof 1 at 6.40 (+ 0.55) seconds.
% 50.02/17.67 % Length of proof is 11.
% 50.02/17.67 % Level of proof is 2.
% 50.02/17.67 % Maximum clause weight is 93.000.
% 50.02/17.67 % Given clauses 3431.
% 50.02/17.67
% 50.02/17.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------