%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG080+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 08:25:48 AM UTC 2026
% Result : Theorem 21.22s 11.28s
% Output : CNFRefutation 21.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 73 ( 30 unt; 0 def)
% Number of atoms : 148 ( 99 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 113 ( 38 ~; 54 |; 17 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 13 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSPN,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( ( aDimensionOf0(X1) != sz00
& aDimensionOf0(X0) = aDimensionOf0(X1) )
=> sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) ) ) ).
fof(m__1678,hypothesis,
( aVector0(xt)
& aVector0(xs) ) ).
fof(m__1678_01,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt) ).
fof(m__1692,hypothesis,
aDimensionOf0(xs) != sz00 ).
fof(m__1709,hypothesis,
( xp = sziznziztdt0(xs)
& ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(xp,X0) = sdtlbdtrb0(xs,X0) )
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& aVector0(xp) ) ).
fof(m__1726,hypothesis,
( xq = sziznziztdt0(xt)
& ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(xq,X0) = sdtlbdtrb0(xt,X0) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ) ).
fof(m__1746,hypothesis,
( xA = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(xA) ) ).
fof(m__1766,hypothesis,
( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(xB) ) ).
fof(m__1783,hypothesis,
( xC = sdtasasdt0(xp,xp)
& aScalar0(xC) ) ).
fof(m__1800,hypothesis,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ) ).
fof(m__1820,hypothesis,
( xE = sdtasasdt0(xp,xq)
& aScalar0(xE) ) ).
fof(m__1837,hypothesis,
( xF = sdtasdt0(xA,xA)
& aScalar0(xF) ) ).
fof(m__1854,hypothesis,
( xG = sdtasdt0(xB,xB)
& aScalar0(xG) ) ).
fof(m__1873,hypothesis,
( xH = sdtasdt0(xA,xB)
& aScalar0(xH) ) ).
fof(m__2733,hypothesis,
sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))) ).
fof(m__,conjecture,
sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ).
fof(negated_conjecture,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c52,plain,
( ~ aVector0(X0)
| ~ aVector0(X1)
| sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
| aDimensionOf0(X1) = sz00
| aDimensionOf0(X0) != aDimensionOf0(X1) ),
inference(clausification,[status(esa)],[mDefSPN]) ).
cnf(c54,plain,
aVector0(xs),
inference(clausification,[status(esa)],[m__1678]) ).
cnf(c55,plain,
aVector0(xt),
inference(clausification,[status(esa)],[m__1678]) ).
cnf(c57,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(clausification,[status(esa)],[m__1678_01]) ).
cnf(c58,plain,
aDimensionOf0(xs) != sz00,
inference(clausification,[status(esa)],[m__1692]) ).
cnf(c62,plain,
xp = sziznziztdt0(xs),
inference(clausification,[status(esa)],[m__1709]) ).
cnf(c66,plain,
xq = sziznziztdt0(xt),
inference(clausification,[status(esa)],[m__1726]) ).
cnf(c68,plain,
xA = sdtlbdtrb0(xs,aDimensionOf0(xs)),
inference(clausification,[status(esa)],[m__1746]) ).
cnf(c70,plain,
xB = sdtlbdtrb0(xt,aDimensionOf0(xt)),
inference(clausification,[status(esa)],[m__1766]) ).
cnf(c72,plain,
xC = sdtasasdt0(xp,xp),
inference(clausification,[status(esa)],[m__1783]) ).
cnf(c74,plain,
xD = sdtasasdt0(xq,xq),
inference(clausification,[status(esa)],[m__1800]) ).
cnf(c76,plain,
xE = sdtasasdt0(xp,xq),
inference(clausification,[status(esa)],[m__1820]) ).
cnf(c78,plain,
xF = sdtasdt0(xA,xA),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c80,plain,
xG = sdtasdt0(xB,xB),
inference(clausification,[status(esa)],[m__1854]) ).
