%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV014+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 02:46:26 PM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 71 ( 15 unt; 0 def)
% Number of atoms : 193 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 224 ( 102 ~; 95 |; 18 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 119 ( 117 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
party_of_protocol(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
message(sent(a,b,pair(a,an_a_nonce))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
party_of_protocol(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
fresh_to_b(an_a_nonce),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U,V] :
( ( fresh_to_b(V)
& message(sent(U,b,pair(U,V))) )
=> ( b_stored(pair(U,V))
& message(sent(b,t,triple(b,generate_b_nonce(V),encrypt(triple(U,V,generate_expiration_time(V)),bt)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [V,X,Y] :
( ( b_stored(pair(X,Y))
& message(sent(X,b,pair(encrypt(triple(X,V,generate_expiration_time(Y)),bt),encrypt(generate_b_nonce(Y),V)))) )
=> b_holds(key(V,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
party_of_protocol(t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U,V,W] :
( message(sent(U,V,W))
=> intruder_message(W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U,V] :
( intruder_message(pair(U,V))
=> ( intruder_message(V)
& intruder_message(U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [U,V,W] :
( intruder_message(triple(U,V,W))
=> ( intruder_message(W)
& intruder_message(V)
& intruder_message(U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [U,V] :
( ( intruder_message(V)
& intruder_message(U) )
=> intruder_message(pair(U,V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [U,V,W] :
( ( party_of_protocol(W)
& party_of_protocol(V)
& intruder_message(U) )
=> message(sent(V,W,U)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [V,W] :
( ( party_of_protocol(W)
& intruder_message(V) )
=> intruder_holds(key(V,W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U,V,W] :
( ( party_of_protocol(W)
& intruder_holds(key(V,W))
& intruder_message(U) )
=> intruder_message(encrypt(U,V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
? [U] :
( b_holds(key(U,a))
& intruder_holds(key(U,b)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ? [U] :
( b_holds(key(U,a))
& intruder_holds(key(U,b)) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,plain,
party_of_protocol(a),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f33,plain,
message(sent(a,b,pair(a,an_a_nonce))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f40,plain,
party_of_protocol(b),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f41,plain,
fresh_to_b(an_a_nonce),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f42,plain,
! [U,V] :
( ( b_stored(pair(U,V))
& message(sent(b,t,triple(b,generate_b_nonce(V),encrypt(triple(U,V,generate_expiration_time(V)),bt)))) )
| ~ fresh_to_b(V)
| ~ message(sent(U,b,pair(U,V))) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f43,plain,
! [X0,X1] :
( message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt))))
| ~ fresh_to_b(X1)
| ~ message(sent(X0,b,pair(X0,X1))) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( b_stored(pair(X0,X1))
| ~ fresh_to_b(X1)
| ~ message(sent(X0,b,pair(X0,X1))) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [V,X,Y] :
( b_holds(key(V,X))
| ~ b_stored(pair(X,Y))
| ~ message(sent(X,b,pair(encrypt(triple(X,V,generate_expiration_time(Y)),bt),encrypt(generate_b_nonce(Y),V)))) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f46,plain,
! [V,X] :
( b_holds(key(V,X))
| ! [Y] :
( ~ b_stored(pair(X,Y))
| ~ message(sent(X,b,pair(encrypt(triple(X,V,generate_expiration_time(Y)),bt),encrypt(generate_b_nonce(Y),V)))) ) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( b_holds(key(X1,X0))
| ~ b_stored(pair(X0,X2))
| ~ message(sent(X0,b,pair(encrypt(triple(X0,X1,generate_expiration_time(X2)),bt),encrypt(generate_b_nonce(X2),X1)))) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
party_of_protocol(t),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f53,plain,
! [U,V,W] :
( intruder_message(W)
| ~ message(sent(U,V,W)) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f54,plain,
! [W] :
( intruder_message(W)
