%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM474+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 : n008.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 48.68s 22.55s
% Output : CNFRefutation 48.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 24 unt; 0 def)
% Number of atoms : 120 ( 51 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 117 ( 51 ~; 42 |; 20 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aNaturalNumber0(sz00) ).
fof(mAddComm,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ) ).
fof(mAddAsso,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ).
fof(m_AddZero,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ) ).
fof(mAMDistr,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,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__,conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn) ).
fof(negated_conjecture,negated_conjecture,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c0,plain,
aNaturalNumber0(sz00),
inference(clausification,[status(esa)],[mSortsC]) ).
cnf(c5,plain,
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAddComm]) ).
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(c8,plain,
( X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_AddZero]) ).
cnf(c15,plain,
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAMDistr]) ).
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(c65,plain,
aNaturalNumber0(xp),
inference(clausification,[status(esa)],[m__1360]) ).
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(c75,plain,
sdtpldt0(xp,xr) = xq,
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)],[negated_conjecture]) ).
cnf(d0,plain,
sdtasdt0(xl,xq) = sdtasdt0(xl,sK73),
inference(demodulation,[status(thm)],[c62,c69]) ).
cnf(d1,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(demodulation,[status(thm)],[c77,c66]) ).
cnf(d2,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtpldt0(xm,xn),
inference(demodulation,[status(thm)],[d1,c66]) ).
cnf(d3,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtasdt0(xl,sK73),
inference(demodulation,[status(thm)],[d2,c62]) ).
cnf(d4,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtasdt0(xl,xq),
inference(demodulation,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,sdtpldt0(xp,X0)) = sdtpldt0(xm,sdtasdt0(xl,X0)) ),
inference(superposition,[status(thm)],[c66,c15]) ).
cnf(d6,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,sdtpldt0(xp,X0)) = sdtpldt0(xm,sdtasdt0(xl,X0)) ),
inference(resolution,[status(thm)],[c55,d5]) ).
cnf(d7,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xl,sdtpldt0(xp,X0)) = sdtpldt0(xm,sdtasdt0(xl,X0)) ),
inference(resolution,[status(thm)],[c65,d6]) ).
cnf(d8,plain,
( ~ aNaturalNumber0(xr)
| sdtasdt0(xl,sdtpldt0(xp,xr)) != sdtasdt0(xl,xq) ),
inference(superposition,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
( ~ aNaturalNumber0(xr)
| sdtasdt0(xl,xq) != sdtasdt0(xl,xq) ),
inference(demodulation,[status(thm)],[d8,c75]) ).
cnf(d10,plain,
sdtasdt0(xl,xq) != sdtasdt0(xl,xq),
inference(resolution,[status(thm)],[c74,d9]) ).
cnf(d11,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(sz00,sdtpldt0(X0,X1)) ),
inference(superposition,[status(thm)],[c8,c6]) ).
cnf(d12,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(sz00,sdtpldt0(X0,X1)) ),
inference(resolution,[status(thm)],[c0,d11]) ).
cnf(d13,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sdtpldt0(xm,xn) = sdtpldt0(sz00,sdtasdt0(xl,xq)) ),
inference(superposition,[status(thm)],[c69,d12]) ).
cnf(d14,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtasdt0(xl,xq) = sdtpldt0(sz00,sdtasdt0(xl,xq)) ),
inference(demodulation,[status(thm)],[d13,c69]) ).
cnf(d15,plain,
( ~ aNaturalNumber0(xn)
| sdtasdt0(xl,xq) = sdtpldt0(sz00,sdtasdt0(xl,xq)) ),
inference(resolution,[status(thm)],[c56,d14]) ).
cnf(d16,plain,
sdtasdt0(xl,xq) = sdtpldt0(sz00,sdtasdt0(xl,xq)),
inference(resolution,[status(thm)],[c57,d15]) ).
cnf(d17,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(sz00,sdtpldt0(X1,X0)) ),
inference(superposition,[status(thm)],[c5,d12]) ).
cnf(d18,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtpldt0(xn,xm) = sdtpldt0(sz00,sdtasdt0(xl,xq)) ),
inference(superposition,[status(thm)],[c69,d17]) ).
cnf(d19,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtpldt0(xn,xm) = sdtasdt0(xl,xq) ),
inference(demodulation,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
( ~ aNaturalNumber0(xn)
| sdtpldt0(xn,xm) = sdtasdt0(xl,xq) ),
inference(resolution,[status(thm)],[c56,d19]) ).
cnf(d21,plain,
sdtpldt0(xn,xm) = sdtasdt0(xl,xq),
inference(resolution,[status(thm)],[c57,d20]) ).
cnf(d22,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sdtpldt0(xm,xn) = sdtasdt0(xl,xq) ),
inference(superposition,[status(thm)],[d21,c5]) ).
cnf(d23,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtasdt0(xl,xq) = sdtasdt0(xl,xq) ),
inference(demodulation,[status(thm)],[d22,c69]) ).
cnf(d24,plain,
( ~ aNaturalNumber0(xn)
| sdtasdt0(xl,xq) = sdtasdt0(xl,xq) ),
inference(resolution,[status(thm)],[c56,d23]) ).
cnf(d25,plain,
sdtasdt0(xl,xq) = sdtasdt0(xl,xq),
inference(resolution,[status(thm)],[c57,d24]) ).
cnf(d26,plain,
$false,
inference(resolution,[status(thm)],[d25,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM474+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/15.45 % Computer : n008.cluster.edu
% 0.15/15.45 % Model : x86_64 x86_64
% 0.15/15.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/15.45 % Memory : 8046.5625MB
% 0.15/15.45 % OS : Linux 6.8.0-71-generic
% 0.15/15.45 % CPULimit : 300
% 0.15/15.45 % WCLimit : 300
% 0.15/15.45 % DateTime : Sat Sep 26 02:54:56 UTC 2026
% 0.15/15.46 % CPUTime :
% 0.15/15.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.68/22.55 % SZS status Theorem for theBenchmark.p
% 48.68/22.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------