%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM457+1 : 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 : n016.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 08:12:47 AM UTC 2026
% Result : Theorem 12.14s 1.96s
% Output : CNFRefutation 12.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 59 ( 34 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 62 ( 26 ~; 26 |; 3 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aNaturalNumber0(sz00) ).
fof(m_MulZero,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ) ).
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__624,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ) ).
fof(m__,conjecture,
( sdtasdt0(xm,xn) = sz00
=> ( xn = sz00
| xm = sz00 ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( sdtasdt0(xm,xn) = sz00
=> ( xn = sz00
| xm = sz00 ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c0,plain,
aNaturalNumber0(sz00),
inference(clausification,[status(esa)],[mSortsC]) ).
cnf(c13,plain,
( sdtasdt0(X0,sz00) = sz00
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulZero]) ).
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(c23,plain,
aNaturalNumber0(xm),
inference(clausification,[status(esa)],[m__624]) ).
cnf(c24,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__624]) ).
cnf(c25,plain,
sdtasdt0(xm,xn) = sz00,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c26,plain,
xm != sz00,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c27,plain,
xn != sz00,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| xm = sz00
| xn = X0
| sz00 != sdtasdt0(xm,X0) ),
inference(superposition,[status(thm)],[c25,c19]) ).
cnf(d1,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| xn = X0
| sz00 != sdtasdt0(xm,X0) ),
inference(resolution,[status(thm)],[c26,d0]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| xn = X0
| sz00 != sdtasdt0(xm,X0) ),
inference(resolution,[status(thm)],[c23,d1]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(X0)
| xn = X0
| sz00 != sdtasdt0(xm,X0) ),
inference(resolution,[status(thm)],[c24,d2]) ).
cnf(d4,plain,
sdtasdt0(xm,sz00) = sz00,
inference(resolution,[status(thm)],[c13,c23]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(sz00)
| xn = sz00
| sz00 != sz00 ),
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( xn = sz00
| sz00 != sz00 ),
inference(resolution,[status(thm)],[c0,d5]) ).
cnf(d7,plain,
sz00 != sz00,
inference(resolution,[status(thm)],[c27,d6]) ).
cnf(d8,plain,
$false,
inference(equality_resolution,[status(thm)],[d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM457+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n016.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 02:54:14 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.14/1.96 % SZS status Theorem for theBenchmark.p
% 12.14/1.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------