%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV331-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 : Fri Sep 25 03:12:57 PM UTC 2026
% Result : Unsatisfiable 4.01s 0.92s
% Output : Proof 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 24 unt; 0 def)
% Number of atoms : 52 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-4 aty)
% Number of variables : 25 ( 3 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OCrypt__imp__keysFor_0) ).
fof(f4_nnf,plain,
! [V_K,V_X,V_H] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_K,V_X,V_H] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_in(X0,c_Message_OkeysFor(X2),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(X0,X1),X2,tc_Message_Omsg)
| ~ c_in(X0,c_Message_OsymKeys,tc_nat) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(c_in(X0,c_Message_OsymKeys,tc_nat),true,ifeq(c_in(c_Message_Omsg_OCrypt(X0,X1),X2,tc_Message_Omsg),true,c_in(X0,c_Message_OkeysFor(X2),tc_nat),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f2,negated_conjecture,
c_in(v_K,c_Message_OsymKeys,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2_nnf,plain,
c_in(v_K,c_Message_OsymKeys,tc_nat),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
c_in(v_K,c_Message_OsymKeys,tc_nat),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi1,negated_conjecture,
c_in(v_K,c_Message_OsymKeys,tc_nat) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f3,negated_conjecture,
c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f3_nnf,plain,
c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(hi2,negated_conjecture,
c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h0,plain,
c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi1,hi2]) ).
cnf(f5,axiom,
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_Onew__keys__not__used_0) ).
fof(f5_nnf,plain,
! [V_K,V_evs] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_K,V_evs] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_in(c_Message_Omsg_OKey(X0),c_Event_Oused(X1),tc_Message_Omsg)
| ~ c_in(X1,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(X0,c_Message_OsymKeys,tc_nat)
| ~ c_in(X0,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X1))),tc_nat) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi4,axiom,
ifeq(c_in(X0,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,X1))),tc_nat),true,ifeq(c_in(X0,c_Message_OsymKeys,tc_nat),true,ifeq(c_in(X1,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),true,c_in(c_Message_Omsg_OKey(X0),c_Event_Oused(X1),tc_Message_Omsg),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f0,negated_conjecture,
c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(hi0,negated_conjecture,
c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t3,plain,
c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg) = true,
inference(hyper_resolution,[status(thm)],[hi4,h0,hi1,hi0]) ).
cnf(t15,plain,
c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f1,negated_conjecture,
~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(goal_0,negated_conjecture,
c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg) != true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t15]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV331-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.34 % Computer : n017.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Thu Sep 24 19:10:31 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.01/0.92 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.01/0.92 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------