%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV331-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 09:07:26 AM UTC 2026
% Result : Unsatisfiable 89.15s 12.94s
% Output : CNFRefutation 89.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 10 ( 1 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_5,axiom,
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('theBenchmark.p',cls_conjecture_5) ).
cnf(c_384,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(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_2,axiom,
c_in(v_K,c_Message_OsymKeys,tc_nat),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_387,plain,
c_in(v_K,c_Message_OsymKeys,tc_nat),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_388,plain,
~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_389,plain,
c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Public_OCrypt__imp__keysFor_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(VAR_0,c_Message_OkeysFor(VAR_2),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(VAR_0,VAR_1),VAR_2,tc_Message_Omsg)
| ~ c_in(VAR_0,c_Message_OsymKeys,tc_nat) ),
file('theBenchmark.p',cls_Public_OCrypt__imp__keysFor_0) ).
cnf(c_395,plain,
( c_in(A,c_Message_OkeysFor(C),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(A,B),C,tc_Message_Omsg)
| ~ c_in(A,c_Message_OsymKeys,tc_nat) ),
inference(clausify,[status(thm)],[cls_Public_OCrypt__imp__keysFor_0]) ).
fof(cls_Yahalom_Onew__keys__not__used_0,axiom,
! [VAR_0,VAR_1] :
( c_in(c_Message_Omsg_OKey(VAR_0),c_Event_Oused(VAR_1),tc_Message_Omsg)
| ~ c_in(VAR_1,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(VAR_0,c_Message_OsymKeys,tc_nat)
| ~ c_in(VAR_0,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,VAR_1))),tc_nat) ),
file('theBenchmark.p',cls_Yahalom_Onew__keys__not__used_0) ).
cnf(c_398,plain,
( c_in(c_Message_Omsg_OKey(A),c_Event_Oused(B),tc_Message_Omsg)
| ~ c_in(B,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(A,c_Message_OsymKeys,tc_nat)
| ~ c_in(A,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,B))),tc_nat) ),
inference(clausify,[status(thm)],[cls_Yahalom_Onew__keys__not__used_0]) ).
cnf(c_13186,plain,
( c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat)
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat) ),
inference(resolve,[status(thm)],[c_395,c_384]) ).
cnf(c_4302,plain,
c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat),
inference(resolve,[status(thm)],[c_387,c_13186]) ).
cnf(c_13187,plain,
( c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg)
| ~ c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat) ),
inference(resolve,[status(thm)],[c_4302,c_398]) ).
cnf(c_13188,plain,
( c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg)
| ~ c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(resolve,[status(thm)],[c_387,c_13187]) ).
cnf(c_13189,plain,
c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg),
inference(resolve,[status(thm)],[c_389,c_13188]) ).
cnf(c_13185,plain,
$false,
inference(resolve,[status(thm)],[c_388,c_13189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV331-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n007.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 13:31:09 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 3849905 was started by sandbox on n007,
% 0.16/0.43 % Sat Sep 26 13:31:09 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.28/0.58
% 0.28/0.58 % From the command line: assign(max_seconds, 300).
% 89.15/12.94
% 89.15/12.94 % given #500 (I,wt=13): 860 -class_Orderings_Oord(A) | -c_in(B,c_SetInterval_OgreaterThanLessThan(C,D,A),A) | c_less(B,D,A) # tptp_name(cls_SetInterval_OgreaterThanLessThan__iff_1) # clausal_fof(1). [assumption].
% 89.15/12.94
% 89.15/12.94 % given #1000 (I,wt=36): 1554 -class_Numeral_Onumber(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Ring__and__Field_Oordered__field(A) | -c_less(B,c_times(C,c_Numeral_Onumber__of(D,A),A),A) | -c_less(c_Numeral_Onumber__of(D,A),c_0,A) | c_less(C,c_divide(B,c_Numeral_Onumber__of(D,A),A),A) | c_less(c_0,c_Numeral_Onumber__of(D,A),A) # tptp_name(cls_NatSimprocs_Oless__divide__eq__number__of_4) # clausal_fof(1). [assumption].
% 89.15/12.94
% 89.15/12.94 % given #1500 (I,wt=17): 2293 -class_Ring__and__Field_Ocomm__ring__1(A) | -c_in(B,c_IntDef_OInts,A) | -c_in(C,c_IntDef_OInts,A) | c_in(c_times(C,B,A),c_IntDef_OInts,A) # tptp_name(cls_IntDef_OInts__mult_0) # clausal_fof(1). [assumption].
% 89.15/12.94
% 89.15/12.94 % given #2000 (I,wt=4): 2902 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # tptp_name(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) # clausal_fof(1). [assumption].
% 89.15/12.94
% 89.15/12.94 % given #2500 (I,wt=21): 3416 -c_in(A,c_Relation_Odiag(B,C),tc_prod(C,C)) | c_Pair(c_Main_OdiagE__1(B,A,C),c_Main_OdiagE__1(B,A,C),C,C) = A. [copy(3415),flip(b)].
% 89.15/12.94
% 89.15/12.94 % given #3000 (I,wt=16): 4009 -class_Ring__and__Field_Ocomm__ring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_uminus(c_1,A),B,A) | c_lessequals(c_uminus(B,A),c_1,A). [resolve(63,b,51,a)].
% 89.15/12.94
% 89.15/12.94 % SZS status Unsatisfiable for theBenchmark
% 89.15/12.94
% 89.15/12.94 % Proof 1 at 11.10 (+ 0.94) seconds.
% 89.15/12.94 % Length of proof is 8.
% 89.15/12.94 % Level of proof is 2.
% 89.15/12.94 % Maximum clause weight is 23.000.
% 89.15/12.94 % Given clauses 3280.
% 89.15/12.94
% 89.15/12.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------