%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV235+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 09:01:42 AM UTC 2026
% Result : Theorem 200.91s 29.46s
% Output : CNFRefutation 200.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 65 ( 29 unt; 0 def)
% Number of atoms : 144 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 148 ( 69 ~; 66 |; 8 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 117 ( 16 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(xor_commutative,axiom,
! [X0,X1] : xor(X0,X1) = xor(X1,X0) ).
fof(xor_associative,axiom,
! [X0,X1,X2] : xor(X0,xor(X1,X2)) = xor(xor(X0,X1),X2) ).
fof(encryption_decryption_cancellation,axiom,
! [X0,X1] : decrypt(X0,crypt(X0,X1)) = X1 ).
fof(xor_rules_1,axiom,
! [X0] : xor(X0,id) = X0 ).
fof(xor_rules_2,axiom,
! [X0] : xor(X0,X0) = id ).
fof(key_part_import___part_1,axiom,
! [X0,X1] :
( ( p(X1)
& p(X0) )
=> p(crypt(xor(km,xor(kp,X1)),X0)) ) ).
fof(key_part_import___part_3,axiom,
! [X0,X1,X2] :
( ( p(X1)
& p(crypt(xor(km,xor(X1,kp)),X2))
& p(X0) )
=> p(crypt(xor(km,X1),xor(X2,X0))) ) ).
fof(key_translate,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( p(crypt(xor(km,exp),X4))
& p(crypt(xor(km,imp),X3))
& p(X2)
& p(crypt(X0,X1)) )
=> p(crypt(xor(X4,X5),decrypt(xor(X2,X3),crypt(X0,X1)))) ) ).
fof(combine_with_XOR,axiom,
! [X0,X1] :
( ( p(X1)
& p(X0) )
=> p(xor(X0,X1)) ) ).
fof(encrypt_knowledge,axiom,
! [X0,X1] :
( ( p(X0)
& p(X1) )
=> p(crypt(X0,X1)) ) ).
fof(initial_knowledge_of_intruder_2,axiom,
p(imp) ).
fof(initial_knowledge_of_intruder_4,axiom,
p(id) ).
fof(initial_knowledge_of_intruder_11,axiom,
p(exp) ).
fof(an_account_number,axiom,
p(a) ).
fof(find_pin,conjecture,
p(crypt(pp,a)) ).
fof(negated_conjecture,negated_conjecture,
~ p(crypt(pp,a)),
inference(negate_conjecture,[status(cth)],[find_pin]) ).
cnf(c0,plain,
xor(X0,X1) = xor(X1,X0),
inference(clausification,[status(esa)],[xor_commutative]) ).
cnf(c1,plain,
xor(xor(X0,X1),X2) = xor(X0,xor(X1,X2)),
inference(clausification,[status(esa)],[xor_associative]) ).
cnf(c2,plain,
decrypt(X0,crypt(X0,X1)) = X1,
inference(clausification,[status(esa)],[encryption_decryption_cancellation]) ).
cnf(c3,plain,
xor(X0,id) = X0,
inference(clausification,[status(esa)],[xor_rules_1]) ).
cnf(c4,plain,
xor(X0,X0) = id,
inference(clausification,[status(esa)],[xor_rules_2]) ).
cnf(c7,plain,
( p(crypt(xor(km,xor(kp,X0)),X1))
| ~ p(X1)
| ~ p(X0) ),
inference(clausification,[status(esa)],[key_part_import___part_1]) ).
cnf(c9,plain,
( p(crypt(xor(km,X0),xor(X1,X2)))
| ~ p(X2)
| ~ p(X0)
| ~ p(crypt(xor(km,xor(X0,kp)),X1)) ),
inference(clausification,[status(esa)],[key_part_import___part_3]) ).
cnf(c12,plain,
( ~ p(crypt(xor(km,imp),X3))
| ~ p(crypt(xor(km,exp),X0))
| ~ p(crypt(X4,X5))
| ~ p(X2)
| p(crypt(xor(X0,X1),decrypt(xor(X2,X3),crypt(X4,X5)))) ),
inference(clausification,[status(esa)],[key_translate]) ).
cnf(c13,plain,
( p(xor(X1,X0))
| ~ p(X1)
| ~ p(X0) ),
inference(clausification,[status(esa)],[combine_with_XOR]) ).
cnf(c15,plain,
( p(crypt(X0,X1))
| ~ p(X1)
| ~ p(X0) ),
inference(clausification,[status(esa)],[encrypt_knowledge]) ).
cnf(c17,plain,
p(imp),
inference(clausification,[status(esa)],[initial_knowledge_of_intruder_2]) ).
cnf(c19,plain,
p(id),
inference(clausification,[status(esa)],[initial_knowledge_of_intruder_4]) ).
cnf(c26,plain,
p(exp),
inference(clausification,[status(esa)],[initial_knowledge_of_intruder_11]) ).
cnf(c27,plain,
p(a),
inference(clausification,[status(esa)],[an_account_number]) ).
cnf(c28,plain,
~ p(crypt(pp,a)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
xor(id,X0) = X0,
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d1,plain,
xor(X2,xor(X0,X1)) = xor(X0,xor(X1,X2)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d2,plain,
( ~ p(xor(X1,X2))
| ~ p(X0)
| p(xor(X2,xor(X0,X1))) ),
inference(superposition,[status(thm)],[d1,c13]) ).
