%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV234+2 : 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 : n004.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 59.20s 7.99s
% Output : CNFRefutation 59.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 52 ( 37 unt; 0 def)
% Number of atoms : 82 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 28 ~; 25 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 74 ( 6 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(encrypt_data_cmd,axiom,
! [X0,X1] :
( ( public(X1)
& public(X0) )
=> public(enc(enc(inv(xor(data,km)),X0),X1)) ) ).
fof(key_import_cmd,axiom,
! [X0,X1,X2] :
( ( public(enc(xor(km,imp),X0))
& public(enc(xor(X0,X1),X2))
& public(X1) )
=> public(enc(xor(km,X1),X2)) ) ).
fof(encrypt_decrypt_cancel,axiom,
! [X0,X1,X2] : enc(X0,enc(inv(X0),X1)) = X1 ).
fof(xor_commutes,axiom,
! [X0,X1,X2] : xor(X0,X1) = xor(X1,X0) ).
fof(xor_assosciative,axiom,
! [X0,X1,X2] : xor(X0,xor(X1,X2)) = xor(xor(X0,X1),X2) ).
fof(xor_self_cancel,axiom,
! [X0,X1,X2] : xor(X0,X0) = z ).
fof(xor_zero,axiom,
! [X0,X1,X2] : xor(X0,z) = X0 ).
fof(initial_knowledge2,axiom,
public(data) ).
fof(initial_knowledge5,axiom,
public(enc(xor(kek,pin),pp)) ).
fof(initial_knowledge8,axiom,
public(a) ).
fof(initial_knowledge9,axiom,
public(enc(xor(km,imp),xor(kek,xor(pin,data)))) ).
fof(co1,conjecture,
public(enc(pp,a)) ).
fof(negated_conjecture,negated_conjecture,
~ public(enc(pp,a)),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c4,plain,
( public(enc(enc(inv(xor(data,km)),X0),X1))
| ~ public(X1)
| ~ public(X0) ),
inference(clausification,[status(esa)],[encrypt_data_cmd]) ).
cnf(c5,plain,
( public(enc(xor(km,X0),X2))
| ~ public(enc(xor(km,imp),X1))
| ~ public(enc(xor(X1,X0),X2))
| ~ public(X0) ),
inference(clausification,[status(esa)],[key_import_cmd]) ).
cnf(c7,plain,
enc(X0,enc(inv(X0),X1)) = X1,
inference(clausification,[status(esa)],[encrypt_decrypt_cancel]) ).
cnf(c8,plain,
xor(X0,X1) = xor(X1,X0),
inference(clausification,[status(esa)],[xor_commutes]) ).
cnf(c9,plain,
xor(X0,xor(X1,X2)) = xor(xor(X0,X1),X2),
inference(clausification,[status(esa)],[xor_assosciative]) ).
cnf(c10,plain,
xor(X0,X0) = z,
inference(clausification,[status(esa)],[xor_self_cancel]) ).
cnf(c11,plain,
xor(X0,z) = X0,
inference(clausification,[status(esa)],[xor_zero]) ).
cnf(c13,plain,
public(data),
inference(clausification,[status(esa)],[initial_knowledge2]) ).
cnf(c16,plain,
public(enc(xor(kek,pin),pp)),
inference(clausification,[status(esa)],[initial_knowledge5]) ).
cnf(c19,plain,
public(a),
inference(clausification,[status(esa)],[initial_knowledge8]) ).
cnf(c20,plain,
public(enc(xor(km,imp),xor(kek,xor(pin,data)))),
inference(clausification,[status(esa)],[initial_knowledge9]) ).
cnf(c21,plain,
~ public(enc(pp,a)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( public(enc(enc(inv(xor(km,data)),X0),X1))
| ~ public(X1)
| ~ public(X0) ),
inference(demodulation,[status(thm)],[c4,c8]) ).
cnf(d1,plain,
enc(X0,X1) = enc(inv(inv(X0)),X1),
inference(superposition,[status(thm)],[c7,c7]) ).
cnf(d2,plain,
enc(inv(X0),enc(X0,X1)) = X1,
inference(superposition,[status(thm)],[d1,c7]) ).
