%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM461+2 : 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 : n019.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 08:12:48 AM UTC 2026
% Result : Theorem 26.21s 9.04s
% Output : CNFRefutation 26.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 10 unt; 0 def)
% Number of atoms : 204 ( 121 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 259 ( 105 ~; 131 |; 19 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 8 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(m__840,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xl) ) ).
fof(m__840_03,hypothesis,
( sdtlseqdt0(xl,xn)
& ? [X0] :
( sdtpldt0(xl,X0) = xn
& aNaturalNumber0(X0) )
& xl != xn ) ).
fof(m__873,hypothesis,
aNaturalNumber0(xm) ).
fof(m__,conjecture,
( ( sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
| ? [X0] :
( sdtpldt0(sdtpldt0(xl,xm),X0) = sdtpldt0(xn,xm)
& aNaturalNumber0(X0) ) )
& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
& ( sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| ? [X0] :
( sdtpldt0(sdtpldt0(xm,xl),X0) = sdtpldt0(xm,xn)
& aNaturalNumber0(X0) ) )
& sdtpldt0(xm,xl) != sdtpldt0(xm,xn) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( sdtlseqdt0(sdtpldt0(xl,xm),sdtpldt0(xn,xm))
| ? [X0] :
( sdtpldt0(sdtpldt0(xl,xm),X0) = sdtpldt0(xn,xm)
& aNaturalNumber0(X0) ) )
& sdtpldt0(xl,xm) != sdtpldt0(xn,xm)
& ( sdtlseqdt0(sdtpldt0(xm,xl),sdtpldt0(xm,xn))
| ? [X0] :
( sdtpldt0(sdtpldt0(xm,xl),X0) = sdtpldt0(xm,xn)
& aNaturalNumber0(X0) ) )
& sdtpldt0(xm,xl) != sdtpldt0(xm,xn) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
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(c17,plain,
( X1 = X0
| sdtpldt0(X2,X1) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAddCanc]) ).
cnf(c18,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| X0 = X2
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X1) != sdtpldt0(X2,X1) ),
inference(clausification,[status(esa)],[mAddCanc]) ).
cnf(c35,plain,
aNaturalNumber0(xl),
inference(clausification,[status(esa)],[m__840]) ).
cnf(c36,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__840]) ).
cnf(c37,plain,
xl != xn,
inference(clausification,[status(esa)],[m__840_03]) ).
cnf(c38,plain,
aNaturalNumber0(sK46),
inference(clausification,[status(esa)],[m__840_03]) ).
cnf(c39,plain,
sdtpldt0(xl,sK46) = xn,
inference(clausification,[status(esa)],[m__840_03]) ).
cnf(c41,plain,
aNaturalNumber0(xm),
inference(clausification,[status(esa)],[m__873]) ).
cnf(c42,plain,
( sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtpldt0(xm,xl),X1) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(sdtpldt0(xl,xm),X0) != sdtpldt0(xn,xm) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(sdtpldt0(xl,xm),X1) != sdtpldt0(xn,xm)
| sdtpldt0(xm,sdtpldt0(xl,X0)) != sdtpldt0(xm,xn) ),
inference(superposition,[status(thm)],[c6,c42]) ).
cnf(d1,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xm,sdtpldt0(xl,X1)) != sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(sdtpldt0(xl,xm),X0) != sdtpldt0(xn,xm) ),
inference(resolution,[status(thm)],[c35,d0]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xm,sdtpldt0(xl,X1)) != sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(sdtpldt0(xl,xm),X0) != sdtpldt0(xn,xm) ),
inference(resolution,[status(thm)],[c41,d1]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK46)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(sdtpldt0(xl,xm),X0) != sdtpldt0(xn,xm)
| sdtpldt0(xm,xn) != sdtpldt0(xm,xn) ),
inference(superposition,[status(thm)],[c39,d2]) ).
cnf(d4,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(sdtpldt0(xl,xm),X0) != sdtpldt0(xn,xm) ),
inference(resolution,[status(thm)],[c38,d3]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(sdtpldt0(xm,xl),X0) != sdtpldt0(xn,xm) ),
inference(superposition,[status(thm)],[c5,d4]) ).
cnf(d6,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(sdtpldt0(xm,xl),X0) != sdtpldt0(xn,xm) ),
inference(resolution,[status(thm)],[c35,d5]) ).
cnf(d7,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(sdtpldt0(xm,xl),X0) != sdtpldt0(xn,xm) ),
inference(resolution,[status(thm)],[c41,d6]) ).
