%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG050+1 : TPTP v9.3.1. Released v4.0.0.
% 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 08:25:42 AM UTC 2026
% Result : Theorem 21.82s 3.37s
% Output : CNFRefutation 21.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 10 unt; 0 def)
% Number of atoms : 52 ( 25 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 56 ( 26 ~; 21 |; 2 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSZeroSc,axiom,
aScalar0(sz0z00) ).
fof(mLERef,axiom,
! [X0] :
( aScalar0(X0)
=> sdtlseqdt0(X0,X0) ) ).
fof(mDefSPZ,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( ( aDimensionOf0(X1) = sz00
& aDimensionOf0(X0) = aDimensionOf0(X1) )
=> sdtasasdt0(X0,X1) = sz0z00 ) ) ).
fof(m__1542,hypothesis,
aVector0(xs) ).
fof(m__,conjecture,
( ( aDimensionOf0(xs) != sz00
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( aDimensionOf0(xs) != sz00
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) )
=> sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c7,plain,
aScalar0(sz0z00),
inference(clausification,[status(esa)],[mSZeroSc]) ).
cnf(c30,plain,
( sdtlseqdt0(X0,X0)
| ~ aScalar0(X0) ),
inference(clausification,[status(esa)],[mLERef]) ).
cnf(c51,plain,
( sdtasasdt0(X1,X0) = sz0z00
| ~ aVector0(X1)
| ~ aVector0(X0)
| aDimensionOf0(X1) != aDimensionOf0(X0)
| aDimensionOf0(X0) != sz00 ),
inference(clausification,[status(esa)],[mDefSPZ]) ).
cnf(c53,plain,
aVector0(xs),
inference(clausification,[status(esa)],[m__1542]) ).
cnf(c55,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs))
| aDimensionOf0(xs) = sz00 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c56,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
aDimensionOf0(xs) = sz00,
inference(resolution,[status(thm)],[c56,c55]) ).
cnf(d1,plain,
( ~ aVector0(xs)
| ~ aVector0(X0)
| sdtasasdt0(X0,xs) = sz0z00
| aDimensionOf0(xs) != sz00
| aDimensionOf0(X0) != sz00 ),
inference(superposition,[status(thm)],[d0,c51]) ).
cnf(d2,plain,
( ~ aVector0(xs)
| ~ aVector0(X0)
| sdtasasdt0(X0,xs) = sz0z00
| sz00 != sz00
| aDimensionOf0(X0) != sz00 ),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ aVector0(X0)
| sdtasasdt0(X0,xs) = sz0z00
| sz00 != sz00
| aDimensionOf0(X0) != sz00 ),
inference(resolution,[status(thm)],[c53,d2]) ).
cnf(d4,plain,
( ~ aVector0(xs)
| sdtasasdt0(xs,xs) = sz0z00
| sz00 != sz00
| sz00 != sz00 ),
inference(superposition,[status(thm)],[d0,d3]) ).
cnf(d5,plain,
( sdtasasdt0(xs,xs) = sz0z00
| sz00 != sz00 ),
inference(resolution,[status(thm)],[c53,d4]) ).
cnf(d6,plain,
sdtasasdt0(xs,xs) = sz0z00,
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
~ sdtlseqdt0(sz0z00,sz0z00),
inference(demodulation,[status(thm)],[c56,d6]) ).
cnf(d8,plain,
~ aScalar0(sz0z00),
inference(resolution,[status(thm)],[d7,c30]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c7,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG050+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n026.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 05:55:25 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.82/3.37 % SZS status Theorem for theBenchmark.p
% 21.82/3.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------