cnf(d3,plain,
( ~ public(X1)
| ~ public(enc(xor(km,data),X0))
| public(enc(X0,X1)) ),
inference(superposition,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
public(enc(xor(pin,kek),pp)),
inference(demodulation,[status(thm)],[c16,c8]) ).
cnf(d5,plain,
xor(X2,xor(X0,X1)) = xor(X0,xor(X1,X2)),
inference(superposition,[status(thm)],[c9,c8]) ).
cnf(d6,plain,
public(enc(xor(km,imp),xor(kek,xor(data,pin)))),
inference(demodulation,[status(thm)],[c20,c8]) ).
cnf(d7,plain,
( public(enc(xor(km,X0),X1))
| ~ public(enc(xor(xor(kek,xor(data,pin)),X0),X1))
| ~ public(X0) ),
inference(resolution,[status(thm)],[d6,c5]) ).
cnf(d8,plain,
( public(enc(xor(km,X0),X1))
| ~ public(enc(xor(kek,xor(xor(data,pin),X0)),X1))
| ~ public(X0) ),
inference(demodulation,[status(thm)],[d7,c9]) ).
cnf(d9,plain,
( public(enc(xor(km,X0),X1))
| ~ public(enc(xor(kek,xor(data,xor(pin,X0))),X1))
| ~ public(X0) ),
inference(demodulation,[status(thm)],[d8,c9]) ).
cnf(d10,plain,
( public(enc(xor(km,X0),X1))
| ~ public(enc(xor(data,xor(xor(pin,X0),kek)),X1))
| ~ public(X0) ),
inference(demodulation,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
( public(enc(xor(km,X0),X1))
| ~ public(enc(xor(data,xor(pin,xor(X0,kek))),X1))
| ~ public(X0) ),
inference(demodulation,[status(thm)],[d10,c9]) ).
cnf(d12,plain,
xor(z,X0) = X0,
inference(superposition,[status(thm)],[c8,c11]) ).
cnf(d13,plain,
X0 = xor(X0,z),
inference(superposition,[status(thm)],[d12,c8]) ).
cnf(d14,plain,
xor(X0,X1) = xor(X0,xor(X1,z)),
inference(superposition,[status(thm)],[c9,d13]) ).
cnf(d15,plain,
xor(X1,X0) = xor(X1,X0),
inference(demodulation,[status(thm)],[d14,c11]) ).
cnf(d16,plain,
xor(X0,xor(X0,X1)) = xor(z,X1),
inference(superposition,[status(thm)],[c10,c9]) ).
cnf(d17,plain,
xor(X1,xor(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
X1 = xor(X0,xor(X0,X1)),
inference(superposition,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
xor(X1,X2) = xor(X0,xor(X2,xor(X0,X1))),
inference(superposition,[status(thm)],[d5,d18]) ).
cnf(d20,plain,
( public(enc(xor(km,data),X0))
| ~ public(data)
| ~ public(enc(xor(kek,pin),X0)) ),
inference(superposition,[status(thm)],[d19,d11]) ).
cnf(d21,plain,
( ~ public(data)
| ~ public(enc(xor(pin,kek),X0))
| public(enc(xor(km,data),X0)) ),
inference(demodulation,[status(thm)],[d20,c8]) ).
cnf(d22,plain,
( ~ public(enc(xor(pin,kek),X0))
| public(enc(xor(km,data),X0)) ),
inference(resolution,[status(thm)],[c13,d21]) ).
cnf(d23,plain,
public(enc(xor(km,data),pp)),
inference(resolution,[status(thm)],[d22,d4]) ).
cnf(d24,plain,
( public(enc(pp,X0))
| ~ public(X0) ),
inference(resolution,[status(thm)],[d23,d3]) ).
cnf(d25,plain,
~ public(a),
inference(resolution,[status(thm)],[d24,c21]) ).
cnf(d26,plain,
$false,
inference(resolution,[status(thm)],[c19,d25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV234+2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 13:21:07 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 59.20/7.99 % SZS status Theorem for theBenchmark.p
% 59.20/7.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------