cnf(d3,plain,
X0 = xor(id,X0),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d4,plain,
( ~ p(xor(X0,X1))
| ~ p(id)
| p(xor(X1,X0)) ),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ p(xor(X1,X0))
| p(xor(X0,X1)) ),
inference(resolution,[status(thm)],[c19,d4]) ).
cnf(d6,plain,
X0 = xor(X0,id),
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d7,plain,
( p(xor(id,X0))
| ~ p(X0) ),
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( p(X0)
| ~ p(X0) ),
inference(demodulation,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
( ~ p(X1)
| ~ p(X0)
| p(crypt(X0,X1)) ),
inference(resolution,[status(thm)],[d8,c15]) ).
cnf(d10,plain,
( ~ p(X0)
| ~ p(X1)
| p(crypt(X0,X1)) ),
inference(resolution,[status(thm)],[d8,d9]) ).
cnf(d11,plain,
( ~ p(crypt(xor(km,exp),id))
| ~ p(crypt(xor(km,imp),X2))
| ~ p(crypt(X3,X4))
| ~ p(X1)
| p(crypt(X0,decrypt(xor(X1,X2),crypt(X3,X4)))) ),
inference(superposition,[status(thm)],[d3,c12]) ).
cnf(d12,plain,
( ~ p(crypt(xor(km,exp),id))
| ~ p(crypt(xor(km,imp),id))
| ~ p(crypt(X2,X3))
| ~ p(X0)
| p(crypt(X1,decrypt(X0,crypt(X2,X3)))) ),
inference(superposition,[status(thm)],[d6,d11]) ).
cnf(d13,plain,
( ~ p(X0)
| ~ p(X1)
| p(crypt(xor(km,xor(X0,kp)),X1)) ),
inference(superposition,[status(thm)],[c0,c7]) ).
cnf(d14,plain,
( p(crypt(xor(km,X1),xor(X0,X2)))
| ~ p(X1)
| ~ p(X2)
| ~ p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[d13,c9]) ).
cnf(d15,plain,
( ~ p(X1)
| ~ p(X0)
| ~ p(X2)
| p(crypt(xor(km,X0),xor(X1,X2))) ),
inference(resolution,[status(thm)],[d8,d14]) ).
cnf(d16,plain,
( ~ p(X1)
| ~ p(X0)
| ~ p(X0)
| p(crypt(xor(km,X1),id)) ),
inference(superposition,[status(thm)],[c4,d15]) ).
cnf(d17,plain,
( ~ p(X1)
| ~ p(X0)
| p(crypt(xor(km,X0),id)) ),
inference(resolution,[status(thm)],[d8,d16]) ).
cnf(d18,plain,
( p(crypt(xor(km,exp),id))
| ~ p(X0) ),
inference(resolution,[status(thm)],[d17,c26]) ).
cnf(d19,plain,
( ~ p(X0)
| p(crypt(xor(km,exp),id)) ),
inference(resolution,[status(thm)],[d8,d18]) ).
cnf(d20,plain,
p(crypt(xor(km,exp),id)),
inference(resolution,[status(thm)],[d19,c19]) ).
cnf(d21,plain,
( ~ p(crypt(xor(km,imp),id))
| p(crypt(X3,decrypt(X0,crypt(X1,X2))))
| ~ p(crypt(X1,X2))
| ~ p(X0) ),
inference(resolution,[status(thm)],[d20,d12]) ).
cnf(d22,plain,
( p(crypt(xor(km,imp),id))
| ~ p(X0) ),
inference(resolution,[status(thm)],[d17,c17]) ).
cnf(d23,plain,
( ~ p(X0)
| p(crypt(xor(km,imp),id)) ),
inference(resolution,[status(thm)],[d8,d22]) ).
cnf(d24,plain,
p(crypt(xor(km,imp),id)),
inference(resolution,[status(thm)],[d23,c19]) ).
cnf(d25,plain,
( ~ p(crypt(X2,X3))
| p(crypt(X1,decrypt(X0,crypt(X2,X3))))
| ~ p(X0) ),
inference(resolution,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
( ~ p(crypt(X2,X3))
| ~ p(X1)
| p(crypt(X0,decrypt(X1,crypt(X2,X3)))) ),
inference(resolution,[status(thm)],[d8,d25]) ).
cnf(d27,plain,
( ~ p(crypt(X0,X1))
| ~ p(X0)
| p(crypt(X2,X1)) ),
inference(superposition,[status(thm)],[c2,d26]) ).
cnf(d28,plain,
( ~ p(crypt(X2,X1))
| ~ p(X2)
| p(crypt(X0,X1)) ),
inference(resolution,[status(thm)],[d8,d27]) ).
cnf(d29,plain,
( ~ p(X0)
| ~ p(X2)
| p(crypt(X1,X2))
| ~ p(X0) ),
inference(resolution,[status(thm)],[d28,d10]) ).
cnf(d30,plain,
( p(crypt(X1,X0))
| ~ p(X0) ),
inference(factoring,[status(thm)],[d29]) ).
cnf(d31,plain,
( ~ p(X1)
| p(crypt(X0,X1)) ),
inference(resolution,[status(thm)],[d8,d30]) ).
cnf(d32,plain,
~ p(a),
inference(resolution,[status(thm)],[d31,c28]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[c27,d32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV235+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n005.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 13:21:01 UTC 2026
% 0.18/0.40 % CPUTime :
% 0.18/0.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 200.91/29.46 % SZS status Theorem for theBenchmark.p
% 200.91/29.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------