| ! [U,V] : ~ message(sent(U,V,W)) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( intruder_message(X2)
| ~ message(sent(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [U,V] :
( ( intruder_message(V)
& intruder_message(U) )
| ~ intruder_message(pair(U,V)) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f58,plain,
! [X0,X1] :
( intruder_message(X1)
| ~ intruder_message(pair(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f59,plain,
! [U,V,W] :
( ( intruder_message(W)
& intruder_message(V)
& intruder_message(U) )
| ~ intruder_message(triple(U,V,W)) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f61,plain,
! [X0,X1,X2] :
( intruder_message(X1)
| ~ intruder_message(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,plain,
! [X0,X1,X2] :
( intruder_message(X2)
| ~ intruder_message(triple(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f68,plain,
! [U,V] :
( intruder_message(pair(U,V))
| ~ intruder_message(V)
| ~ intruder_message(U) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f69,plain,
! [X0,X1] :
( intruder_message(pair(X0,X1))
| ~ intruder_message(X1)
| ~ intruder_message(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f77,plain,
! [U,V,W] :
( message(sent(V,W,U))
| ~ party_of_protocol(W)
| ~ party_of_protocol(V)
| ~ intruder_message(U) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f78,plain,
! [X0,X1,X2] :
( message(sent(X1,X2,X0))
| ~ party_of_protocol(X2)
| ~ party_of_protocol(X1)
| ~ intruder_message(X0) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f79,plain,
! [V,W] :
( intruder_holds(key(V,W))
| ~ party_of_protocol(W)
| ~ intruder_message(V) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f80,plain,
! [X0,X1] :
( intruder_holds(key(X0,X1))
| ~ party_of_protocol(X1)
| ~ intruder_message(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
! [U,V,W] :
( intruder_message(encrypt(U,V))
| ~ party_of_protocol(W)
| ~ intruder_holds(key(V,W))
| ~ intruder_message(U) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f82,plain,
! [U,V] :
( intruder_message(encrypt(U,V))
| ! [W] :
( ~ party_of_protocol(W)
| ~ intruder_holds(key(V,W))
| ~ intruder_message(U) ) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f83,plain,
! [X0,X1,X2] :
( intruder_message(encrypt(X0,X1))
| ~ party_of_protocol(X2)
| ~ intruder_holds(key(X1,X2))
| ~ intruder_message(X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f89,plain,
! [U] :
( ~ b_holds(key(U,a))
| ~ intruder_holds(key(U,b)) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f90,plain,
! [X0] :
( ~ b_holds(key(X0,a))
| ~ intruder_holds(key(X0,b)) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ party_of_protocol(X1)
| ~ intruder_message(X2)
| intruder_message(encrypt(X0,X2))
| ~ party_of_protocol(X1)
| ~ intruder_message(X0) ),
inference(resolution,[status(thm)],[f83,f80]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ intruder_message(X2)
| intruder_message(encrypt(X0,X2))
| ~ party_of_protocol(X1)
| ~ intruder_message(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f92]) ).
fof(f94,plain,
intruder_message(pair(a,an_a_nonce)),
inference(resolution,[status(thm)],[f55,f33]) ).
fof(f95,plain,
intruder_message(an_a_nonce),
inference(resolution,[status(thm)],[f94,f58]) ).
fof(f97,plain,
! [X0,X1] :
( intruder_message(triple(b,generate_b_nonce(X1),encrypt(triple(X0,X1,generate_expiration_time(X1)),bt)))
| ~ fresh_to_b(X1)
| ~ message(sent(X0,b,pair(X0,X1))) ),
inference(resolution,[status(thm)],[f43,f55]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ party_of_protocol(b)
| ~ party_of_protocol(X0)
| ~ intruder_message(pair(encrypt(triple(X0,X2,generate_expiration_time(X1)),bt),encrypt(generate_b_nonce(X1),X2)))
| b_holds(key(X2,X0))
| ~ b_stored(pair(X0,X1)) ),
inference(resolution,[status(thm)],[f47,f78]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ~ party_of_protocol(X0)
| ~ intruder_message(pair(encrypt(triple(X0,X2,generate_expiration_time(X1)),bt),encrypt(generate_b_nonce(X1),X2)))
| b_holds(key(X2,X0))
| ~ b_stored(pair(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f114,f40]) ).
fof(f126,plain,
! [X0,X1] :
( intruder_message(encrypt(triple(X0,X1,generate_expiration_time(X1)),bt))
| ~ fresh_to_b(X1)
| ~ message(sent(X0,b,pair(X0,X1))) ),
inference(resolution,[status(thm)],[f97,f62]) ).
