%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW957+1 : TPTP v9.3.1. Released v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 09:12:35 AM UTC 2026
% Result : Theorem 30.32s 4.91s
% Output : CNFRefutation 30.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 61 ( 36 unt; 0 def)
% Number of atoms : 89 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 25 ~; 20 |; 1 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 3 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax45,axiom,
! [X0,X1] : 'constr$usplit'('constr$uconcat'(X0,X1)) = 'tuple$u2'(X0,X1) ).
fof(ax46,axiom,
! [X0,X1,X2,X3] : 'constr$uxor'('constr$uconcat'(X0,X2),'constr$uconcat'(X1,X3)) = 'constr$uconcat'('constr$uxor'(X0,X1),'constr$uxor'(X2,X3)) ).
fof(ax47,axiom,
! [X0,X1] : 'constr$uC'('constr$uxor'(X0,X1)) = 'constr$uxor'('constr$uC'(X0),'constr$uC'(X1)) ).
fof(ax48,axiom,
! [X0] : 'constr$uxor'(X0,X0) = 'constr$uZERO' ).
fof(ax49,axiom,
! [X0] : 'constr$uxor'(X0,'constr$uZERO') = X0 ).
fof(ax50,axiom,
! [X0,X1] : 'constr$uxor'(X0,X1) = 'constr$uxor'(X1,X0) ).
fof(ax51,axiom,
! [X0,X1,X2] : 'constr$uxor'(X0,'constr$uxor'(X1,X2)) = 'constr$uxor'('constr$uxor'(X0,X1),X2) ).
fof(ax52,axiom,
! [X0,X1] :
( ( 'pred$uattacker'(X1)
& 'pred$uattacker'(X0) )
=> 'pred$uattacker'('constr$uxor'(X0,X1)) ) ).
fof(ax54,axiom,
! [X0] :
( 'pred$uattacker'(X0)
=> 'pred$uattacker'('constr$usplit'(X0)) ) ).
fof(ax58,axiom,
! [X0,X1] :
( 'pred$uattacker'('tuple$uenc$uoracle$uout$u2'(X0,X1))
=> 'pred$uattacker'(X1) ) ).
fof(ax59,axiom,
! [X0] :
( 'pred$uattacker'(X0)
=> 'pred$uattacker'('tuple$uenc$uoracle$uin$u1'(X0)) ) ).
fof(ax62,axiom,
'pred$uattacker'('constr$uZERO') ).
fof(ax72,axiom,
! [X0,X1] :
( 'pred$uattacker'('tuple$uB$uout$u1'(X0,X1))
=> 'pred$uattacker'(X1) ) ).
fof(ax74,axiom,
! [X0,X1] :
( 'pred$uattacker'('tuple$u2'(X0,X1))
=> 'pred$uattacker'(X0) ) ).
fof(ax81,axiom,
! [X0] :
( 'pred$uattacker'('tuple$uenc$uoracle$uin$u1'(X0))
=> 'pred$uattacker'('tuple$uenc$uoracle$uout$u2'('name$uv','constr$uxor'('constr$uconcat'(X0,'constr$uC'(X0)),'constr$uRC4'('name$uv','name$uKab')))) ) ).
fof(ax82,axiom,
'pred$uattacker'('tuple$uB$uout$u1'('name$uv','constr$uxor'('constr$uconcat'('name$uobjective','constr$uC'('name$uobjective')),'constr$uRC4'('name$uv','name$uKab')))) ).
fof(co0,conjecture,
'pred$uattacker'('name$uobjective') ).
fof(negated_conjecture,negated_conjecture,
~ 'pred$uattacker'('name$uobjective'),
inference(negate_conjecture,[status(cth)],[co0]) ).
cnf(c45,plain,
'constr$usplit'('constr$uconcat'(X0,X1)) = 'tuple$u2'(X0,X1),
inference(clausification,[status(esa)],[ax45]) ).
cnf(c46,plain,
'constr$uxor'('constr$uconcat'(X0,X1),'constr$uconcat'(X2,X3)) = 'constr$uconcat'('constr$uxor'(X0,X2),'constr$uxor'(X1,X3)),
inference(clausification,[status(esa)],[ax46]) ).
cnf(c47,plain,
'constr$uC'('constr$uxor'(X0,X1)) = 'constr$uxor'('constr$uC'(X0),'constr$uC'(X1)),
inference(clausification,[status(esa)],[ax47]) ).
cnf(c48,plain,
'constr$uxor'(X0,X0) = 'constr$uZERO',
inference(clausification,[status(esa)],[ax48]) ).
