%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM478+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 : 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 08:12:52 AM UTC 2026
% Result : Theorem 24.07s 5.75s
% Output : CNFRefutation 24.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 56 ( 22 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 57 ( 26 ~; 21 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMulComm,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ).
fof(mMulAsso,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ) ).
fof(m__1524,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xl) ) ).
fof(m__1553,hypothesis,
aNaturalNumber0(xn) ).
fof(m__,conjecture,
( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl)
| sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl)
| sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c9,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMulComm]) ).
cnf(c10,plain,
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMulAsso]) ).
cnf(c57,plain,
aNaturalNumber0(xl),
inference(clausification,[status(esa)],[m__1524]) ).
cnf(c58,plain,
aNaturalNumber0(xm),
inference(clausification,[status(esa)],[m__1524]) ).
cnf(c63,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__1553]) ).
cnf(c64,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c65,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c66,plain,
sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sdtsldt0(xm,xl),X0)) ),
inference(superposition,[status(thm)],[c65,c10]) ).
cnf(d1,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sdtsldt0(xm,xl),X0)) ),
inference(resolution,[status(thm)],[c64,d0]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sdtsldt0(xm,xl),X0)) ),
inference(resolution,[status(thm)],[c57,d1]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(X0,sdtsldt0(xm,xl))) ),
inference(superposition,[status(thm)],[c9,d2]) ).
cnf(d4,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(X0,sdtsldt0(xm,xl))) ),
inference(resolution,[status(thm)],[c64,d3]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(xn)
| sdtasdt0(xn,xm) != sdtasdt0(xm,xn) ),
inference(superposition,[status(thm)],[d4,c66]) ).
cnf(d6,plain,
sdtasdt0(xn,xm) != sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c63,d5]) ).
cnf(d7,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| sdtasdt0(xm,xn) != sdtasdt0(xm,xn) ),
inference(superposition,[status(thm)],[c9,d6]) ).
cnf(d8,plain,
( ~ aNaturalNumber0(xn)
| sdtasdt0(xm,xn) != sdtasdt0(xm,xn) ),
inference(resolution,[status(thm)],[c58,d7]) ).
cnf(d9,plain,
sdtasdt0(xm,xn) != sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c63,d8]) ).
cnf(d10,plain,
$false,
inference(equality_resolution,[status(thm)],[d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM478+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 26 02:54:35 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.07/5.75 % SZS status Theorem for theBenchmark.p
% 24.07/5.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------