%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM475+2 : 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 : n007.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 52.90s 9.23s
% Output : CNFRefutation 52.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 82 ( 28 unt; 2 def)
% Number of atoms : 229 ( 73 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 269 ( 122 ~; 119 |; 20 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 10 !; 3 ?)
% 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(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(m__1324,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ) ).
fof(m__1324_04,hypothesis,
( doDivides0(xl,sdtpldt0(xm,xn))
& ? [X0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) )
& doDivides0(xl,xm)
& ? [X0] :
( xm = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) ) ).
fof(m__1360,hypothesis,
( xp = sdtsldt0(xm,xl)
& xm = sdtasdt0(xl,xp)
& aNaturalNumber0(xp) ) ).
fof(m__1379,hypothesis,
( xq = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& aNaturalNumber0(xq) ) ).
fof(m__1422,hypothesis,
( xr = sdtmndt0(xq,xp)
& sdtpldt0(xp,xr) = xq
& aNaturalNumber0(xr) ) ).
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(c26,plain,
( sdtpldt0(X2,X0) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mDefLE]) ).
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(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(c62,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,sK73),
inference(clausification,[status(esa)],[m__1324_04]) ).
cnf(c66,plain,
xm = sdtasdt0(xl,xp),
inference(clausification,[status(esa)],[m__1360]) ).
cnf(c69,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(clausification,[status(esa)],[m__1379]) ).
cnf(c74,plain,
aNaturalNumber0(xr),
inference(clausification,[status(esa)],[m__1422]) ).
cnf(c77,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(clausification,[status(esa)],[m__1459]) ).
cnf(c78,plain,
xn != sdtasdt0(xl,xr),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(demodulation,[status(thm)],[c77,c66]) ).
cnf(d1,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) = sdtpldt0(xm,xn),
inference(demodulation,[status(thm)],[d0,c66]) ).
cnf(d2,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) = sdtasdt0(xl,xq),
inference(demodulation,[status(thm)],[d1,c69]) ).
cnf(d3,plain,
( ~ sdtlseqdt0(X1,sdtpldt0(X1,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtpldt0(X1,X0))
| X0 = sdtmndt0(sdtpldt0(X1,X0),X1) ),
inference(equality_resolution,[status(thm)],[c29]) ).
cnf(d4,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| xn = sdtmndt0(sdtpldt0(xm,xn),xm)
| ~ sdtlseqdt0(xm,sdtasdt0(xl,xq)) ),
inference(superposition,[status(thm)],[c69,d3]) ).
cnf(d5,plain,
( ~ sdtlseqdt0(xm,sdtasdt0(xl,xq))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| xn = sdtmndt0(sdtasdt0(xl,xq),xm) ),
inference(demodulation,[status(thm)],[d4,c69]) ).
cnf(d6,plain,
( ~ sdtlseqdt0(xm,sdtasdt0(xl,xq))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xq))
| xn = sdtmndt0(sdtasdt0(xl,xq),xm) ),
inference(demodulation,[status(thm)],[d5,c69]) ).
cnf(d7,plain,
( ~ sdtlseqdt0(xm,sdtasdt0(xl,xq))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtasdt0(xl,xq))
| xn = sdtmndt0(sdtasdt0(xl,xq),xm) ),
inference(resolution,[status(thm)],[c56,d6]) ).
cnf(d8,plain,
( ~ sdtlseqdt0(xm,sdtasdt0(xl,xq))
| ~ aNaturalNumber0(sdtasdt0(xl,xq))
| xn = sdtmndt0(sdtasdt0(xl,xq),xm) ),
inference(resolution,[status(thm)],[c57,d7]) ).
cnf(d9,plain,
sdtasdt0(xl,xq) = sdtasdt0(xl,sK73),
inference(demodulation,[status(thm)],[c62,c69]) ).
cnf(d10,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtasdt0(xl,sK73)) ),
inference(superposition,[status(thm)],[c62,c3]) ).
cnf(d11,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xl,xq)) ),
inference(demodulation,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtasdt0(xl,xq)) ),
inference(resolution,[status(thm)],[c56,d11]) ).
cnf(d13,plain,
aNaturalNumber0(sdtasdt0(xl,xq)),
inference(resolution,[status(thm)],[c57,d12]) ).
cnf(d14,plain,
( ~ sdtlseqdt0(xm,sdtasdt0(xl,xq))
| xn = sdtmndt0(sdtasdt0(xl,xq),xm) ),
inference(resolution,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
( sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,sK73) != X0 ),
inference(superposition,[status(thm)],[c62,c26]) ).
cnf(d16,plain,
( sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,xq) != X0 ),
inference(demodulation,[status(thm)],[d15,d9]) ).
cnf(d17,plain,
( sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,xq) != X0 ),
inference(resolution,[status(thm)],[c56,d16]) ).
cnf(d18,plain,
( sdtlseqdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,xq) != X0 ),
inference(resolution,[status(thm)],[c57,d17]) ).
cnf(d19,plain,
( sdtlseqdt0(xm,sdtasdt0(xl,xq))
| ~ aNaturalNumber0(sdtasdt0(xl,xq)) ),
inference(equality_resolution,[status(thm)],[d18]) ).
cnf(d20,plain,
sdtlseqdt0(xm,sdtasdt0(xl,xq)),
inference(resolution,[status(thm)],[d13,d19]) ).
