%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX186+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 : n013.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 03:13:22 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 5 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 34 ( 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,X2] : nil != cons(X,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Z] : drop(s(Z),nil) = nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Z,X2,X3] : drop(s(Z),cons(X2,X3)) = drop(Z,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
? [N,Xs,Ys] :
~ ( drop(N,Xs) = drop(N,Ys)
=> Xs = Ys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ? [N,Xs,Ys] :
~ ( drop(N,Xs) = drop(N,Ys)
=> Xs = Ys ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,plain,
! [X0,X1] : nil != cons(X0,X1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
! [X0] : drop(s(X0),nil) = nil,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
! [X0,X1,X2] : drop(s(X0),cons(X1,X2)) = drop(X0,X2),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
! [N,Xs,Ys] :
( Xs = Ys
| drop(N,Xs) != drop(N,Ys) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f20,plain,
! [Xs,Ys] :
( Xs = Ys
| ! [N] : drop(N,Xs) != drop(N,Ys) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( X1 = X2
| drop(X0,X1) != drop(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f24,plain,
! [X0,X1] :
( nil = X1
| nil != drop(s(X0),X1) ),
inference(paramodulation,[status(thm)],[f16,f21]) ).
fof(f35,plain,
! [X0,X1,X2] :
( nil = cons(X2,X1)
| nil != drop(X0,X1) ),
inference(paramodulation,[status(thm)],[f17,f24]) ).
fof(f38,plain,
! [X0,X1] : nil != drop(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f35,f13]) ).
fof(f40,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f16,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX186+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 10:30:05 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.043763 seconds
% 0.12/0.40 % CPU time: 0.133634 seconds
% 0.12/0.40 % Total memory used: 58.005 MB
% 0.12/0.40 % Net memory used: 57.573 MB
%------------------------------------------------------------------------------