%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SYN986+1.003 : 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 : n009.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 09:34:29 AM UTC 2026
% Result : Theorem 9.50s 2.46s
% Output : CNFRefutation 9.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 37 ( 17 ~; 12 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 40 ( 4 sgn 5 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(hyp1,axiom,
! [X0] : r(X0,zero,succ(X0)) ).
fof(hyp2,axiom,
! [X0,X1,X2,X3] :
( r(X0,X1,X2)
=> ( r(X2,X1,X3)
=> r(X0,succ(X1),X3) ) ) ).
fof(ck,conjecture,
? [X0,X1,X2,X3] :
( r(zero,X2,X3)
& r(zero,X1,X2)
& r(zero,X0,X1)
& r(zero,zero,X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1,X2,X3] :
( r(zero,X2,X3)
& r(zero,X1,X2)
& r(zero,X0,X1)
& r(zero,zero,X0) ),
inference(negate_conjecture,[status(cth)],[ck]) ).
cnf(c0,plain,
r(X0,zero,succ(X0)),
inference(clausification,[status(esa)],[hyp1]) ).
cnf(c1,plain,
( r(X0,succ(X1),X3)
| ~ r(X2,X1,X3)
| ~ r(X0,X1,X2) ),
inference(clausification,[status(esa)],[hyp2]) ).
cnf(c2,plain,
( ~ r(zero,X2,X3)
| ~ r(zero,X1,X2)
| ~ r(zero,X0,X1)
| ~ r(zero,zero,X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ r(zero,X0,X1)
| ~ r(zero,X1,X2)
| ~ r(zero,succ(zero),X0) ),
inference(resolution,[status(thm)],[c0,c2]) ).
cnf(d1,plain,
( r(X0,succ(zero),X1)
| ~ r(succ(X0),zero,X1) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d2,plain,
r(X0,succ(zero),succ(succ(X0))),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
( ~ r(zero,succ(succ(zero)),X0)
| ~ r(zero,X0,X1) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( r(X0,succ(succ(zero)),X1)
| ~ r(succ(succ(X0)),succ(zero),X1) ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d5,plain,
r(X0,succ(succ(zero)),succ(succ(succ(succ(X0))))),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
~ r(zero,succ(succ(succ(succ(zero)))),X0),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( r(X0,succ(succ(succ(zero))),X1)
| ~ r(succ(succ(succ(succ(X0)))),succ(succ(zero)),X1) ),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d8,plain,
r(X0,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( r(X0,succ(succ(succ(succ(zero)))),X1)
| ~ r(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))),succ(succ(succ(zero))),X1) ),
inference(resolution,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
r(X0,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))))))),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN986+1.003 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n009.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 18:53:44 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.50/2.46 % SZS status Theorem for theBenchmark.p
% 9.50/2.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------