%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWX220+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 24.68s 3.84s
% Output : CNFRefutation 24.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 15 unt; 0 def)
% Number of atoms : 68 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 73 ( 40 ~; 28 |; 1 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 116 ( 44 sgn 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_025,axiom,
! [X0,X1] : index(cons(X0,X1),zero) = just(X0) ).
fof(axiom_026,axiom,
! [X0,X1,X2] : index(cons(X0,X1),suc(X2)) = index(X1,X2) ).
fof(axiom_027,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_029,axiom,
! [X0,X1,X2,X3] :
( tc(X0,lam(X1),arr(X2,X3))
<=> tc(cons(X2,X0),X1,X3) ) ).
fof(axiom_031,axiom,
! [X0,X1,X2,X3] :
( index(X0,X2) = just(X3)
=> ( tc(X0,var(X2),X1)
<=> X3 = X1 ) ) ).
fof(goal_032,conjecture,
? [X0] : tc(nil,X0,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] : tc(nil,X0,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))),
inference(negate_conjecture,[status(cth)],[goal_032]) ).
cnf(c24,plain,
index(cons(X0,X1),zero) = just(X0),
inference(clausification,[status(esa)],[axiom_025]) ).
cnf(c25,plain,
index(cons(X0,X1),suc(X2)) = index(X1,X2),
inference(clausification,[status(esa)],[axiom_026]) ).
cnf(c28,plain,
( ~ tc(X0,X2,X3)
| ~ tc(X0,X1,arr(X3,X4))
| tc(X0,app(X1,X2,X3),X4) ),
inference(clausification,[status(esa)],[axiom_027]) ).
cnf(c31,plain,
( ~ tc(cons(X2,X0),X1,X3)
| tc(X0,lam(X1),arr(X2,X3)) ),
inference(clausification,[status(esa)],[axiom_029]) ).
cnf(c34,plain,
( X2 != X3
| tc(X0,var(X1),X3)
| index(X0,X1) != just(X2) ),
inference(clausification,[status(esa)],[axiom_031]) ).
cnf(c35,plain,
~ tc(nil,X0,arr(arr(a,arr(b,c)),arr(b,arr(a,c)))),
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)],[c25,c34]) ).
cnf(d1,plain,
( tc(cons(X5,cons(X0,X1)),var(suc(suc(X2))),X4)
| X3 != X4
| index(X1,X2) != just(X3) ),
inference(superposition,[status(thm)],[c25,d0]) ).
cnf(d2,plain,
( tc(cons(X4,cons(X5,cons(X0,X1))),var(suc(suc(zero))),X3)
| X2 != X3
| just(X0) != just(X2) ),
inference(superposition,[status(thm)],[c24,d1]) ).
cnf(d3,plain,
( tc(cons(X2,cons(X3,cons(X0,X4))),var(suc(suc(zero))),X1)
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
tc(cons(X0,cons(X1,cons(X2,X3))),var(suc(suc(zero))),X2),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
( tc(cons(X4,cons(X0,X1)),var(suc(zero)),X3)
| X2 != X3
| just(X0) != just(X2) ),
inference(superposition,[status(thm)],[c24,d0]) ).
cnf(d6,plain,
( tc(cons(X2,cons(X0,X3)),var(suc(zero)),X1)
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
tc(cons(X0,cons(X1,X2)),var(suc(zero)),X1),
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
( tc(cons(X0,X1),var(zero),X3)
| X2 != X3
| just(X0) != just(X2) ),
inference(superposition,[status(thm)],[c24,c34]) ).
cnf(d9,plain,
( tc(cons(X0,X2),var(zero),X1)
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[d8]) ).
cnf(d10,plain,
tc(cons(X0,X1),var(zero),X0),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
~ tc(cons(arr(a,arr(b,c)),nil),X0,arr(b,arr(a,c))),
inference(resolution,[status(thm)],[c31,c35]) ).
cnf(d12,plain,
~ tc(cons(b,cons(arr(a,arr(b,c)),nil)),X0,arr(a,c)),
inference(resolution,[status(thm)],[d11,c31]) ).
cnf(d13,plain,
~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,c),
inference(resolution,[status(thm)],[d12,c31]) ).
cnf(d14,plain,
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2,arr(X1,c))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,X1) ),
inference(resolution,[status(thm)],[d13,c28]) ).
cnf(d15,plain,
( ~ tc(cons(X1,cons(a,cons(b,cons(arr(a,arr(b,c)),nil)))),X2,c)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,X1) ),
inference(resolution,[status(thm)],[d14,c31]) ).
cnf(d16,plain,
( ~ tc(cons(X1,cons(a,cons(b,cons(arr(a,arr(b,c)),nil)))),X4,arr(X3,c))
| ~ tc(cons(X1,cons(a,cons(b,cons(arr(a,arr(b,c)),nil)))),X2,X3)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,X1) ),
inference(resolution,[status(thm)],[d15,c28]) ).
cnf(d17,plain,
( ~ tc(cons(X0,cons(a,cons(b,cons(arr(a,arr(b,c)),nil)))),X6,arr(X5,arr(X2,c)))
| ~ tc(cons(X0,cons(a,cons(b,cons(arr(a,arr(b,c)),nil)))),X4,X5)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3,X0)
| ~ tc(cons(X0,cons(a,cons(b,cons(arr(a,arr(b,c)),nil)))),X1,X2) ),
inference(resolution,[status(thm)],[d16,c28]) ).
cnf(d18,plain,
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X4,arr(X0,arr(X1,c)))
| ~ tc(cons(arr(X0,arr(X1,c)),cons(a,cons(b,cons(arr(a,arr(b,c)),nil)))),X3,X1)
| ~ tc(cons(arr(X0,arr(X1,c)),cons(a,cons(b,cons(arr(a,arr(b,c)),nil)))),X2,X0) ),
inference(resolution,[status(thm)],[d17,d10]) ).
cnf(d19,plain,
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2,arr(a,arr(X0,c)))
| ~ tc(cons(arr(a,arr(X0,c)),cons(a,cons(b,cons(arr(a,arr(b,c)),nil)))),X1,X0) ),
inference(resolution,[status(thm)],[d18,d7]) ).
cnf(d20,plain,
~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,arr(a,arr(b,c))),
inference(resolution,[status(thm)],[d19,d4]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[d20,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX220+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 16:58:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.68/3.84 % SZS status Theorem for theBenchmark.p
% 24.68/3.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------