%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV798-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 09:09:08 AM UTC 2026
% Result : Unsatisfiable 227.23s 30.48s
% Output : CNFRefutation 227.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 43 ( 31 unt; 0 def)
% Number of atoms : 60 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 21 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 5 con; 0-3 aty)
% Number of variables : 104 ( 40 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_set__empty_1,axiom,
! [VAR_0] : c_List_Oset(c_List_Olist_ONil(VAR_0),VAR_0) = c_Orderings_Obot__class_Obot(tc_fun(VAR_0,tc_bool)),
file('theBenchmark.p',cls_set__empty_1) ).
cnf(c_102,plain,
c_List_Oset(c_List_Olist_ONil(A),A) = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),
inference(clausify,[status(thm)],[cls_set__empty_1]) ).
fof(cls_bot1E_0,axiom,
! [VAR_0,VAR_1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(VAR_0,tc_bool)),VAR_1)),
file('theBenchmark.p',cls_bot1E_0) ).
cnf(c_116,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B)),
inference(clausify,[status(thm)],[cls_bot1E_0]) ).
fof(cls_keymode_Oinduct_0,axiom,
! [VAR_0,VAR_1] :
( ~ hBOOL(hAPP(VAR_0,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(VAR_0,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(VAR_0,VAR_1)) ),
file('theBenchmark.p',cls_keymode_Oinduct_0) ).
cnf(c_144,plain,
( ~ hBOOL(hAPP(A,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(A,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(A,B)) ),
inference(clausify,[status(thm)],[cls_keymode_Oinduct_0]) ).
fof(cls_eq__Nil__appendI_0,axiom,
! [VAR_0,VAR_1] : VAR_0 = c_List_Oappend(c_List_Olist_ONil(VAR_1),VAR_0,VAR_1),
file('theBenchmark.p',cls_eq__Nil__appendI_0) ).
cnf(c_158,plain,
A = c_List_Oappend(c_List_Olist_ONil(B),A,B),
inference(clausify,[status(thm)],[cls_eq__Nil__appendI_0]) ).
cnf(c_159,plain,
c_List_Oappend(c_List_Olist_ONil(A),B,A) = B,
inference(copy,[status(thm)],[c_158]) ).
fof(cls_in__set__conv__decomp_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : hBOOL(c_in(VAR_0,c_List_Oset(c_List_Oappend(VAR_1,c_List_Olist_OCons(VAR_0,VAR_2,VAR_3),VAR_3),VAR_3),VAR_3)),
file('theBenchmark.p',cls_in__set__conv__decomp_1) ).
cnf(c_270,plain,
hBOOL(c_in(A,c_List_Oset(c_List_Oappend(B,c_List_Olist_OCons(A,C,D),D),D),D)),
inference(clausify,[status(thm)],[cls_in__set__conv__decomp_1]) ).
fof(cls_Nonce__supply1_0,axiom,
! [VAR_0] : ~ hBOOL(c_in(c_Message_Omsg_ONonce(c_Public_Osko__Public__XNonce__supply1__1__1(VAR_0)),c_Event_Oused(VAR_0),tc_Message_Omsg)),
file('theBenchmark.p',cls_Nonce__supply1_0) ).
cnf(c_393,plain,
~ hBOOL(c_in(c_Message_Omsg_ONonce(c_Public_Osko__Public__XNonce__supply1__1__1(A)),c_Event_Oused(A),tc_Message_Omsg)),
inference(clausify,[status(thm)],[cls_Nonce__supply1_0]) ).
fof(cls_insert__code_1,axiom,
! [VAR_0,VAR_1,VAR_2] : hBOOL(hAPP(c_Set_Oinsert(VAR_0,VAR_1,VAR_2),VAR_0)),
file('theBenchmark.p',cls_insert__code_1) ).
cnf(c_476,plain,
hBOOL(hAPP(c_Set_Oinsert(A,B,C),A)),
inference(clausify,[status(thm)],[cls_insert__code_1]) ).
fof(cls_insert__code_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ hBOOL(hAPP(c_Set_Oinsert(VAR_2,VAR_0,VAR_3),VAR_1))
| VAR_2 = VAR_1
| hBOOL(hAPP(VAR_0,VAR_1)) ),
file('theBenchmark.p',cls_insert__code_0) ).
cnf(c_479,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(C,A,D),B))
| C = B
| hBOOL(hAPP(A,B)) ),
inference(clausify,[status(thm)],[cls_insert__code_0]) ).
fof(cls_insert__code_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ hBOOL(hAPP(VAR_1,VAR_3))
| hBOOL(hAPP(c_Set_Oinsert(VAR_0,VAR_1,VAR_2),VAR_3)) ),
file('theBenchmark.p',cls_insert__code_2) ).
cnf(c_484,plain,
( ~ hBOOL(hAPP(B,D))
| hBOOL(hAPP(c_Set_Oinsert(A,B,C),D)) ),
inference(clausify,[status(thm)],[cls_insert__code_2]) ).
