%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM462+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 : n020.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 49.17s 7.25s
% Output : CNFRefutation 49.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 10 unt; 0 def)
% Number of atoms : 238 ( 117 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 323 ( 138 ~; 156 |; 22 &)
% ( 0 <=>; 7 =>; 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 10 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB_02,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ) ).
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(mMulCanc,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ) ).
fof(m__897,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xl)
& aNaturalNumber0(xm) ) ).
fof(m__897_03,hypothesis,
( sdtlseqdt0(xl,xn)
& ? [X0] :
( sdtpldt0(xl,X0) = xn
& aNaturalNumber0(X0) )
& xl != xn
& xm != sz00 ) ).
fof(m__,conjecture,
( ( sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ? [X0] :
( sdtpldt0(sdtasdt0(xl,xm),X0) = sdtasdt0(xn,xm)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ? [X0] :
( sdtpldt0(sdtasdt0(xm,xl),X0) = sdtasdt0(xm,xn)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xm,xl) != sdtasdt0(xm,xn) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( sdtlseqdt0(sdtasdt0(xl,xm),sdtasdt0(xn,xm))
| ? [X0] :
( sdtpldt0(sdtasdt0(xl,xm),X0) = sdtasdt0(xn,xm)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xl,xm) != sdtasdt0(xn,xm)
& ( sdtlseqdt0(sdtasdt0(xm,xl),sdtasdt0(xm,xn))
| ? [X0] :
( sdtpldt0(sdtasdt0(xm,xl),X0) = sdtasdt0(xm,xn)
& aNaturalNumber0(X0) ) )
& sdtasdt0(xm,xl) != sdtasdt0(xm,xn) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c4,plain,
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mSortsB_02]) ).
cnf(c9,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMulComm]) ).
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(c19,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| X0 = sz00 ),
inference(clausification,[status(esa)],[mMulCanc]) ).
cnf(c39,plain,
aNaturalNumber0(xm),
inference(clausification,[status(esa)],[m__897]) ).
cnf(c40,plain,
aNaturalNumber0(xl),
inference(clausification,[status(esa)],[m__897]) ).
cnf(c41,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__897]) ).
cnf(c42,plain,
xm != sz00,
inference(clausification,[status(esa)],[m__897_03]) ).
cnf(c43,plain,
xl != xn,
inference(clausification,[status(esa)],[m__897_03]) ).
cnf(c44,plain,
aNaturalNumber0(sK49),
inference(clausification,[status(esa)],[m__897_03]) ).
cnf(c45,plain,
sdtpldt0(xl,sK49) = xn,
inference(clausification,[status(esa)],[m__897_03]) ).
cnf(c47,plain,
( sdtpldt0(sdtasdt0(xm,xl),X1) != sdtasdt0(xm,xn)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(sdtasdt0(xl,xm),X0) != sdtasdt0(xn,xm) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtpldt0(sdtasdt0(xm,xl),X1) != sdtasdt0(xm,xn)
| sdtpldt0(sdtasdt0(xm,xl),X0) != sdtasdt0(xn,xm) ),
inference(superposition,[status(thm)],[c9,c47]) ).
cnf(d1,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtpldt0(sdtasdt0(xm,xl),X1) != sdtasdt0(xn,xm)
| sdtpldt0(sdtasdt0(xm,xl),X0) != sdtasdt0(xm,xn) ),
inference(resolution,[status(thm)],[c39,d0]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtpldt0(sdtasdt0(xm,xl),X1) != sdtasdt0(xm,xn)
| sdtpldt0(sdtasdt0(xm,xl),X0) != sdtasdt0(xn,xm) ),
inference(resolution,[status(thm)],[c40,d1]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X1)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtpldt0(sdtasdt0(xm,xl),X1) != sdtasdt0(xm,xn)
| sdtasdt0(xm,sdtpldt0(xl,X0)) != sdtasdt0(xn,xm) ),
inference(superposition,[status(thm)],[c15,d2]) ).
cnf(d4,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtasdt0(xm,sdtpldt0(xl,X1)) != sdtasdt0(xn,xm)
| sdtpldt0(sdtasdt0(xm,xl),X0) != sdtasdt0(xm,xn) ),
inference(resolution,[status(thm)],[c39,d3]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtasdt0(xm,sdtpldt0(xl,X1)) != sdtasdt0(xn,xm)
| sdtpldt0(sdtasdt0(xm,xl),X0) != sdtasdt0(xm,xn) ),
inference(resolution,[status(thm)],[c40,d4]) ).
