%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWX222+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 09:15:41 AM UTC 2026
% Result : Theorem 17.30s 7.92s
% Output : CNFRefutation 17.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 38 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 17 ~; 10 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 5 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_026,axiom,
! [X0] :
( nf(lam(X0))
<=> nf(X0) ) ).
fof(axiom_027,axiom,
! [X0] : nf(var(X0)) ).
fof(axiom_029,axiom,
! [X0,X1] : index(cons(X0,X1),zero) = just(X0) ).
fof(axiom_033,axiom,
! [X0,X1,X2,X3] :
( tc(X0,lam(X1),arr(X2,X3))
<=> tc(cons(X2,X0),X1,X3) ) ).
fof(axiom_035,axiom,
! [X0,X1,X2,X3] :
( index(X0,X2) = just(X3)
=> ( tc(X0,var(X2),X1)
<=> X3 = X1 ) ) ).
fof(goal_036,conjecture,
? [X0] :
( tc(nil,X0,arr(a,arr(b,b)))
& nf(X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] :
( tc(nil,X0,arr(a,arr(b,b)))
& nf(X0) ),
inference(negate_conjecture,[status(cth)],[goal_036]) ).
cnf(c28,plain,
( ~ nf(X0)
| nf(lam(X0)) ),
inference(clausification,[status(esa)],[axiom_026]) ).
cnf(c29,plain,
nf(var(X0)),
inference(clausification,[status(esa)],[axiom_027]) ).
cnf(c31,plain,
index(cons(X0,X1),zero) = just(X0),
inference(clausification,[status(esa)],[axiom_029]) ).
cnf(c38,plain,
( ~ tc(cons(X2,X0),X1,X3)
| tc(X0,lam(X1),arr(X2,X3)) ),
inference(clausification,[status(esa)],[axiom_033]) ).
cnf(c41,plain,
( X2 != X3
| tc(X0,var(X1),X3)
| index(X0,X1) != just(X2) ),
inference(clausification,[status(esa)],[axiom_035]) ).
cnf(c42,plain,
( ~ tc(nil,X0,arr(a,arr(b,b)))
| ~ nf(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ nf(lam(X0))
| ~ tc(cons(a,nil),X0,arr(b,b)) ),
inference(resolution,[status(thm)],[c38,c42]) ).
cnf(d1,plain,
( ~ tc(cons(b,cons(a,nil)),X0,b)
| ~ nf(lam(lam(X0))) ),
inference(resolution,[status(thm)],[d0,c38]) ).
cnf(d2,plain,
( tc(cons(X0,X1),var(zero),X3)
| X2 != X3
| just(X0) != just(X2) ),
inference(superposition,[status(thm)],[c31,c41]) ).
cnf(d3,plain,
( tc(cons(X0,X2),var(zero),X1)
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
tc(cons(X0,X1),var(zero),X0),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
~ nf(lam(lam(var(zero)))),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
~ nf(lam(var(zero))),
inference(resolution,[status(thm)],[d5,c28]) ).
cnf(d7,plain,
~ nf(var(zero)),
inference(resolution,[status(thm)],[d6,c28]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c29,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX222+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.39 % Computer : n015.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Sat Sep 26 17:02:19 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.30/7.92 % SZS status Theorem for theBenchmark.p
% 17.30/7.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------