%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM475+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 : n011.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 08:12:51 AM UTC 2026
% Result : Theorem 26.09s 7.27s
% Output : CNFRefutation 26.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 96 ( 33 unt; 3 def)
% Number of atoms : 279 ( 105 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 331 ( 148 ~; 155 |; 15 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 16 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aNaturalNumber0(sz00) ).
fof(mSortsB,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ) ).
fof(mSortsB_02,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ) ).
fof(m_AddZero,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ) ).
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(mDefLE,definition,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(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(mDefQuot,definition,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ) ).
fof(m__1324,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ) ).
fof(m__1324_04,hypothesis,
( doDivides0(xl,sdtpldt0(xm,xn))
& doDivides0(xl,xm) ) ).
fof(m__1347,hypothesis,
xl != sz00 ).
fof(m__1360,hypothesis,
xp = sdtsldt0(xm,xl) ).
fof(m__1379,hypothesis,
xq = sdtsldt0(sdtpldt0(xm,xn),xl) ).
fof(m__1395,hypothesis,
sdtlseqdt0(xp,xq) ).
fof(m__1422,hypothesis,
xr = sdtmndt0(xq,xp) ).
fof(m__1459,hypothesis,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn) ).
fof(m__,conjecture,
xn = sdtasdt0(xl,xr) ).
fof(negated_conjecture,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c0,plain,
aNaturalNumber0(sz00),
inference(clausification,[status(esa)],[mSortsC]) ).
cnf(c3,plain,
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mSortsB]) ).
cnf(c4,plain,
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mSortsB_02]) ).
cnf(c8,plain,
( X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_AddZero]) ).
cnf(c17,plain,
( X1 = X0
| sdtpldt0(X2,X1) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAddCanc]) ).
cnf(c26,plain,
( sdtpldt0(X2,X0) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefLE]) ).
cnf(c27,plain,
( aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| X1 != sdtmndt0(X2,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefDiff]) ).
cnf(c28,plain,
( ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X2) = X1
| X2 != sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefDiff]) ).
cnf(c29,plain,
( ~ aNaturalNumber0(X2)
| X1 = sdtmndt0(X2,X0)
| sdtpldt0(X0,X1) != X2
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefDiff]) ).
cnf(c50,plain,
( X0 = sz00
| ~ doDivides0(X0,X1)
| aNaturalNumber0(X2)
| X2 != sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefQuot]) ).
cnf(c51,plain,
( X0 = sz00
| ~ doDivides0(X0,X1)
| X1 = sdtasdt0(X0,X2)
| X2 != sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefQuot]) ).
cnf(c55,plain,
aNaturalNumber0(xl),
inference(clausification,[status(esa)],[m__1324]) ).
cnf(c56,plain,
aNaturalNumber0(xm),
inference(clausification,[status(esa)],[m__1324]) ).
cnf(c57,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__1324]) ).
cnf(c58,plain,
doDivides0(xl,xm),
inference(clausification,[status(esa)],[m__1324_04]) ).
cnf(c59,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(clausification,[status(esa)],[m__1324_04]) ).
cnf(c60,plain,
xl != sz00,
inference(clausification,[status(esa)],[m__1347]) ).
cnf(c61,plain,
xp = sdtsldt0(xm,xl),
inference(clausification,[status(esa)],[m__1360]) ).
cnf(c62,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(clausification,[status(esa)],[m__1379]) ).
cnf(c63,plain,
sdtlseqdt0(xp,xq),
inference(clausification,[status(esa)],[m__1395]) ).
cnf(c64,plain,
xr = sdtmndt0(xq,xp),
inference(clausification,[status(esa)],[m__1422]) ).
cnf(c65,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(clausification,[status(esa)],[m__1459]) ).
cnf(c66,plain,
xn != sdtasdt0(xl,xr),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| xm = sdtasdt0(xl,X0)
| xl = sz00
| X0 != xp ),
inference(superposition,[status(thm)],[c61,c51]) ).
