%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM494+1 : 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 : n010.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 08:12:55 AM UTC 2026
% Result : Theorem 70.70s 10.66s
% Output : CNFRefutation 70.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 12 unt; 1 def)
% Number of atoms : 185 ( 49 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 241 ( 111 ~; 103 |; 17 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ) ).
fof(mAddAsso,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ).
fof(mAddCanc,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ) ).
fof(mDefDiff,definition,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ) ).
fof(mMonAdd,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ) ) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ) ).
fof(m__1870,hypothesis,
sdtlseqdt0(xp,xn) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp) ).
fof(m__1894,hypothesis,
( sdtlseqdt0(xr,xn)
& xr != xn ) ).
fof(m__,conjecture,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c3,plain,
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mSortsB]) ).
cnf(c6,plain,
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAddAsso]) ).
cnf(c18,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| X0 = X2
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X1) != sdtpldt0(X2,X1) ),
inference(clausification,[status(esa)],[mAddCanc]) ).
cnf(c27,plain,
( aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| X1 != sdtmndt0(X2,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefDiff]) ).
cnf(c38,plain,
( ~ aNaturalNumber0(X0)
| X0 = X1
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1) ),
inference(clausification,[status(esa)],[mMonAdd]) ).
cnf(c70,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c71,plain,
aNaturalNumber0(xm),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c72,plain,
aNaturalNumber0(xp),
inference(clausification,[status(esa)],[m__1837]) ).
cnf(c76,plain,
sdtlseqdt0(xp,xn),
inference(clausification,[status(esa)],[m__1870]) ).
cnf(c77,plain,
xr = sdtmndt0(xn,xp),
inference(clausification,[status(esa)],[m__1883]) ).
cnf(c78,plain,
xr != xn,
inference(clausification,[status(esa)],[m__1894]) ).
cnf(c79,plain,
sdtlseqdt0(xr,xn),
inference(clausification,[status(esa)],[m__1894]) ).
cnf(c81,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(X0)
| X0 != xr ),
inference(superposition,[status(thm)],[c77,c27]) ).
cnf(d1,plain,
( ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(X0)
| X0 != xr ),
inference(resolution,[status(thm)],[c70,d0]) ).
cnf(d2,plain,
( ~ sdtlseqdt0(xp,xn)
| aNaturalNumber0(X0)
| X0 != xr ),
inference(resolution,[status(thm)],[c72,d1]) ).
cnf(d3,plain,
( aNaturalNumber0(X0)
| X0 != xr ),
inference(resolution,[status(thm)],[c76,d2]) ).
cnf(d4,plain,
aNaturalNumber0(xr),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(superposition,[status(thm)],[c6,c81]) ).
cnf(d6,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp)))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c70,d5]) ).
cnf(d7,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp)))
| ~ aNaturalNumber0(xp)
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c71,d6]) ).
cnf(d8,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp)))
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c72,d7]) ).
cnf(d9,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp))) ),
inference(superposition,[status(thm)],[c6,d8]) ).
cnf(d10,plain,
( ~ sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp)))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c71,d9]) ).
cnf(d11,plain,
( ~ sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xm,xp)),sdtpldt0(xn,sdtpldt0(xm,xp)))
| ~ aNaturalNumber0(xr)
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c72,d10]) ).
cnf(d12,plain,
( ~ aNaturalNumber0(xr)
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
| ~ sdtlseqdt0(xr,xn)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| xr = xn ),
inference(resolution,[status(thm)],[c38,d11]) ).
cnf(d13,plain,
( ~ sdtlseqdt0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| xr = xn
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c70,d12]) ).
cnf(d14,plain,
( ~ sdtlseqdt0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c78,d13]) ).
cnf(d15,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| sdtpldt0(sdtpldt0(xr,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(resolution,[status(thm)],[c79,d14]) ).
cnf(d16,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xr,sdtpldt0(xm,xp)) ),
inference(superposition,[status(thm)],[d15,c6]) ).
cnf(d17,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xr,sdtpldt0(xm,xp)) ),
inference(resolution,[status(thm)],[c71,d16]) ).
cnf(d18,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xr,sdtpldt0(xm,xp)) ),
inference(resolution,[status(thm)],[c72,d17]) ).
cnf(d19,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| sdtpldt0(xr,sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)) ),
inference(superposition,[status(thm)],[d18,c6]) ).
cnf(d20,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| sdtpldt0(xr,sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)) ),
inference(resolution,[status(thm)],[c70,d19]) ).
cnf(d21,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| sdtpldt0(xr,sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)) ),
inference(resolution,[status(thm)],[c71,d20]) ).
cnf(d22,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| sdtpldt0(xr,sdtpldt0(xm,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)) ),
inference(resolution,[status(thm)],[c72,d21]) ).
cnf(d23,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(xr)
| xr = X0
| sdtpldt0(xn,sdtpldt0(xm,xp)) != sdtpldt0(X0,sdtpldt0(xm,xp)) ),
inference(superposition,[status(thm)],[d22,c18]) ).
cnf(d24,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| ~ aNaturalNumber0(xn)
| xr = xn ),
inference(equality_resolution,[status(thm)],[d23]) ).
cnf(d25,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xm,xp))
| xr = xn ),
inference(resolution,[status(thm)],[c70,d24]) ).
cnf(d26,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xm,xp)) ),
inference(resolution,[status(thm)],[c78,d25]) ).
cnf(d27,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[d26,c3]) ).
cnf(d28,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c71,d27]) ).
cnf(d29,plain,
~ aNaturalNumber0(xr),
inference(resolution,[status(thm)],[c72,d28]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[d29,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM494+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 02:59:15 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 70.70/10.66 % SZS status Theorem for theBenchmark.p
% 70.70/10.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------