fof(cls_not__Cons__self_0,axiom,
! [VAR_0,VAR_1,VAR_2] : VAR_0 != c_List_Olist_OCons(VAR_1,VAR_0,VAR_2),
file('theBenchmark.p',cls_not__Cons__self_0) ).
cnf(c_551,plain,
A != c_List_Olist_OCons(B,A,C),
inference(clausify,[status(thm)],[cls_not__Cons__self_0]) ).
cnf(c_552,plain,
c_List_Olist_OCons(A,B,C) != B,
inference(copy,[status(thm)],[c_551]) ).
fof(cls_used__Gets_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(VAR_0,VAR_1),VAR_2,tc_Event_Oevent)) = c_Event_Oused(VAR_2),
file('theBenchmark.p',cls_used__Gets_0) ).
cnf(c_581,plain,
c_Event_Oused(c_List_Olist_OCons(c_Event_Oevent_OGets(A,B),C,tc_Event_Oevent)) = c_Event_Oused(C),
inference(clausify,[status(thm)],[cls_used__Gets_0]) ).
fof(cls_Says__imp__used_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ hBOOL(c_in(c_Event_Oevent_OSays(VAR_2,VAR_3,VAR_0),c_List_Oset(VAR_1,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(VAR_0,c_Event_Oused(VAR_1),tc_Message_Omsg)) ),
file('theBenchmark.p',cls_Says__imp__used_0) ).
cnf(c_592,plain,
( ~ hBOOL(c_in(c_Event_Oevent_OSays(C,D,A),c_List_Oset(B,tc_Event_Oevent),tc_Event_Oevent))
| hBOOL(c_in(A,c_Event_Oused(B),tc_Message_Omsg)) ),
inference(clausify,[status(thm)],[cls_Says__imp__used_0]) ).
cnf(c_789,plain,
~ hBOOL(hAPP(c_List_Oset(c_List_Olist_ONil(A),A),B)),
inference(paramod,[status(thm)],[c_102,c_116]) ).
cnf(c_938,plain,
hBOOL(c_in(A,c_List_Oset(c_List_Olist_OCons(A,B,C),C),C)),
inference(paramod,[status(thm)],[c_159,c_270]) ).
cnf(c_1584,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,A,B),c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,A,B),C)) ),
inference(resolve,[status(thm)],[c_476,c_144]) ).
cnf(c_1699,plain,
hBOOL(hAPP(c_Set_Oinsert(A,c_Set_Oinsert(B,C,D),E),B)),
inference(resolve,[status(thm)],[c_484,c_476]) ).
cnf(c_21819,plain,
hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,c_Set_Oinsert(c_Public_Okeymode_OEncryption,A,B),C),D)),
inference(resolve,[status(thm)],[c_1584,c_1699]) ).
cnf(c_21830,plain,
( c_Public_Okeymode_OSignature = C
| hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OEncryption,A,B),C)) ),
inference(resolve,[status(thm)],[c_21819,c_479]) ).
cnf(c_21865,plain,
( c_Public_Okeymode_OEncryption = A
| hBOOL(hAPP(B,A))
| c_Public_Okeymode_OSignature = A ),
inference(resolve,[status(thm)],[c_21830,c_479]) ).
cnf(c_21884,plain,
( c_Public_Okeymode_OEncryption = A
| c_Public_Okeymode_OSignature = A ),
inference(resolve,[status(thm)],[c_21865,c_789]) ).
cnf(c_22059,plain,
B != c_List_Olist_OCons(A,B,C),
inference(copy,[status(thm)],[c_552]) ).
cnf(c_22060,plain,
c_Public_Okeymode_OEncryption = c_List_Olist_OCons(A,c_Public_Okeymode_OSignature,B),
inference(resolve,[status(thm)],[c_21884,c_22059]) ).
cnf(c_21885,plain,
c_List_Olist_OCons(A,c_Public_Okeymode_OSignature,B) = c_Public_Okeymode_OEncryption,
inference(copy,[status(thm)],[c_22060]) ).
cnf(c_22061,plain,
c_Event_Oused(c_Public_Okeymode_OEncryption) = c_Event_Oused(c_Public_Okeymode_OSignature),
inference(paramod,[status(thm)],[c_21885,c_581]) ).
cnf(c_21898,plain,
c_Event_Oused(c_Public_Okeymode_OSignature) = c_Event_Oused(c_Public_Okeymode_OEncryption),
inference(copy,[status(thm)],[c_22061]) ).
cnf(c_21914,plain,
hBOOL(c_in(A,c_List_Oset(c_Public_Okeymode_OEncryption,B),B)),
inference(paramod,[status(thm)],[c_21885,c_938]) ).
