%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX200+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 : Thu Sep 24 03:13:25 PM UTC 2026
% Result : Theorem 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 46 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 45 ( 19 ~; 16 |; 5 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [Z] : ~ leqNat(s(Z),z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Y] : merge(nil,Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
ord(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Y,Y2,Xs] :
( ord(cons(Y,cons(Y2,Xs)))
<=> ( ord(cons(Y2,Xs))
& leqNat(Y,Y2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,conjecture,
? [Xs,Ys] :
~ ( ord(Xs)
=> ( ~ ord(Ys)
=> ord(merge(Xs,Ys)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ ? [Xs,Ys] :
~ ( ord(Xs)
=> ( ~ ord(Ys)
=> ord(merge(Xs,Ys)) ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f24,plain,
! [X0] : ~ leqNat(s(X0),z),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f29,plain,
! [X0] : merge(nil,X0) = X0,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f37,plain,
ord(nil),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f39,plain,
! [Y,Y2,Xs] :
( ( ~ ord(cons(Y2,Xs))
| ~ leqNat(Y,Y2)
| ord(cons(Y,cons(Y2,Xs))) )
& ( ( ord(cons(Y2,Xs))
& leqNat(Y,Y2) )
| ~ ord(cons(Y,cons(Y2,Xs))) ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f40,plain,
( ! [Y,Y2,Xs] :
( ~ ord(cons(Y2,Xs))
| ~ leqNat(Y,Y2)
| ord(cons(Y,cons(Y2,Xs))) )
& ! [Y,Y2,Xs] :
( ( ord(cons(Y2,Xs))
& leqNat(Y,Y2) )
| ~ ord(cons(Y,cons(Y2,Xs))) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( leqNat(X0,X1)
| ~ ord(cons(X0,cons(X1,X2))) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f44,plain,
! [Xs,Ys] :
( ord(merge(Xs,Ys))
| ord(Ys)
| ~ ord(Xs) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f45,plain,
! [Xs] :
( ! [Ys] :
( ord(merge(Xs,Ys))
| ord(Ys) )
| ~ ord(Xs) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ord(merge(X0,X1))
| ord(X1)
| ~ ord(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f70,plain,
! [X0] :
( ord(X0)
| ord(X0)
| ~ ord(nil) ),
inference(paramodulation,[status(thm)],[f29,f46]) ).
fof(f71,plain,
! [X0] :
( ord(X0)
| ~ ord(nil) ),
inference(duplicate_literals_removal,[status(thm)],[f70]) ).
fof(f72,plain,
! [X0] : ord(X0),
inference(forward_subsumption_resolution,[status(thm)],[f71,f37]) ).
fof(f78,plain,
! [X0,X1] : leqNat(X0,X1),
inference(backward_subsumption_resolution,[status(thm)],[f41,f72]) ).
fof(f80,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f24,f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX200+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 % Computer : n009.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Mon Sep 21 10:32:28 UTC 2026
% 0.20/0.48 % CPUTime :
% 0.20/0.49 % Drodi V4.1.1
% 0.20/0.52 % Refutation found
% 0.20/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.60 % Elapsed time: 0.113277 seconds
% 0.25/0.60 % CPU time: 0.115505 seconds
% 0.25/0.60 % Total memory used: 6.452 MB
% 0.25/0.60 % Net memory used: 6.441 MB
%------------------------------------------------------------------------------