%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWX221+1 : TPTP v9.3.1. Released v9.3.0.
% 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 09:15:41 AM UTC 2026
% Result : Theorem 21.74s 10.07s
% Output : CNFRefutation 21.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 20 unt; 0 def)
% Number of atoms : 105 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 112 ( 60 ~; 41 |; 4 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 124 ( 32 sgn 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_021,axiom,
! [X0,X1,X2,X3] : app(X0,X1,X2) != lam(X3) ).
fof(axiom_023,axiom,
! [X0,X1] : lam(X0) != var(X1) ).
fof(axiom_024,axiom,
! [X0,X1,X2] :
( X0 != lam(proj1Lam(X0))
=> ( nf(app(X0,X1,X2))
<=> ( nf(X1)
& nf(X0) ) ) ) ).
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_030,axiom,
! [X0,X1,X2] : index(cons(X0,X1),suc(X2)) = index(X1,X2) ).
fof(axiom_031,axiom,
! [X0,X1,X2,X3,X4] :
( tc(X0,app(X2,X3,X4),X1)
<=> ( tc(X0,X3,X4)
& tc(X0,X2,arr(X4,X1)) ) ) ).
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(arr(a,arr(b,c)),arr(b,arr(a,c))))
& nf(X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] :
( tc(nil,X0,arr(arr(a,arr(b,c)),arr(b,arr(a,c))))
& nf(X0) ),
inference(negate_conjecture,[status(cth)],[goal_036]) ).
cnf(c20,plain,
app(X0,X1,X2) != lam(X3),
inference(clausification,[status(esa)],[axiom_021]) ).
cnf(c22,plain,
lam(X0) != var(X1),
inference(clausification,[status(esa)],[axiom_023]) ).
cnf(c25,plain,
( ~ nf(X1)
| ~ nf(X0)
| nf(app(X0,X1,X2))
| X0 = lam(proj1Lam(X0)) ),
inference(clausification,[status(esa)],[axiom_024]) ).
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(c32,plain,
index(cons(X0,X1),suc(X2)) = index(X1,X2),
inference(clausification,[status(esa)],[axiom_030]) ).
cnf(c35,plain,
( ~ tc(X0,X2,X3)
| ~ tc(X0,X1,arr(X3,X4))
| tc(X0,app(X1,X2,X3),X4) ),
inference(clausification,[status(esa)],[axiom_031]) ).
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(arr(a,arr(b,c)),arr(b,arr(a,c))))
| ~ nf(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( tc(cons(X0,X1),var(suc(X2)),X4)
| X3 != X4
| index(X1,X2) != just(X3) ),
inference(superposition,[status(thm)],[c32,c41]) ).
cnf(d1,plain,
( tc(cons(X4,cons(X0,X1)),var(suc(zero)),X3)
| X2 != X3
| just(X0) != just(X2) ),
inference(superposition,[status(thm)],[c31,d0]) ).
cnf(d2,plain,
( tc(cons(X2,cons(X0,X3)),var(suc(zero)),X1)
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[d1]) ).
cnf(d3,plain,
tc(cons(X0,cons(X1,X2)),var(suc(zero)),X1),
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
( tc(cons(X0,X1),var(zero),X3)
| X2 != X3
| just(X0) != just(X2) ),
inference(superposition,[status(thm)],[c31,c41]) ).
cnf(d5,plain,
( tc(cons(X0,X2),var(zero),X1)
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
tc(cons(X0,X1),var(zero),X0),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( ~ nf(lam(X0))
| ~ tc(cons(arr(a,arr(b,c)),nil),X0,arr(b,arr(a,c))) ),
inference(resolution,[status(thm)],[c38,c42]) ).
cnf(d8,plain,
( ~ tc(cons(b,cons(arr(a,arr(b,c)),nil)),X0,arr(a,c))
| ~ nf(lam(lam(X0))) ),
inference(resolution,[status(thm)],[d7,c38]) ).
cnf(d9,plain,
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,c)
| ~ nf(lam(lam(lam(X0)))) ),
inference(resolution,[status(thm)],[d8,c38]) ).
cnf(d10,plain,
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,X2)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,arr(X2,c))
| ~ nf(lam(lam(lam(app(X0,X1,X2))))) ),
inference(resolution,[status(thm)],[d9,c35]) ).