cnf(c82,plain,
xH = sdtasdt0(xA,xB),
inference(clausification,[status(esa)],[m__1873]) ).
cnf(c93,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(clausification,[status(esa)],[m__2733]) ).
cnf(c94,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
xB = sdtlbdtrb0(xt,aDimensionOf0(xs)),
inference(demodulation,[status(thm)],[c70,c57]) ).
cnf(d1,plain,
( ~ aVector0(xt)
| ~ aVector0(X0)
| sdtasasdt0(X0,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(xt,aDimensionOf0(xt))))
| aDimensionOf0(xt) = sz00
| aDimensionOf0(X0) != aDimensionOf0(xs) ),
inference(superposition,[status(thm)],[c57,c52]) ).
cnf(d2,plain,
( ~ aVector0(xt)
| ~ aVector0(X0)
| sdtasasdt0(X0,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(xt,aDimensionOf0(xt))))
| aDimensionOf0(xs) = sz00
| aDimensionOf0(X0) != aDimensionOf0(xs) ),
inference(demodulation,[status(thm)],[d1,c57]) ).
cnf(d3,plain,
( ~ aVector0(xt)
| ~ aVector0(X0)
| sdtasasdt0(X0,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),xq),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(xt,aDimensionOf0(xt))))
| aDimensionOf0(xs) = sz00
| aDimensionOf0(X0) != aDimensionOf0(xs) ),
inference(demodulation,[status(thm)],[d2,c66]) ).
cnf(d4,plain,
( ~ aVector0(xt)
| ~ aVector0(X0)
| sdtasasdt0(X0,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),xq),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(xt,aDimensionOf0(xs))))
| aDimensionOf0(xs) = sz00
| aDimensionOf0(X0) != aDimensionOf0(xs) ),
inference(demodulation,[status(thm)],[d3,c57]) ).
cnf(d5,plain,
( ~ aVector0(xt)
| ~ aVector0(X0)
| sdtasasdt0(X0,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),xq),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),xB))
| aDimensionOf0(xs) = sz00
| aDimensionOf0(X0) != aDimensionOf0(xs) ),
inference(demodulation,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( ~ aVector0(X0)
| sdtasasdt0(X0,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),xq),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),xB))
| aDimensionOf0(xs) = sz00
| aDimensionOf0(X0) != aDimensionOf0(xs) ),
inference(resolution,[status(thm)],[c55,d5]) ).
cnf(d7,plain,
( ~ aVector0(X0)
| sdtasasdt0(X0,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),xq),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),xB))
| aDimensionOf0(X0) != aDimensionOf0(xs) ),
inference(resolution,[status(thm)],[c58,d6]) ).
cnf(d8,plain,
( ~ aVector0(xs)
| sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),xq),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),xB)) ),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
( ~ aVector0(xs)
| sdtasasdt0(xs,xt) = sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),xB)) ),
inference(demodulation,[status(thm)],[d8,c62]) ).
cnf(d10,plain,
( ~ aVector0(xs)
| sdtasasdt0(xs,xt) = sdtpldt0(xE,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),xB)) ),
inference(demodulation,[status(thm)],[d9,c76]) ).
cnf(d11,plain,
( ~ aVector0(xs)
| sdtasasdt0(xs,xt) = sdtpldt0(xE,sdtasdt0(xA,xB)) ),
inference(demodulation,[status(thm)],[d10,c68]) ).
cnf(d12,plain,
( ~ aVector0(xs)
| sdtasasdt0(xs,xt) = sdtpldt0(xE,xH) ),
inference(demodulation,[status(thm)],[d11,c82]) ).
cnf(d13,plain,
sdtasasdt0(xs,xt) = sdtpldt0(xE,xH),
inference(resolution,[status(thm)],[c54,d12]) ).
cnf(d14,plain,
( ~ aVector0(X0)
| ~ aVector0(X0)
| sdtasasdt0(X0,X0) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X0)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X0,aDimensionOf0(X0))))
| aDimensionOf0(X0) = sz00 ),
inference(equality_resolution,[status(thm)],[c52]) ).