cnf(c_21989,plain,
~ hBOOL(c_in(c_Message_Omsg_ONonce(c_Public_Osko__Public__XNonce__supply1__1__1(c_Public_Okeymode_OSignature)),c_Event_Oused(c_Public_Okeymode_OEncryption),tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_21898,c_393]) ).
cnf(c_22057,plain,
hBOOL(c_in(A,c_Event_Oused(c_Public_Okeymode_OEncryption),tc_Message_Omsg)),
inference(resolve,[status(thm)],[c_21914,c_592]) ).
cnf(c_22058,plain,
$false,
inference(resolve,[status(thm)],[c_22057,c_21989]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV798-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 15:03:31 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 1150318 was started by sandbox2 on n016,
% 0.08/0.35 % Sat Sep 26 15:03:31 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 227.23/30.47
% 227.23/30.47 % given #500 (I,wt=51): 744 -hBOOL(c_in(A,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))) | hBOOL(c_in(B,c_Event_Obad,tc_Message_Oagent)) | hBOOL(c_in(hAPP(c_Message_Omsg_OKey,C),c_Message_Oanalz(c_Event_Oknows(c_Message_Oagent_OSpy,A)),tc_Message_Omsg)) | -hBOOL(c_in(c_Event_Oevent_OSays(B,B,c_Message_Omsg_OCrypt(C,c_Message_Omsg_ONonce(D))),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)) | hBOOL(c_in(c_Event_Oevent_OSays(B,B,v_sko__NS__Shared__Mirabelle__XIssues__def__1(B,B,c_Message_Omsg_OCrypt(C,c_Message_Omsg_ONonce(D)),A)),c_List_Oset(A,tc_Event_Oevent),tc_Event_Oevent)). [factor(712,b,c)].
% 227.23/30.47
% 227.23/30.47 % given #1000 (F,wt=15): 5159 c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oimage(c_Message_Omsg_OKey,c_Message_OsymKeys,tc_nat,tc_Message_Omsg),A,tc_fun(tc_Message_Omsg,tc_bool)) != c_List_Oset(c_List_Olist_ONil(tc_Message_Omsg),tc_Message_Omsg). [para(3093(a,1),801(a,1,1,2))].
% 227.23/30.47
% 227.23/30.47 % given #1500 (W,wt=8): 9593 hBOOL(hAPP(c_Message_Osynth(c_Message_Oanalz(c_NS__Shared__Mirabelle_Ons__shared)),c_Message_Omsg_OMPair(v_evs,v_evs))). [resolve(3406,a,670,b)].
% 227.23/30.47
% 227.23/30.47 % given #2000 (T,wt=9): 8209 hBOOL(hAPP(c_Message_Oparts(c_Set_Oinsert(A,c_Message_Oparts(c_NS__Shared__Mirabelle_Ons__shared),B)),v_evs)). [resolve(1144,b,2868,a)].
% 227.23/30.47
% 227.23/30.47 % given #2500 (F,wt=16): 15193 c_Set_Oimage(A,c_Message_Oparts(c_Set_Oimage(c_Message_Omsg_OKey,c_Message_Osynth(B),C,tc_Message_Omsg)),tc_Message_Omsg,D) != c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool)). [para(3104(a,1),6261(a,1,2,1,2))].
% 227.23/30.47
% 227.23/30.47 % given #3000 (W,wt=9): 17566 c_Message_Oanalzp(c_Message_Oparts(c_Set_Oinsert(A,c_Message_Osynth(c_Message_Oparts(c_Event_Obad)),B)),c_Message_Oagent_OSpy). [para(3645(a,1),8235(a,1,1,2))].
% 227.23/30.47
% 227.23/30.47 % given #3500 (T,wt=10): 11593 c_Message_Oanalzp(c_Message_Osynth(c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OMPair(A,B),C,tc_Message_Omsg))),B). [para(468(a,1),7095(a,1,1))].
% 227.23/30.47
% 227.23/30.47 % given #4000 (F,wt=20): 12102 c_Lattices_Oupper__semilattice__class_Osup(A,c_Set_Oimage(c_Message_Omsg_OKey,c_Lattices_Oupper__semilattice__class_Osup(c_Event_Obad,B,tc_fun(tc_nat,tc_bool)),tc_nat,tc_Message_Omsg),tc_fun(tc_Message_Omsg,tc_bool)) != c_List_Oset(c_List_Olist_ONil(tc_Message_Omsg),tc_Message_Omsg). [para(1016(a,1),3671(a,1))].
% 227.23/30.48
% 227.23/30.48 % SZS status Unsatisfiable for theBenchmark
% 227.23/30.48
% 227.23/30.48 % Proof 1 at 4.61 (+ 1.09) seconds.
% 227.23/30.48 % Length of proof is 28.
% 227.23/30.48 % Level of proof is 9.
% 227.23/30.48 % Maximum clause weight is 16.000.
% 227.23/30.48 % Given clauses 4486.
% 227.23/30.48
% 227.23/30.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------