fof(f127,plain,
! [X0,X1] :
( intruder_message(generate_b_nonce(X1))
| ~ fresh_to_b(X1)
| ~ message(sent(X0,b,pair(X0,X1))) ),
inference(resolution,[status(thm)],[f97,f61]) ).
fof(f139,plain,
( intruder_message(generate_b_nonce(an_a_nonce))
| ~ fresh_to_b(an_a_nonce) ),
inference(resolution,[status(thm)],[f127,f33]) ).
fof(f141,plain,
intruder_message(generate_b_nonce(an_a_nonce)),
inference(forward_subsumption_resolution,[status(thm)],[f139,f41]) ).
fof(f145,plain,
! [X0,X1,X2] :
( ~ intruder_message(encrypt(generate_b_nonce(X1),X2))
| ~ intruder_message(encrypt(triple(X0,X2,generate_expiration_time(X1)),bt))
| ~ party_of_protocol(X0)
| b_holds(key(X2,X0))
| ~ b_stored(pair(X0,X1)) ),
inference(resolution,[status(thm)],[f115,f69]) ).
fof(f146,plain,
! [X0,X1] :
( ~ fresh_to_b(X1)
| ~ message(sent(X0,b,pair(X0,X1)))
| ~ intruder_message(encrypt(generate_b_nonce(X1),X1))
| ~ party_of_protocol(X0)
| b_holds(key(X1,X0))
| ~ b_stored(pair(X0,X1)) ),
inference(resolution,[status(thm)],[f145,f126]) ).
fof(f148,plain,
! [X0,X1] :
( ~ fresh_to_b(X0)
| ~ message(sent(X1,b,pair(X1,X0)))
| ~ intruder_message(encrypt(generate_b_nonce(X0),X0))
| ~ party_of_protocol(X1)
| b_holds(key(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f44]) ).
fof(f149,plain,
( ~ fresh_to_b(an_a_nonce)
| ~ intruder_message(encrypt(generate_b_nonce(an_a_nonce),an_a_nonce))
| ~ party_of_protocol(a)
| b_holds(key(an_a_nonce,a)) ),
inference(resolution,[status(thm)],[f148,f33]) ).
fof(f151,plain,
( ~ fresh_to_b(an_a_nonce)
| ~ intruder_message(encrypt(generate_b_nonce(an_a_nonce),an_a_nonce))
| b_holds(key(an_a_nonce,a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f32]) ).
fof(f154,plain,
( ~ intruder_message(encrypt(generate_b_nonce(an_a_nonce),an_a_nonce))
| b_holds(key(an_a_nonce,a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f41]) ).
fof(f155,plain,
! [X0] :
( ~ intruder_message(an_a_nonce)
| ~ party_of_protocol(X0)
| ~ intruder_message(generate_b_nonce(an_a_nonce))
| b_holds(key(an_a_nonce,a)) ),
inference(resolution,[status(thm)],[f154,f93]) ).
fof(f156,plain,
! [X0] :
( ~ intruder_message(an_a_nonce)
| ~ party_of_protocol(X0)
| b_holds(key(an_a_nonce,a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f141]) ).
fof(f157,plain,
! [X0] :
( ~ party_of_protocol(X0)
| b_holds(key(an_a_nonce,a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f95]) ).
fof(f158,plain,
! [X0] :
( ~ intruder_holds(key(an_a_nonce,b))
| ~ party_of_protocol(X0) ),
inference(resolution,[status(thm)],[f157,f90]) ).
fof(f159,plain,
! [X0] :
( ~ party_of_protocol(b)
| ~ intruder_message(an_a_nonce)
| ~ party_of_protocol(X0) ),
inference(resolution,[status(thm)],[f158,f80]) ).
fof(f160,plain,
! [X0] :
( ~ party_of_protocol(b)
| ~ party_of_protocol(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f95]) ).
fof(f162,plain,
! [X0] : ~ party_of_protocol(X0),
inference(forward_subsumption_resolution,[status(thm)],[f160,f40]) ).
fof(f163,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f50,f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV014+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n018.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 08:28:58 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.18/0.48 % Refutation found
% 0.18/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.53 % Elapsed time: 0.083209 seconds
% 0.18/0.53 % CPU time: 0.148404 seconds
% 0.18/0.53 % Total memory used: 14.945 MB
% 0.18/0.53 % Net memory used: 14.885 MB
%------------------------------------------------------------------------------