cnf(d15,plain,
( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| aDimensionOf0(xs) = sz00 ),
inference(resolution,[status(thm)],[d14,c54]) ).
cnf(d16,plain,
( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(xp,sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d15,c62]) ).
cnf(d17,plain,
( sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(xp,xp),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d16,c62]) ).
cnf(d18,plain,
( sdtasasdt0(xs,xs) = sdtpldt0(xC,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d17,c72]) ).
cnf(d19,plain,
( sdtasasdt0(xs,xs) = sdtpldt0(xC,sdtasdt0(xA,sdtlbdtrb0(xs,aDimensionOf0(xs))))
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d18,c68]) ).
cnf(d20,plain,
( sdtasasdt0(xs,xs) = sdtpldt0(xC,sdtasdt0(xA,xA))
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d19,c68]) ).
cnf(d21,plain,
( sdtasasdt0(xs,xs) = sdtpldt0(xC,xF)
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d20,c78]) ).
cnf(d22,plain,
sdtasasdt0(xs,xs) = sdtpldt0(xC,xF),
inference(resolution,[status(thm)],[c58,d21]) ).
cnf(d23,plain,
( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))
| aDimensionOf0(xt) = sz00 ),
inference(resolution,[status(thm)],[d14,c55]) ).
cnf(d24,plain,
( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d23,c57]) ).
cnf(d25,plain,
( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(xq,sziznziztdt0(xt)),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d24,c66]) ).
cnf(d26,plain,
( sdtasasdt0(xt,xt) = sdtpldt0(sdtasasdt0(xq,xq),sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d25,c66]) ).
cnf(d27,plain,
( sdtasasdt0(xt,xt) = sdtpldt0(xD,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xt)),sdtlbdtrb0(xt,aDimensionOf0(xt))))
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d26,c74]) ).
cnf(d28,plain,
( sdtasasdt0(xt,xt) = sdtpldt0(xD,sdtasdt0(sdtlbdtrb0(xt,aDimensionOf0(xs)),sdtlbdtrb0(xt,aDimensionOf0(xt))))
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d27,c57]) ).
cnf(d29,plain,
( sdtasasdt0(xt,xt) = sdtpldt0(xD,sdtasdt0(xB,sdtlbdtrb0(xt,aDimensionOf0(xt))))
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d28,d0]) ).
cnf(d30,plain,
( sdtasasdt0(xt,xt) = sdtpldt0(xD,sdtasdt0(xB,sdtlbdtrb0(xt,aDimensionOf0(xs))))
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d29,c57]) ).
cnf(d31,plain,
( sdtasasdt0(xt,xt) = sdtpldt0(xD,sdtasdt0(xB,xB))
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d30,d0]) ).
cnf(d32,plain,
( sdtasasdt0(xt,xt) = sdtpldt0(xD,xG)
| aDimensionOf0(xs) = sz00 ),
inference(demodulation,[status(thm)],[d31,c80]) ).
cnf(d33,plain,
sdtasasdt0(xt,xt) = sdtpldt0(xD,xG),
inference(resolution,[status(thm)],[c58,d32]) ).
cnf(d34,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtpldt0(xD,xG))),
inference(demodulation,[status(thm)],[c94,d33]) ).
cnf(d35,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(demodulation,[status(thm)],[d34,d22]) ).
cnf(d36,plain,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtasasdt0(xs,xt)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(demodulation,[status(thm)],[d35,d13]) ).
cnf(d37,plain,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(demodulation,[status(thm)],[d36,d13]) ).
cnf(d38,plain,
$false,
inference(resolution,[status(thm)],[c93,d37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG080+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.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 06:00:16 UTC 2026
% 0.03/0.37 % CPUTime :
% 0.03/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.22/11.28 % SZS status Theorem for theBenchmark.p
% 21.22/11.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------