%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SWX222+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 07:02:10 PM UTC 2026
% Result : Theorem 8.55s 1.44s
% Output : CNFRefutation 8.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 40 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 15 ~; 12 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 27 ( 2 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goal_036,plain,
? [E] :
( nf(E)
& tc(nil,E,arr(a,arr(b,b))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_036) ).
fof(goal_036_negated,plain,
~ ? [E] :
( nf(E)
& tc(nil,E,arr(a,arr(b,b))) ),
inference(negate_conjecture,[status(cth)],[goal_036]) ).
cnf(42,plain,
( ~ nf(X0)
| ~ tc(nil,X0,arr(a,arr(b,b))) ),
inference(cnf,[status(esa)],[goal_036_negated]) ).
cnf(l0,plain,
( ~ nf(lam(lam(var(zero))))
| ~ tc(nil,lam(lam(var(zero))),arr(a,arr(b,b))) ),
inference(instantiation,[status(thm)],[42]) ).
fof(axiom_026,plain,
! [E] :
( nf(lam(E))
<=> nf(E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
cnf(28,plain,
( ~ nf(X0)
| nf(lam(X0)) ),
inference(cnf,[status(esa)],[axiom_026]) ).
cnf(l1,plain,
( ~ nf(lam(var(zero)))
| nf(lam(lam(var(zero)))) ),
inference(instantiation,[status(thm)],[28]) ).
fof(axiom_033,plain,
! [X,E,Tx2,T1] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_033) ).
cnf(38,plain,
( ~ tc(cons(X0,X1),X2,X3)
| tc(X1,lam(X2),arr(X0,X3)) ),
inference(cnf,[status(esa)],[axiom_033]) ).
cnf(l2,plain,
( ~ tc(cons(a,nil),lam(var(zero)),arr(b,b))
| tc(nil,lam(lam(var(zero))),arr(a,arr(b,b))) ),
inference(instantiation,[status(thm)],[38]) ).
cnf(l4,plain,
( ~ tc(cons(b,cons(a,nil)),var(zero),b)
| tc(cons(a,nil),lam(var(zero)),arr(b,b)) ),
inference(instantiation,[status(thm)],[38]) ).
cnf(l5,plain,
( ~ nf(var(zero))
| nf(lam(var(zero))) ),
inference(instantiation,[status(thm)],[28]) ).
fof(axiom_027,plain,
! [X4] : nf(var(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
cnf(29,plain,
nf(var(X0)),
inference(cnf,[status(esa)],[axiom_027]) ).
cnf(l6,plain,
nf(var(zero)),
inference(instantiation,[status(thm)],[29]) ).
fof(axiom_035,plain,
! [X,Z,X3,Tx3] :
( index(X,X3) = just(Tx3)
=> ( tc(X,var(X3),Z)
<=> Tx3 = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_035) ).
cnf(41,plain,
( X0 != X1
| index(X2,X3) != just(X0)
| tc(X2,var(X3),X1) ),
inference(cnf,[status(esa)],[axiom_035]) ).
cnf(l7,plain,
( b != b
| index(cons(b,cons(a,nil)),zero) != just(b)
| tc(cons(b,cons(a,nil)),var(zero),b) ),
inference(instantiation,[status(thm)],[41]) ).
fof(axiom_029,plain,
! [Z,Xs] : index(cons(Z,Xs),zero) = just(Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
cnf(31,plain,
index(cons(X0,X1),zero) = just(X0),
inference(cnf,[status(esa)],[axiom_029]) ).
cnf(l20,plain,
index(cons(b,cons(a,nil)),zero) = just(b),
inference(instantiation,[status(thm)],[31]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l4,l5,l6,l7,l20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX222+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.33 % Computer : n007.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 12:33:23 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 % launching worker at depth: 1
% 0.15/0.34 % launching worker at depth: 4
% 0.15/0.34 % launching worker at depth: 6
% 0.15/0.34 % launching worker at depth: 5
% 0.15/0.34 % launching worker at depth: 2
% 0.15/0.34 % launching worker at depth: 7
% 0.15/0.34 % launching worker at depth: 3
% 0.15/0.34 % launching worker at depth: 8
% 0.15/0.34 % launching worker at depth: 9
% 0.15/0.35 % launching worker at depth: 10
% 0.19/0.38 % launching worker at depth: 11
% 8.55/1.44 % SZS status Theorem for theBenchmark
% 8.55/1.44 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------