cnf(d6,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK49)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtpldt0(sdtasdt0(xm,xl),X0) != sdtasdt0(xm,xn)
| sdtasdt0(xm,xn) != sdtasdt0(xn,xm) ),
inference(superposition,[status(thm)],[c45,d5]) ).
cnf(d7,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xn) != sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtpldt0(sdtasdt0(xm,xl),X0) != sdtasdt0(xm,xn) ),
inference(resolution,[status(thm)],[c44,d6]) ).
cnf(d8,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xn) != sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtasdt0(xm,sdtpldt0(xl,X0)) != sdtasdt0(xm,xn) ),
inference(superposition,[status(thm)],[c15,d7]) ).
cnf(d9,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xn) != sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtasdt0(xm,sdtpldt0(xl,X0)) != sdtasdt0(xm,xn) ),
inference(resolution,[status(thm)],[c39,d8]) ).
cnf(d10,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xn) != sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtasdt0(xm,sdtpldt0(xl,X0)) != sdtasdt0(xm,xn) ),
inference(resolution,[status(thm)],[c40,d9]) ).
cnf(d11,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| ~ aNaturalNumber0(sK49)
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xn) != sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtasdt0(xm,xn) != sdtasdt0(xm,xn) ),
inference(superposition,[status(thm)],[c45,d10]) ).
cnf(d12,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xn) != sdtasdt0(xn,xm)
| sdtasdt0(xm,xn) != sdtasdt0(xm,xn)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(resolution,[status(thm)],[c44,d11]) ).
cnf(d13,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xn) != sdtasdt0(xm,xn)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| sdtasdt0(xm,xn) != sdtasdt0(xm,xn) ),
inference(superposition,[status(thm)],[c9,d12]) ).
cnf(d14,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xn) != sdtasdt0(xm,xn)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(resolution,[status(thm)],[c39,d13]) ).
cnf(d15,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xn) != sdtasdt0(xm,xn)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(resolution,[status(thm)],[c41,d14]) ).
cnf(d16,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| sdtasdt0(xl,xm) = sdtasdt0(xn,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(equality_resolution,[status(thm)],[d15]) ).
cnf(d17,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtasdt0(xm,xn) = sdtasdt0(xl,xm) ),
inference(superposition,[status(thm)],[d16,c9]) ).
cnf(d18,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| sdtasdt0(xm,xn) = sdtasdt0(xl,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(resolution,[status(thm)],[c39,d17]) ).
cnf(d19,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| sdtasdt0(xm,xn) = sdtasdt0(xl,xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(resolution,[status(thm)],[c41,d18]) ).
cnf(d20,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(superposition,[status(thm)],[d19,c9]) ).
cnf(d21,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(resolution,[status(thm)],[c39,d20]) ).
cnf(d22,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| sdtasdt0(xm,xl) = sdtasdt0(xm,xn) ),
inference(resolution,[status(thm)],[c40,d21]) ).
cnf(d23,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| xm = sz00
| X0 = xn
| sdtasdt0(xm,X0) != sdtasdt0(xm,xl) ),
inference(superposition,[status(thm)],[d22,c19]) ).
cnf(d24,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| ~ aNaturalNumber0(X0)
| xm = sz00
| sdtasdt0(xm,X0) != sdtasdt0(xm,xl)
| X0 = xn ),
inference(resolution,[status(thm)],[c39,d23]) ).
cnf(d25,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| ~ aNaturalNumber0(X0)
| xm = sz00
| sdtasdt0(xm,X0) != sdtasdt0(xm,xl)
| X0 = xn ),
inference(resolution,[status(thm)],[c41,d24]) ).
cnf(d26,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,X0) != sdtasdt0(xm,xl)
| X0 = xn ),
inference(resolution,[status(thm)],[c42,d25]) ).
cnf(d27,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| ~ aNaturalNumber0(xl)
| xl = xn ),
inference(equality_resolution,[status(thm)],[d26]) ).
cnf(d28,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK49))
| xl = xn ),
inference(resolution,[status(thm)],[c40,d27]) ).
cnf(d29,plain,
~ aNaturalNumber0(sdtasdt0(xm,sK49)),
inference(resolution,[status(thm)],[c43,d28]) ).
cnf(d30,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sK49) ),
inference(resolution,[status(thm)],[d29,c4]) ).
cnf(d31,plain,
~ aNaturalNumber0(sK49),
inference(resolution,[status(thm)],[c39,d30]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[c44,d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM462+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
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 02:51:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 49.17/7.25 % SZS status Theorem for theBenchmark.p
% 49.17/7.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------