%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM474+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 : n012.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 148.16s 22.32s
% Output : CNFRefutation 148.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 102 ( 43 unt; 2 def)
% Number of atoms : 255 ( 112 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 273 ( 120 ~; 126 |; 16 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 73 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aNaturalNumber0(sz00) ).
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(m_AddZero,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ) ).
fof(mMulComm,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,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(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__,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(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(c7,plain,
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_AddZero]) ).
cnf(c8,plain,
( X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_AddZero]) ).
cnf(c9,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMulComm]) ).
cnf(c16,plain,
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAMDistr]) ).
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(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)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xl) = sdtasdt0(xl,X0) ),
inference(resolution,[status(thm)],[c9,c55]) ).
cnf(d1,plain,
( ~ sdtlseqdt0(xp,xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq)
| aNaturalNumber0(X0)
| X0 != xr ),
inference(superposition,[status(thm)],[c64,c27]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(X0)
| X0 != xr ),
inference(resolution,[status(thm)],[c63,d1]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| aNaturalNumber0(xr) ),
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl)
| xl = sz00
| X0 != xp ),
inference(superposition,[status(thm)],[c61,c50]) ).
cnf(d5,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(X0)
| xl = sz00
| X0 != xp ),
inference(resolution,[status(thm)],[c55,d4]) ).
cnf(d6,plain,
( ~ doDivides0(xl,xm)
| aNaturalNumber0(X0)
| xl = sz00
| X0 != xp ),
inference(resolution,[status(thm)],[c56,d5]) ).
cnf(d7,plain,
( aNaturalNumber0(X0)
| xl = sz00
| X0 != xp ),
inference(resolution,[status(thm)],[c58,d6]) ).
cnf(d8,plain,
( aNaturalNumber0(X0)
| X0 != xp ),
inference(resolution,[status(thm)],[c60,d7]) ).
cnf(d9,plain,
aNaturalNumber0(xp),
inference(equality_resolution,[status(thm)],[d8]) ).
cnf(d10,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xq) ),
inference(resolution,[status(thm)],[d9,d3]) ).
cnf(d11,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(d12,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| aNaturalNumber0(X0)
| xl = sz00
| X0 != xq ),
inference(resolution,[status(thm)],[c55,d11]) ).
cnf(d13,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| aNaturalNumber0(X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c60,d12]) ).
cnf(d14,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| aNaturalNumber0(X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c59,d13]) ).
cnf(d15,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| aNaturalNumber0(xq) ),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(xq) ),
inference(resolution,[status(thm)],[d15,c3]) ).
cnf(d17,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c56,d16]) ).
cnf(d18,plain,
aNaturalNumber0(xq),
inference(resolution,[status(thm)],[c57,d17]) ).
cnf(d19,plain,
aNaturalNumber0(xr),
inference(resolution,[status(thm)],[d18,d10]) ).
cnf(d20,plain,
sdtasdt0(xr,xl) = sdtasdt0(xl,xr),
inference(resolution,[status(thm)],[d19,d0]) ).
cnf(d21,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| sdtpldt0(xm,xn) = sdtasdt0(xl,X0)
| xl = sz00
| X0 != xq ),
inference(superposition,[status(thm)],[c62,c51]) ).
cnf(d22,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| xl = sz00
| sdtpldt0(xm,xn) = sdtasdt0(xl,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c55,d21]) ).
cnf(d23,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| sdtpldt0(xm,xn) = sdtasdt0(xl,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c60,d22]) ).
cnf(d24,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| sdtpldt0(xm,xn) = sdtasdt0(xl,X0)
| X0 != xq ),
inference(resolution,[status(thm)],[c59,d23]) ).
cnf(d25,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| sdtpldt0(xm,xn) = sdtasdt0(xl,xq) ),
inference(equality_resolution,[status(thm)],[d24]) ).
cnf(d26,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sdtpldt0(xm,xn) = sdtasdt0(xl,xq) ),
inference(resolution,[status(thm)],[d25,c3]) ).
cnf(d27,plain,
( ~ aNaturalNumber0(xn)
| sdtpldt0(xm,xn) = sdtasdt0(xl,xq) ),
inference(resolution,[status(thm)],[c56,d26]) ).
cnf(d28,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(resolution,[status(thm)],[c57,d27]) ).
cnf(d29,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xq) = sdtasdt0(xq,X0) ),
inference(resolution,[status(thm)],[d18,c9]) ).
cnf(d30,plain,
sdtasdt0(xl,xq) = sdtasdt0(xq,xl),
inference(resolution,[status(thm)],[d29,c55]) ).
cnf(d31,plain,
sdtpldt0(xm,xn) = sdtasdt0(xq,xl),
inference(demodulation,[status(thm)],[d30,d28]) ).
cnf(d32,plain,
( ~ sdtlseqdt0(xp,xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq)
| sdtpldt0(xp,X0) = xq
| X0 != xr ),
inference(superposition,[status(thm)],[c64,c28]) ).
cnf(d33,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| sdtpldt0(xp,X0) = xq
| X0 != xr ),
inference(resolution,[status(thm)],[c63,d32]) ).