cnf(d1,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xm)
| xm = sdtasdt0(xl,X0)
| xl = sz00
| X0 != xp ),
inference(resolution,[status(thm)],[c55,d0]) ).
cnf(d2,plain,
( ~ doDivides0(xl,xm)
| xm = sdtasdt0(xl,X0)
| xl = sz00
| X0 != xp ),
inference(resolution,[status(thm)],[c56,d1]) ).
cnf(d3,plain,
( xm = sdtasdt0(xl,X0)
| xl = sz00
| X0 != xp ),
inference(resolution,[status(thm)],[c58,d2]) ).
cnf(d4,plain,
( xm = sdtasdt0(xl,X0)
| X0 != xp ),
inference(resolution,[status(thm)],[c60,d3]) ).
cnf(d5,plain,
xm = sdtasdt0(xl,xp),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xl,xp))
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| sdtasdt0(xl,xr) = X0
| sdtpldt0(sdtasdt0(xl,xp),xn) != sdtpldt0(sdtasdt0(xl,xp),X0) ),
inference(superposition,[status(thm)],[c65,c17]) ).
cnf(d7,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,xr) = X0
| sdtpldt0(xm,xn) != sdtpldt0(sdtasdt0(xl,xp),X0) ),
inference(demodulation,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,xr) = X0
| sdtpldt0(xm,xn) != sdtpldt0(xm,X0) ),
inference(demodulation,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,xr) = X0
| sdtpldt0(xm,xn) != sdtpldt0(xm,X0) ),
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,xr) = X0
| sdtpldt0(xm,xn) != sdtpldt0(xm,X0) ),
inference(resolution,[status(thm)],[c56,d9]) ).
cnf(d11,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(xn)
| sdtasdt0(xl,xr) = xn ),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xr))
| sdtasdt0(xl,xr) = xn ),
inference(resolution,[status(thm)],[c57,d11]) ).
cnf(d13,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xr)
| sdtasdt0(xl,xr) = xn ),
inference(resolution,[status(thm)],[d12,c4]) ).
cnf(d14,plain,
( ~ aNaturalNumber0(xr)
| sdtasdt0(xl,xr) = xn ),
inference(resolution,[status(thm)],[c55,d13]) ).
cnf(d15,plain,
( ~ sdtlseqdt0(xp,xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq)
| aNaturalNumber0(X0)
| X0 != xr ),
inference(superposition,[status(thm)],[c64,c27]) ).
cnf(d16,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(X0)
| X0 != xr ),
inference(resolution,[status(thm)],[c63,d15]) ).
cnf(d17,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(xr) ),
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl)
| xl = sz00
| X0 != xp ),
inference(superposition,[status(thm)],[c61,c50]) ).
cnf(d19,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(X0)
| xl = sz00
| X0 != xp ),
inference(resolution,[status(thm)],[c55,d18]) ).
cnf(d20,plain,
( ~ doDivides0(xl,xm)
| aNaturalNumber0(X0)
| xl = sz00
| X0 != xp ),
inference(resolution,[status(thm)],[c56,d19]) ).
cnf(d21,plain,
( aNaturalNumber0(X0)
| xl = sz00
| X0 != xp ),
inference(resolution,[status(thm)],[c58,d20]) ).
cnf(d22,plain,
( aNaturalNumber0(X0)
| X0 != xp ),
inference(resolution,[status(thm)],[c60,d21]) ).
cnf(d23,plain,
aNaturalNumber0(xp),
inference(equality_resolution,[status(thm)],[d22]) ).
cnf(d24,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xq) ),
inference(resolution,[status(thm)],[d23,d17]) ).
cnf(d25,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl)
| xl = sz00
| X0 != xq ),
inference(superposition,[status(thm)],[c62,c50]) ).
cnf(d26,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| aNaturalNumber0(X0)
| xl = sz00
| X0 != xq ),
inference(resolution,[status(thm)],[c55,d25]) ).