cnf(d8,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(xm,sdtpldt0(xl,X0)) != sdtpldt0(xn,xm) ),
inference(superposition,[status(thm)],[c6,d7]) ).
cnf(d9,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xm,sdtpldt0(xl,X0)) != sdtpldt0(xn,xm)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ),
inference(resolution,[status(thm)],[c35,d8]) ).
cnf(d10,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xm,sdtpldt0(xl,X0)) != sdtpldt0(xn,xm)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ),
inference(resolution,[status(thm)],[c41,d9]) ).
cnf(d11,plain,
( ~ aNaturalNumber0(sK46)
| sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(xm,xn) != sdtpldt0(xn,xm) ),
inference(superposition,[status(thm)],[c39,d10]) ).
cnf(d12,plain,
( sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xn) != sdtpldt0(xn,xm)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ),
inference(resolution,[status(thm)],[c38,d11]) ).
cnf(d13,plain,
( sdtpldt0(xm,xn) != sdtpldt0(xn,xm)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ),
inference(equality_resolution,[status(thm)],[d12]) ).
cnf(d14,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| sdtpldt0(xm,xn) != sdtpldt0(xm,xn) ),
inference(superposition,[status(thm)],[c5,d13]) ).
cnf(d15,plain,
( ~ aNaturalNumber0(xm)
| sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ),
inference(resolution,[status(thm)],[c36,d14]) ).
cnf(d16,plain,
( sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ),
inference(resolution,[status(thm)],[c41,d15]) ).
cnf(d17,plain,
( sdtpldt0(xm,xl) = sdtpldt0(xm,xn)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ),
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
( sdtpldt0(xl,xm) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| xn = X0
| sdtpldt0(xm,xl) != sdtpldt0(xm,X0) ),
inference(superposition,[status(thm)],[d17,c17]) ).
cnf(d19,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| xn = X0
| sdtpldt0(xm,xl) != sdtpldt0(xm,X0)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ),
inference(resolution,[status(thm)],[c36,d18]) ).
cnf(d20,plain,
( ~ aNaturalNumber0(X0)
| xn = X0
| sdtpldt0(xm,xl) != sdtpldt0(xm,X0)
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ),
inference(resolution,[status(thm)],[c41,d19]) ).
cnf(d21,plain,
( ~ aNaturalNumber0(xl)
| xn = xl
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ),
inference(equality_resolution,[status(thm)],[d20]) ).
cnf(d22,plain,
( xn = xl
| sdtpldt0(xl,xm) = sdtpldt0(xn,xm) ),
inference(resolution,[status(thm)],[c35,d21]) ).
cnf(d23,plain,
( xn = xl
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| X0 = xn
| sdtpldt0(X0,xm) != sdtpldt0(xl,xm) ),
inference(superposition,[status(thm)],[d22,c18]) ).
cnf(d24,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| xn = xl
| sdtpldt0(X0,xm) != sdtpldt0(xl,xm)
| X0 = xn ),
inference(resolution,[status(thm)],[c36,d23]) ).
cnf(d25,plain,
( ~ aNaturalNumber0(X0)
| xn = xl
| sdtpldt0(X0,xm) != sdtpldt0(xl,xm)
| X0 = xn ),
inference(resolution,[status(thm)],[c41,d24]) ).
cnf(d26,plain,
( ~ aNaturalNumber0(xl)
| xn = xl
| xl = xn ),
inference(equality_resolution,[status(thm)],[d25]) ).
cnf(d27,plain,
( xn = xl
| xl = xn ),
inference(resolution,[status(thm)],[c35,d26]) ).
cnf(d28,plain,
xn = xl,
inference(resolution,[status(thm)],[c37,d27]) ).
cnf(d29,plain,
xl != xl,
inference(demodulation,[status(thm)],[c37,d28]) ).
cnf(d30,plain,
$false,
inference(equality_resolution,[status(thm)],[d29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM461+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.60 % Computer : n019.cluster.edu
% 0.10/5.60 % Model : x86_64 x86_64
% 0.10/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.60 % Memory : 8046.5625MB
% 0.10/5.60 % OS : Linux 6.8.0-71-generic
% 0.10/5.60 % CPULimit : 300
% 0.10/5.60 % WCLimit : 300
% 0.10/5.60 % DateTime : Sat Sep 26 02:50:28 UTC 2026
% 0.10/5.61 % CPUTime :
% 0.10/5.61 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.21/9.04 % SZS status Theorem for theBenchmark.p
% 26.21/9.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------