cnf(c49,plain,
'constr$uxor'(X0,'constr$uZERO') = X0,
inference(clausification,[status(esa)],[ax49]) ).
cnf(c50,plain,
'constr$uxor'(X0,X1) = 'constr$uxor'(X1,X0),
inference(clausification,[status(esa)],[ax50]) ).
cnf(c51,plain,
'constr$uxor'(X0,'constr$uxor'(X1,X2)) = 'constr$uxor'('constr$uxor'(X0,X1),X2),
inference(clausification,[status(esa)],[ax51]) ).
cnf(c52,plain,
( 'pred$uattacker'('constr$uxor'(X0,X1))
| ~ 'pred$uattacker'(X1)
| ~ 'pred$uattacker'(X0) ),
inference(clausification,[status(esa)],[ax52]) ).
cnf(c54,plain,
( 'pred$uattacker'('constr$usplit'(X0))
| ~ 'pred$uattacker'(X0) ),
inference(clausification,[status(esa)],[ax54]) ).
cnf(c58,plain,
( 'pred$uattacker'(X1)
| ~ 'pred$uattacker'('tuple$uenc$uoracle$uout$u2'(X0,X1)) ),
inference(clausification,[status(esa)],[ax58]) ).
cnf(c59,plain,
( 'pred$uattacker'('tuple$uenc$uoracle$uin$u1'(X0))
| ~ 'pred$uattacker'(X0) ),
inference(clausification,[status(esa)],[ax59]) ).
cnf(c62,plain,
'pred$uattacker'('constr$uZERO'),
inference(clausification,[status(esa)],[ax62]) ).
cnf(c72,plain,
( 'pred$uattacker'(X1)
| ~ 'pred$uattacker'('tuple$uB$uout$u1'(X0,X1)) ),
inference(clausification,[status(esa)],[ax72]) ).
cnf(c74,plain,
( 'pred$uattacker'(X0)
| ~ 'pred$uattacker'('tuple$u2'(X0,X1)) ),
inference(clausification,[status(esa)],[ax74]) ).
cnf(c81,plain,
( 'pred$uattacker'('tuple$uenc$uoracle$uout$u2'('name$uv','constr$uxor'('constr$uconcat'(X0,'constr$uC'(X0)),'constr$uRC4'('name$uv','name$uKab'))))
| ~ 'pred$uattacker'('tuple$uenc$uoracle$uin$u1'(X0)) ),
inference(clausification,[status(esa)],[ax81]) ).
cnf(c82,plain,
'pred$uattacker'('tuple$uB$uout$u1'('name$uv','constr$uxor'('constr$uconcat'('name$uobjective','constr$uC'('name$uobjective')),'constr$uRC4'('name$uv','name$uKab')))),
inference(clausification,[status(esa)],[ax82]) ).
cnf(c83,plain,
~ 'pred$uattacker'('name$uobjective'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'constr$uxor'('constr$uZERO',X0) = X0,
inference(superposition,[status(thm)],[c50,c49]) ).
cnf(d1,plain,
'constr$uZERO' = 'constr$uxor'(X0,X0),
inference(superposition,[status(thm)],[c48,c50]) ).
cnf(d2,plain,
'constr$uxor'('constr$uconcat'(X0,X1),'constr$uconcat'(X0,X2)) = 'constr$uconcat'('constr$uZERO','constr$uxor'(X1,X2)),
inference(superposition,[status(thm)],[c48,c46]) ).
cnf(d3,plain,
'constr$uZERO' = 'constr$uconcat'('constr$uZERO','constr$uxor'(X1,X1)),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
'constr$uZERO' = 'constr$uconcat'('constr$uZERO','constr$uZERO'),
inference(demodulation,[status(thm)],[d3,c48]) ).
cnf(d5,plain,
( ~ 'pred$uattacker'('tuple$uenc$uoracle$uin$u1'(X0))
| 'pred$uattacker'('tuple$uenc$uoracle$uout$u2'('name$uv','constr$uxor'('constr$uRC4'('name$uv','name$uKab'),'constr$uconcat'(X0,'constr$uC'(X0))))) ),
inference(demodulation,[status(thm)],[c81,c50]) ).
cnf(d6,plain,
'constr$uZERO' = 'constr$uC'('constr$uxor'(X0,X0)),
inference(superposition,[status(thm)],[c47,d1]) ).
cnf(d7,plain,
'constr$uZERO' = 'constr$uC'('constr$uZERO'),
inference(demodulation,[status(thm)],[d6,c48]) ).