cnf(d27,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| aNaturalNumber0(X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c60,d26]) ).
cnf(d28,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| aNaturalNumber0(X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c59,d27]) ).
cnf(d29,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| aNaturalNumber0(xq) ),
inference(equality_resolution,[status(thm)],[d28]) ).
cnf(d30,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(xq) ),
inference(resolution,[status(thm)],[d29,c3]) ).
cnf(d31,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c56,d30]) ).
cnf(d32,plain,
aNaturalNumber0(xq),
inference(resolution,[status(thm)],[c57,d31]) ).
cnf(d33,plain,
aNaturalNumber0(xr),
inference(resolution,[status(thm)],[d32,d24]) ).
cnf(d34,plain,
sdtasdt0(xl,xr) = xn,
inference(resolution,[status(thm)],[d33,d14]) ).
cnf(d35,plain,
xn != xn,
inference(demodulation,[status(thm)],[c66,d34]) ).
cnf(d36,plain,
xn = sdtpldt0(sz00,xn),
inference(resolution,[status(thm)],[c8,c57]) ).
cnf(d37,plain,
( ~ sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| xn = sdtmndt0(X0,sz00)
| xn != X0 ),
inference(superposition,[status(thm)],[d36,c29]) ).
cnf(d38,plain,
( ~ sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| xn = sdtmndt0(X0,sz00)
| xn != X0 ),
inference(resolution,[status(thm)],[c0,d37]) ).
cnf(d39,plain,
( ~ sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0)
| xn = sdtmndt0(X0,sz00)
| xn != X0 ),
inference(resolution,[status(thm)],[c57,d38]) ).
cnf(d40,plain,
( ~ sdtlseqdt0(sz00,xn)
| ~ aNaturalNumber0(xn)
| xn = sdtmndt0(xn,sz00) ),
inference(equality_resolution,[status(thm)],[d39]) ).
cnf(d41,plain,
( ~ sdtlseqdt0(sz00,xn)
| xn = sdtmndt0(xn,sz00) ),
inference(resolution,[status(thm)],[c57,d40]) ).
cnf(d42,plain,
( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| xn != X0 ),
inference(superposition,[status(thm)],[d36,c26]) ).
cnf(d43,plain,
( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| xn != X0 ),
inference(resolution,[status(thm)],[c0,d42]) ).
cnf(d44,plain,
( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0)
| xn != X0 ),
inference(resolution,[status(thm)],[c57,d43]) ).
cnf(d45,plain,
( sdtlseqdt0(sz00,xn)
| ~ aNaturalNumber0(xn) ),
inference(equality_resolution,[status(thm)],[d44]) ).
cnf(d46,plain,
sdtlseqdt0(sz00,xn),
inference(resolution,[status(thm)],[c57,d45]) ).
cnf(d47,plain,
xn = sdtmndt0(xn,sz00),
inference(resolution,[status(thm)],[d46,d41]) ).
cnf(d48,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
inference(equality_resolution,[status(thm)],[c28]) ).
cnf(d49,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| sdtpldt0(sz00,sdtmndt0(xn,sz00)) = xn ),
inference(resolution,[status(thm)],[d48,d46]) ).
cnf(d50,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| sdtpldt0(sz00,xn) = xn ),
inference(demodulation,[status(thm)],[d49,d47]) ).
cnf(d51,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| xn = xn ),
inference(demodulation,[status(thm)],[d50,d36]) ).
cnf(d52,plain,
( ~ aNaturalNumber0(xn)
| xn = xn ),
inference(resolution,[status(thm)],[c0,d51]) ).
cnf(d53,plain,
xn = xn,
inference(resolution,[status(thm)],[c57,d52]) ).
cnf(d54,plain,
$false,
inference(resolution,[status(thm)],[d53,d35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM475+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 02:54:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.09/7.27 % SZS status Theorem for theBenchmark.p
% 26.09/7.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------