%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX223+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 : n002.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 0.17s 0.60s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 16 unt; 0 def)
% Number of atoms : 146 ( 29 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 169 ( 79 ~; 62 |; 19 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 144 ( 142 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X,X2,X3,X4] : app(X,X2,X3) != lam(X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,X2] : lam(X) != var(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Y,Z,X2] :
( Y != lam(proj1Lam(Y))
=> ( nf(app(Y,Z,X2))
<=> ( nf(Z)
& nf(Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f30,axiom,
! [Z,Xs,N] : index(cons(Z,Xs),suc(N)) = index(Xs,N),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X,Z,F,X2,Tx] :
( tc(X,app(F,X2,Tx),Z)
<=> ( tc(X,X2,Tx)
& tc(X,F,arr(Tx,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(arr(a,arr(a,b)),arr(a,b)))
& nf(E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ? [E] :
( tc(nil,E,arr(arr(a,arr(a,b)),arr(a,b)))
& nf(E) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f58,plain,
! [X0,X1,X2,X3] : app(X0,X1,X2) != lam(X3),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f60,plain,
! [X0,X1] : lam(X0) != var(X1),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f61,plain,
! [Y,Z,X2] :
( ( nf(app(Y,Z,X2))
<=> ( nf(Z)
& nf(Y) ) )
| Y = lam(proj1Lam(Y)) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f62,plain,
! [Y,Z,X2] :
( ( ( ~ nf(Z)
| ~ nf(Y)
| nf(app(Y,Z,X2)) )
& ( ( nf(Z)
& nf(Y) )
| ~ nf(app(Y,Z,X2)) ) )
| Y = lam(proj1Lam(Y)) ),
inference(NNF_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [Y] :
( ( ! [Z] :
( ~ nf(Z)
| ~ nf(Y)
| ! [X2] : nf(app(Y,Z,X2)) )
& ! [Z] :
( ( nf(Z)
& nf(Y) )
| ! [X2] : ~ nf(app(Y,Z,X2)) ) )
| Y = lam(proj1Lam(Y)) ),
inference(miniscoping,[status(thm)],[f62]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ nf(X1)
| ~ nf(X0)
| nf(app(X0,X1,X2))
| X0 = lam(proj1Lam(X0)) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
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(f75,plain,
! [X0,X1,X2] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f76,plain,
! [X,Z,F,X2,Tx] :
( ( ~ tc(X,X2,Tx)
| ~ tc(X,F,arr(Tx,Z))
| tc(X,app(F,X2,Tx),Z) )
& ( ( tc(X,X2,Tx)
& tc(X,F,arr(Tx,Z)) )
| ~ tc(X,app(F,X2,Tx),Z) ) ),
inference(NNF_transformation,[status(thm)],[f31]) ).
fof(f77,plain,
( ! [X,Z,F,X2,Tx] :
( ~ tc(X,X2,Tx)
| ~ tc(X,F,arr(Tx,Z))
| tc(X,app(F,X2,Tx),Z) )
& ! [X,Z,F,X2,Tx] :
( ( tc(X,X2,Tx)
& tc(X,F,arr(Tx,Z)) )
| ~ tc(X,app(F,X2,Tx),Z) ) ),
inference(miniscoping,[status(thm)],[f76]) ).
fof(f80,plain,
! [X0,X1,X2,X3,X4] :
( ~ tc(X0,X2,X3)
| ~ tc(X0,X1,arr(X3,X4))
| tc(X0,app(X1,X2,X3),X4) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
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(arr(a,arr(a,b)),arr(a,b)))
| ~ nf(E) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f97,plain,
! [X0] :
( ~ tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,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(f108,plain,
! [X0,X1] : tc(cons(X0,X1),var(zero),X0),
inference(resolution,[status(thm)],[f98,f74]) ).
fof(f109,plain,
! [X0,X1,X2,X3] :
( tc(cons(X3,X0),var(suc(X1)),X2)
| index(X0,X1) != just(X2) ),
inference(paramodulation,[status(thm)],[f75,f98]) ).