cnf(d34,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| sdtpldt0(xp,xr) = xq ),
inference(equality_resolution,[status(thm)],[d33]) ).
cnf(d35,plain,
( ~ aNaturalNumber0(xq)
| sdtpldt0(xp,xr) = xq ),
inference(resolution,[status(thm)],[d9,d34]) ).
cnf(d36,plain,
sdtpldt0(xp,xr) = xq,
inference(resolution,[status(thm)],[d18,d35]) ).
cnf(d37,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| xm = sdtasdt0(xl,X0)
| xl = sz00
| X0 != xp ),
inference(superposition,[status(thm)],[c61,c51]) ).
cnf(d38,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xm)
| xm = sdtasdt0(xl,X0)
| xl = sz00
| X0 != xp ),
inference(resolution,[status(thm)],[c55,d37]) ).
cnf(d39,plain,
( ~ doDivides0(xl,xm)
| xm = sdtasdt0(xl,X0)
| xl = sz00
| X0 != xp ),
inference(resolution,[status(thm)],[c56,d38]) ).
cnf(d40,plain,
( xm = sdtasdt0(xl,X0)
| xl = sz00
| X0 != xp ),
inference(resolution,[status(thm)],[c58,d39]) ).
cnf(d41,plain,
( xm = sdtasdt0(xl,X0)
| X0 != xp ),
inference(resolution,[status(thm)],[c60,d40]) ).
cnf(d42,plain,
xm = sdtasdt0(xl,xp),
inference(equality_resolution,[status(thm)],[d41]) ).
cnf(d43,plain,
sdtasdt0(xp,xl) = sdtasdt0(xl,xp),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d44,plain,
sdtasdt0(xp,xl) = xm,
inference(demodulation,[status(thm)],[d43,d42]) ).
cnf(d45,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtpldt0(X0,X1),xl) = sdtpldt0(sdtasdt0(X0,xl),sdtasdt0(X1,xl)) ),
inference(resolution,[status(thm)],[c16,c55]) ).
cnf(d46,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtpldt0(xp,X0),xl) = sdtpldt0(sdtasdt0(xp,xl),sdtasdt0(X0,xl)) ),
inference(resolution,[status(thm)],[d9,d45]) ).
cnf(d47,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtpldt0(xp,X0),xl) = sdtpldt0(xm,sdtasdt0(X0,xl)) ),
inference(demodulation,[status(thm)],[d46,d44]) ).
cnf(d48,plain,
sdtasdt0(sdtpldt0(xp,xr),xl) = sdtpldt0(xm,sdtasdt0(xr,xl)),
inference(resolution,[status(thm)],[d47,d19]) ).
cnf(d49,plain,
sdtasdt0(xq,xl) = sdtpldt0(xm,sdtasdt0(xr,xl)),
inference(demodulation,[status(thm)],[d48,d36]) ).
cnf(d50,plain,
sdtpldt0(xm,xn) = sdtpldt0(xm,sdtasdt0(xr,xl)),
inference(demodulation,[status(thm)],[d49,d31]) ).
cnf(d51,plain,
sdtpldt0(xm,xn) = sdtpldt0(xm,sdtasdt0(xl,xr)),
inference(demodulation,[status(thm)],[d50,d20]) ).
cnf(d52,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(demodulation,[status(thm)],[c65,d42]) ).
cnf(d53,plain,
sdtpldt0(xm,sdtasdt0(xl,xr)) != sdtpldt0(xm,xn),
inference(demodulation,[status(thm)],[d52,d42]) ).
cnf(d54,plain,
sdtpldt0(xm,xn) != sdtpldt0(xm,xn),
inference(demodulation,[status(thm)],[d53,d51]) ).
cnf(d55,plain,
xn = sdtpldt0(sz00,xn),
inference(resolution,[status(thm)],[c8,c57]) ).
cnf(d56,plain,
sdtpldt0(xm,sz00) = xm,
inference(resolution,[status(thm)],[c7,c56]) ).
cnf(d57,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(X0,sz00),X1) = sdtpldt0(X0,sdtpldt0(sz00,X1)) ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(d58,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xm,sz00),X0) = sdtpldt0(xm,sdtpldt0(sz00,X0)) ),
inference(resolution,[status(thm)],[d57,c56]) ).
cnf(d59,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(xm,X0) = sdtpldt0(xm,sdtpldt0(sz00,X0)) ),
inference(demodulation,[status(thm)],[d58,d56]) ).
cnf(d60,plain,
sdtpldt0(xm,xn) = sdtpldt0(xm,sdtpldt0(sz00,xn)),
inference(resolution,[status(thm)],[d59,c57]) ).
cnf(d61,plain,
sdtpldt0(xm,xn) = sdtpldt0(xm,xn),
inference(demodulation,[status(thm)],[d60,d55]) ).
cnf(d62,plain,
$false,
inference(resolution,[status(thm)],[d61,d54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM474+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 02:53:50 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 148.16/22.32 % SZS status Theorem for theBenchmark.p
% 148.16/22.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------