%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX221+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 : n010.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 0.25s 0.84s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 18 unt; 0 def)
% Number of atoms : 152 ( 30 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 175 ( 83 ~; 64 |; 19 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 154 ( 152 !; 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(b,c)),arr(b,arr(a,c))))
& nf(E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ? [E] :
( tc(nil,E,arr(arr(a,arr(b,c)),arr(b,arr(a,c))))
& 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(b,c)),arr(b,arr(a,c))))
| ~ nf(E) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f97,plain,
! [X0] :
( ~ tc(nil,X0,arr(arr(a,arr(b,c)),arr(b,arr(a,c))))
| ~ 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(f123,plain,
! [X0] :
( ~ nf(lam(X0))
| ~ tc(cons(arr(a,arr(b,c)),nil),X0,arr(b,arr(a,c))) ),
inference(resolution,[status(thm)],[f87,f97]) ).
fof(f130,plain,
! [X0,X1,X2] : tc(cons(X0,cons(X1,X2)),var(suc(zero)),X1),
inference(resolution,[status(thm)],[f109,f74]) ).
fof(f131,plain,
! [X0,X1,X2,X3,X4] :
( tc(cons(X3,cons(X4,X0)),var(suc(suc(X1))),X2)
| index(X0,X1) != just(X2) ),
inference(paramodulation,[status(thm)],[f75,f109]) ).
fof(f143,plain,
! [X0] :
( ~ tc(cons(b,cons(arr(a,arr(b,c)),nil)),X0,arr(a,c))
| ~ nf(lam(lam(X0))) ),
inference(resolution,[status(thm)],[f123,f87]) ).
fof(f147,plain,
! [X0] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,c)
| ~ nf(lam(lam(lam(X0)))) ),
inference(resolution,[status(thm)],[f143,f87]) ).
fof(f148,plain,
! [X0,X1,X2] :
( ~ 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)],[f147,f80]) ).
fof(f185,plain,
! [X0,X1,X2,X3] : tc(cons(X0,cons(X1,cons(X2,X3))),var(suc(suc(zero))),X2),
inference(resolution,[status(thm)],[f131,f74]) ).
fof(f218,plain,
! [X0,X1,X2,X3,X4] :
( ~ 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)],[f148,f80]) ).
fof(f347,plain,
! [X0,X1] :
( ~ 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)],[f218,f185]) ).
fof(f449,plain,
! [X0,X1] :
( ~ nf(lam(lam(app(app(var(suc(suc(zero))),X1,a),X0,b))))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,a)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,b) ),
inference(resolution,[status(thm)],[f347,f71]) ).
fof(f452,plain,
! [X0] :
( ~ 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)],[f449,f108]) ).
fof(f454,plain,
! [X0] :
( ~ nf(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)],[f452,f71]) ).
fof(f455,plain,
~ nf(lam(app(app(var(suc(suc(zero))),var(zero),a),var(suc(zero)),b))),
inference(resolution,[status(thm)],[f454,f130]) ).
fof(f457,plain,
~ nf(app(app(var(suc(suc(zero))),var(zero),a),var(suc(zero)),b)),
inference(resolution,[status(thm)],[f455,f71]) ).
fof(f458,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)],[f457,f66]) ).
fof(f459,plain,
( ~ nf(var(suc(zero)))
| ~ nf(app(var(suc(suc(zero))),var(zero),a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f458,f58]) ).
fof(f460,plain,
~ nf(app(var(suc(suc(zero))),var(zero),a)),
inference(forward_subsumption_resolution,[status(thm)],[f459,f72]) ).
fof(f461,plain,
( ~ nf(var(zero))
| ~ nf(var(suc(suc(zero))))
| var(suc(suc(zero))) = lam(proj1Lam(var(suc(suc(zero))))) ),
inference(resolution,[status(thm)],[f460,f66]) ).
fof(f462,plain,
( ~ nf(var(zero))
| ~ nf(var(suc(suc(zero)))) ),
inference(forward_subsumption_resolution,[status(thm)],[f461,f60]) ).
fof(f463,plain,
~ nf(var(zero)),
inference(forward_subsumption_resolution,[status(thm)],[f462,f72]) ).
fof(f464,plain,
$false,
inference(resolution,[status(thm)],[f463,f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX221+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n010.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 10:35:55 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.50 % Drodi V4.1.1
% 0.25/0.84 % Refutation found
% 0.25/0.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.25/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.89 % Elapsed time: 0.391762 seconds
% 0.25/0.89 % CPU time: 2.605526 seconds
% 0.25/0.89 % Total memory used: 145.861 MB
% 0.25/0.89 % Net memory used: 143.109 MB
%------------------------------------------------------------------------------