%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX222+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 : Thu Sep 24 03:13:29 PM UTC 2026
% Result : Theorem 0.12s 0.46s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 67 ( 16 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 72 ( 34 ~; 25 |; 8 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 62 ( 60 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [E] :
( nf(lam(E))
<=> nf(E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X4] : nf(var(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [Z,Xs] : index(cons(Z,Xs),zero) = just(Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [X,E,Tx2,T1] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [X,Z,X3,Tx3] :
( index(X,X3) = just(Tx3)
=> ( tc(X,var(X3),Z)
<=> Tx3 = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
? [E] :
( tc(nil,E,arr(a,arr(b,b)))
& nf(E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ? [E] :
( tc(nil,E,arr(a,arr(b,b)))
& nf(E) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f68,plain,
! [E] :
( ( ~ nf(E)
| nf(lam(E)) )
& ( nf(E)
| ~ nf(lam(E)) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f69,plain,
( ! [E] :
( ~ nf(E)
| nf(lam(E)) )
& ! [E] :
( nf(E)
| ~ nf(lam(E)) ) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f71,plain,
! [X0] :
( ~ nf(X0)
| nf(lam(X0)) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f72,plain,
! [X0] : nf(var(X0)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f74,plain,
! [X0,X1] : index(cons(X0,X1),zero) = just(X0),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f84,plain,
! [X,E,Tx2,T1] :
( ( ~ tc(cons(Tx2,X),E,T1)
| tc(X,lam(E),arr(Tx2,T1)) )
& ( tc(cons(Tx2,X),E,T1)
| ~ tc(X,lam(E),arr(Tx2,T1)) ) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f85,plain,
( ! [X,E,Tx2,T1] :
( ~ tc(cons(Tx2,X),E,T1)
| tc(X,lam(E),arr(Tx2,T1)) )
& ! [X,E,Tx2,T1] :
( tc(cons(Tx2,X),E,T1)
| ~ tc(X,lam(E),arr(Tx2,T1)) ) ),
inference(miniscoping,[status(thm)],[f84]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( ~ tc(cons(X2,X0),X1,X3)
| tc(X0,lam(X1),arr(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f91,plain,
! [X,Z,X3,Tx3] :
( ( tc(X,var(X3),Z)
<=> Tx3 = Z )
| index(X,X3) != just(Tx3) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f92,plain,
! [X,Z,X3,Tx3] :
( ( ( Tx3 != Z
| tc(X,var(X3),Z) )
& ( Tx3 = Z
| ~ tc(X,var(X3),Z) ) )
| index(X,X3) != just(Tx3) ),
inference(NNF_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
! [X,X3,Tx3] :
( ( ! [Z] :
( Tx3 != Z
| tc(X,var(X3),Z) )
& ! [Z] :
( Tx3 = Z
| ~ tc(X,var(X3),Z) ) )
| index(X,X3) != just(Tx3) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f95,plain,
! [X0,X1,X2,X3] :
( X2 != X3
| tc(X0,var(X1),X3)
| index(X0,X1) != just(X2) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f96,plain,
! [E] :
( ~ tc(nil,E,arr(a,arr(b,b)))
| ~ nf(E) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f97,plain,
! [X0] :
( ~ tc(nil,X0,arr(a,arr(b,b)))
| ~ nf(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( tc(X0,var(X1),X2)
| index(X0,X1) != just(X2) ),
inference(destructive_equality_resolution,[status(thm)],[f95]) ).
fof(f151,plain,
! [X0] :
( ~ nf(lam(X0))
| ~ tc(cons(a,nil),X0,arr(b,b)) ),
inference(resolution,[status(thm)],[f87,f97]) ).
fof(f156,plain,
! [X0] :
( ~ tc(cons(b,cons(a,nil)),X0,b)
| ~ nf(lam(lam(X0))) ),
inference(resolution,[status(thm)],[f151,f87]) ).
fof(f161,plain,
! [X0] :
( ~ nf(lam(lam(var(X0))))
| index(cons(b,cons(a,nil)),X0) != just(b) ),
inference(resolution,[status(thm)],[f98,f156]) ).
fof(f191,plain,
~ nf(lam(lam(var(zero)))),
inference(resolution,[status(thm)],[f161,f74]) ).
fof(f209,plain,
~ nf(lam(var(zero))),
inference(resolution,[status(thm)],[f191,f71]) ).
fof(f210,plain,
~ nf(var(zero)),
inference(resolution,[status(thm)],[f209,f71]) ).
fof(f211,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f210,f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX222+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 10:30:42 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.41 % Drodi V4.1.1
% 0.12/0.46 % Refutation found
% 0.12/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.50 % Elapsed time: 0.099510 seconds
% 0.16/0.50 % CPU time: 0.274713 seconds
% 0.16/0.50 % Total memory used: 44.647 MB
% 0.16/0.50 % Net memory used: 44.386 MB
%------------------------------------------------------------------------------