cnf(d21,plain,
xn = sdtmndt0(sdtasdt0(xl,xq),xm),
inference(resolution,[status(thm)],[d20,d14]) ).
cnf(d22,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,sdtasdt0(xl,xr)))
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(xm)
| sdtasdt0(xl,xr) = sdtmndt0(sdtpldt0(xm,sdtasdt0(xl,xr)),xm)
| ~ sdtlseqdt0(xm,sdtasdt0(xl,xq)) ),
inference(superposition,[status(thm)],[d2,d3]) ).
cnf(d23,plain,
( ~ sdtlseqdt0(xm,sdtasdt0(xl,xq))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtpldt0(xm,sdtasdt0(xl,xr)))
| sdtasdt0(xl,xr) = sdtmndt0(sdtasdt0(xl,xq),xm) ),
inference(demodulation,[status(thm)],[d22,d2]) ).
cnf(d24,plain,
( ~ sdtlseqdt0(xm,sdtasdt0(xl,xq))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtpldt0(xm,sdtasdt0(xl,xr)))
| sdtasdt0(xl,xr) = xn ),
inference(demodulation,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
( ~ sdtlseqdt0(xm,sdtasdt0(xl,xq))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xq))
| sdtasdt0(xl,xr) = xn ),
inference(demodulation,[status(thm)],[d24,d2]) ).
cnf(d26,plain,
( ~ sdtlseqdt0(xm,sdtasdt0(xl,xq))
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xq))
| sdtasdt0(xl,xr) = xn ),
inference(resolution,[status(thm)],[c56,d25]) ).
cnf(d27,plain,
( ~ sdtlseqdt0(xm,sdtasdt0(xl,xq))
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| sdtasdt0(xl,xr) = xn ),
inference(resolution,[status(thm)],[d13,d26]) ).
cnf(d28,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,xr))
| sdtasdt0(xl,xr) = xn ),
inference(resolution,[status(thm)],[d20,d27]) ).
cnf(d29,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xr)
| sdtasdt0(xl,xr) = xn ),
inference(resolution,[status(thm)],[d28,c4]) ).
cnf(d30,plain,
( ~ aNaturalNumber0(xr)
| sdtasdt0(xl,xr) = xn ),
inference(resolution,[status(thm)],[c55,d29]) ).
cnf(d31,plain,
sdtasdt0(xl,xr) = xn,
inference(resolution,[status(thm)],[c74,d30]) ).
cnf(d32,plain,
xn != xn,
inference(demodulation,[status(thm)],[c78,d31]) ).
cnf(d33,plain,
xn = sdtpldt0(sz00,xn),
inference(resolution,[status(thm)],[c8,c57]) ).
cnf(d34,plain,
( ~ sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| xn = sdtmndt0(X0,sz00)
| xn != X0 ),
inference(superposition,[status(thm)],[d33,c29]) ).
cnf(d35,plain,
( ~ sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| xn = sdtmndt0(X0,sz00)
| xn != X0 ),
inference(resolution,[status(thm)],[c0,d34]) ).
cnf(d36,plain,
( ~ sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0)
| xn = sdtmndt0(X0,sz00)
| xn != X0 ),
inference(resolution,[status(thm)],[c57,d35]) ).
cnf(d37,plain,
( ~ sdtlseqdt0(sz00,xn)
| ~ aNaturalNumber0(xn)
| xn = sdtmndt0(xn,sz00) ),
inference(equality_resolution,[status(thm)],[d36]) ).
cnf(d38,plain,
( ~ sdtlseqdt0(sz00,xn)
| xn = sdtmndt0(xn,sz00) ),
inference(resolution,[status(thm)],[c57,d37]) ).
cnf(d39,plain,
( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| xn != X0 ),
inference(superposition,[status(thm)],[d33,c26]) ).
cnf(d40,plain,
( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| xn != X0 ),
inference(resolution,[status(thm)],[c0,d39]) ).
cnf(d41,plain,
( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0)
| xn != X0 ),
inference(resolution,[status(thm)],[c57,d40]) ).
cnf(d42,plain,
( sdtlseqdt0(sz00,xn)
| ~ aNaturalNumber0(xn) ),
inference(equality_resolution,[status(thm)],[d41]) ).
cnf(d43,plain,
sdtlseqdt0(sz00,xn),
inference(resolution,[status(thm)],[c57,d42]) ).
cnf(d44,plain,
xn = sdtmndt0(xn,sz00),
inference(resolution,[status(thm)],[d43,d38]) ).
cnf(d45,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
inference(equality_resolution,[status(thm)],[c28]) ).
cnf(d46,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| sdtpldt0(sz00,sdtmndt0(xn,sz00)) = xn ),
inference(resolution,[status(thm)],[d43,d45]) ).
cnf(d47,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| sdtpldt0(sz00,xn) = xn ),
inference(demodulation,[status(thm)],[d46,d44]) ).
cnf(d48,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| xn = xn ),
inference(demodulation,[status(thm)],[d47,d33]) ).
cnf(d49,plain,
( ~ aNaturalNumber0(xn)
| xn = xn ),
inference(resolution,[status(thm)],[c0,d48]) ).
cnf(d50,plain,
xn = xn,
inference(resolution,[status(thm)],[c57,d49]) ).
cnf(d51,plain,
$false,
inference(resolution,[status(thm)],[d50,d32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM475+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 02:52:08 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.90/9.23 % SZS status Theorem for theBenchmark.p
% 52.90/9.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------