cnf(d8,plain,
( ~ 'pred$uattacker'('tuple$uenc$uoracle$uin$u1'('constr$uZERO'))
| 'pred$uattacker'('tuple$uenc$uoracle$uout$u2'('name$uv','constr$uxor'('constr$uRC4'('name$uv','name$uKab'),'constr$uconcat'('constr$uZERO','constr$uZERO')))) ),
inference(superposition,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ 'pred$uattacker'('tuple$uenc$uoracle$uin$u1'('constr$uZERO'))
| 'pred$uattacker'('tuple$uenc$uoracle$uout$u2'('name$uv','constr$uxor'('constr$uconcat'('constr$uZERO','constr$uZERO'),'constr$uRC4'('name$uv','name$uKab')))) ),
inference(demodulation,[status(thm)],[d8,c50]) ).
cnf(d10,plain,
( ~ 'pred$uattacker'('tuple$uenc$uoracle$uin$u1'('constr$uZERO'))
| 'pred$uattacker'('tuple$uenc$uoracle$uout$u2'('name$uv','constr$uxor'('constr$uZERO','constr$uRC4'('name$uv','name$uKab')))) ),
inference(demodulation,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
( ~ 'pred$uattacker'('tuple$uenc$uoracle$uin$u1'('constr$uZERO'))
| 'pred$uattacker'('tuple$uenc$uoracle$uout$u2'('name$uv','constr$uRC4'('name$uv','name$uKab'))) ),
inference(demodulation,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
( 'pred$uattacker'('constr$uRC4'('name$uv','name$uKab'))
| ~ 'pred$uattacker'('tuple$uenc$uoracle$uin$u1'('constr$uZERO')) ),
inference(resolution,[status(thm)],[d11,c58]) ).
cnf(d13,plain,
( ~ 'pred$uattacker'('constr$uconcat'(X0,X1))
| 'pred$uattacker'('tuple$u2'(X0,X1)) ),
inference(superposition,[status(thm)],[c45,c54]) ).
cnf(d14,plain,
'constr$uxor'(X0,'constr$uxor'(X0,X1)) = 'constr$uxor'('constr$uZERO',X1),
inference(superposition,[status(thm)],[c48,c51]) ).
cnf(d15,plain,
'constr$uxor'(X1,'constr$uxor'(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
( ~ 'pred$uattacker'('constr$uxor'(X0,X1))
| ~ 'pred$uattacker'(X0)
| 'pred$uattacker'(X1) ),
inference(superposition,[status(thm)],[d15,c52]) ).
cnf(d17,plain,
'pred$uattacker'('tuple$uB$uout$u1'('name$uv','constr$uxor'('constr$uRC4'('name$uv','name$uKab'),'constr$uconcat'('name$uobjective','constr$uC'('name$uobjective'))))),
inference(demodulation,[status(thm)],[c82,c50]) ).
cnf(d18,plain,
'pred$uattacker'('constr$uxor'('constr$uRC4'('name$uv','name$uKab'),'constr$uconcat'('name$uobjective','constr$uC'('name$uobjective')))),
inference(resolution,[status(thm)],[d17,c72]) ).
cnf(d19,plain,
( ~ 'pred$uattacker'('constr$uRC4'('name$uv','name$uKab'))
| 'pred$uattacker'('constr$uconcat'('name$uobjective','constr$uC'('name$uobjective'))) ),
inference(resolution,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
( 'pred$uattacker'('tuple$u2'('name$uobjective','constr$uC'('name$uobjective')))
| ~ 'pred$uattacker'('constr$uRC4'('name$uv','name$uKab')) ),
inference(resolution,[status(thm)],[d19,d13]) ).
cnf(d21,plain,
( 'pred$uattacker'('name$uobjective')
| ~ 'pred$uattacker'('constr$uRC4'('name$uv','name$uKab')) ),
inference(resolution,[status(thm)],[d20,c74]) ).
cnf(d22,plain,
~ 'pred$uattacker'('constr$uRC4'('name$uv','name$uKab')),
inference(resolution,[status(thm)],[c83,d21]) ).
cnf(d23,plain,
~ 'pred$uattacker'('tuple$uenc$uoracle$uin$u1'('constr$uZERO')),
inference(resolution,[status(thm)],[d22,d12]) ).
cnf(d24,plain,
~ 'pred$uattacker'('constr$uZERO'),
inference(resolution,[status(thm)],[d23,c59]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[c62,d24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW957+1 : TPTP v9.3.1. Released v7.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 16:40:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.32/4.91 % SZS status Theorem for theBenchmark.p
% 30.32/4.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------