fof(f126,plain,
! [X0] :
( ~ nf(lam(X0))
| ~ tc(cons(arr(a,arr(a,b)),nil),X0,arr(a,b)) ),
inference(resolution,[status(thm)],[f87,f97]) ).
fof(f133,plain,
! [X0,X1,X2] : tc(cons(X0,cons(X1,X2)),var(suc(zero)),X1),
inference(resolution,[status(thm)],[f109,f74]) ).
fof(f144,plain,
! [X0] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,b)
| ~ nf(lam(lam(X0))) ),
inference(resolution,[status(thm)],[f126,f87]) ).
fof(f146,plain,
! [X0,X1,X2] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,X2)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,arr(X2,b))
| ~ nf(lam(lam(app(X0,X1,X2)))) ),
inference(resolution,[status(thm)],[f144,f80]) ).
fof(f154,plain,
! [X0,X1,X2,X3,X4] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,X2)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,arr(X2,arr(X4,b)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X3,X4)
| ~ nf(lam(lam(app(app(X0,X1,X2),X3,X4)))) ),
inference(resolution,[status(thm)],[f146,f80]) ).
fof(f226,plain,
! [X0,X1] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,a)
| ~ nf(lam(lam(app(app(var(suc(zero)),X0,a),X1,a)))) ),
inference(resolution,[status(thm)],[f154,f133]) ).
fof(f268,plain,
! [X0,X1] :
( ~ nf(lam(app(app(var(suc(zero)),X1,a),X0,a)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,a)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a) ),
inference(resolution,[status(thm)],[f226,f71]) ).
fof(f269,plain,
! [X0] :
( ~ nf(lam(app(app(var(suc(zero)),var(zero),a),X0,a)))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a) ),
inference(resolution,[status(thm)],[f268,f108]) ).
fof(f271,plain,
! [X0] :
( ~ nf(app(app(var(suc(zero)),var(zero),a),X0,a))
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a) ),
inference(resolution,[status(thm)],[f269,f71]) ).
fof(f272,plain,
~ nf(app(app(var(suc(zero)),var(zero),a),var(zero),a)),
inference(resolution,[status(thm)],[f271,f108]) ).
fof(f274,plain,
( ~ nf(var(zero))
| ~ nf(app(var(suc(zero)),var(zero),a))
| app(var(suc(zero)),var(zero),a) = lam(proj1Lam(app(var(suc(zero)),var(zero),a))) ),
inference(resolution,[status(thm)],[f272,f66]) ).
fof(f275,plain,
( ~ nf(var(zero))
| ~ nf(app(var(suc(zero)),var(zero),a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f274,f58]) ).
fof(f276,plain,
~ nf(app(var(suc(zero)),var(zero),a)),
inference(forward_subsumption_resolution,[status(thm)],[f275,f72]) ).
fof(f277,plain,
( ~ nf(var(zero))
| ~ nf(var(suc(zero)))
| var(suc(zero)) = lam(proj1Lam(var(suc(zero)))) ),
inference(resolution,[status(thm)],[f276,f66]) ).
fof(f278,plain,
( ~ nf(var(zero))
| ~ nf(var(suc(zero))) ),
inference(forward_subsumption_resolution,[status(thm)],[f277,f60]) ).
fof(f279,plain,
~ nf(var(zero)),
inference(forward_subsumption_resolution,[status(thm)],[f278,f72]) ).
fof(f280,plain,
$false,
inference(resolution,[status(thm)],[f279,f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX223+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n002.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 10:38:16 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.60 % Refutation found
% 0.17/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.63 % Elapsed time: 0.180827 seconds
% 0.26/0.63 % CPU time: 1.143027 seconds
% 0.26/0.63 % Total memory used: 123.114 MB
% 0.26/0.63 % Net memory used: 121.894 MB
%------------------------------------------------------------------------------