cnf(d11,plain,
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,X2)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,arr(X2,arr(X4,c)))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3,X4)
| ~ nf(lam(lam(lam(app(app(X0,X1,X2),X3,X4))))) ),
inference(resolution,[status(thm)],[d10,c35]) ).
cnf(d12,plain,
( tc(cons(X5,cons(X0,X1)),var(suc(suc(X2))),X4)
| X3 != X4
| index(X1,X2) != just(X3) ),
inference(superposition,[status(thm)],[c32,d0]) ).
cnf(d13,plain,
( tc(cons(X4,cons(X5,cons(X0,X1))),var(suc(suc(zero))),X3)
| X2 != X3
| just(X0) != just(X2) ),
inference(superposition,[status(thm)],[c31,d12]) ).
cnf(d14,plain,
( tc(cons(X2,cons(X3,cons(X0,X4))),var(suc(suc(zero))),X1)
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
tc(cons(X0,cons(X1,cons(X2,X3))),var(suc(suc(zero))),X2),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,a)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,b)
| ~ nf(lam(lam(lam(app(app(var(suc(suc(zero))),X0,a),X1,b))))) ),
inference(resolution,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,b)
| ~ nf(lam(lam(lam(app(app(var(suc(suc(zero))),var(zero),a),X0,b))))) ),
inference(resolution,[status(thm)],[d16,d6]) ).
cnf(d18,plain,
( ~ nf(lam(lam(app(app(var(suc(suc(zero))),var(zero),a),X0,b))))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,b) ),
inference(resolution,[status(thm)],[d17,c28]) ).
cnf(d19,plain,
~ nf(lam(lam(app(app(var(suc(suc(zero))),var(zero),a),var(suc(zero)),b)))),
inference(resolution,[status(thm)],[d18,d3]) ).
cnf(d20,plain,
~ nf(lam(app(app(var(suc(suc(zero))),var(zero),a),var(suc(zero)),b))),
inference(resolution,[status(thm)],[d19,c28]) ).
cnf(d21,plain,
~ nf(app(app(var(suc(suc(zero))),var(zero),a),var(suc(zero)),b)),
inference(resolution,[status(thm)],[d20,c28]) ).
cnf(d22,plain,
( ~ nf(var(suc(zero)))
| ~ nf(app(var(suc(suc(zero))),var(zero),a))
| app(var(suc(suc(zero))),var(zero),a) = lam(proj1Lam(app(var(suc(suc(zero))),var(zero),a))) ),
inference(resolution,[status(thm)],[d21,c25]) ).
cnf(d23,plain,
( ~ nf(app(var(suc(suc(zero))),var(zero),a))
| app(var(suc(suc(zero))),var(zero),a) = lam(proj1Lam(app(var(suc(suc(zero))),var(zero),a))) ),
inference(resolution,[status(thm)],[c29,d22]) ).
cnf(d24,plain,
~ nf(app(var(suc(suc(zero))),var(zero),a)),
inference(resolution,[status(thm)],[c20,d23]) ).
cnf(d25,plain,
( ~ nf(var(zero))
| ~ nf(var(suc(suc(zero))))
| var(suc(suc(zero))) = lam(proj1Lam(var(suc(suc(zero))))) ),
inference(resolution,[status(thm)],[d24,c25]) ).
cnf(d26,plain,
( ~ nf(var(zero))
| var(suc(suc(zero))) = lam(proj1Lam(var(suc(suc(zero))))) ),
inference(resolution,[status(thm)],[c29,d25]) ).
cnf(d27,plain,
var(suc(suc(zero))) = lam(proj1Lam(var(suc(suc(zero))))),
inference(resolution,[status(thm)],[d26,c29]) ).
cnf(d28,plain,
var(suc(suc(zero))) != var(X0),
inference(superposition,[status(thm)],[d27,c22]) ).
cnf(d29,plain,
$false,
inference(equality_resolution,[status(thm)],[d28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX221+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n009.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.46 % DateTime : Sat Sep 26 16:58:52 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.74/10.07 % SZS status Theorem for theBenchmark.p
% 21.74/10.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------