%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX190+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 : 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 03:13:23 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 22 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 31 ( 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X,X2,X3] : n(X) != x(X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [Y] : d(n(Y)) = n(z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [F,G] : d(x(F,G)) = x(d(F),d(G)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [E] : opt(x(n(z),E)) = E,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,conjecture,
? [E] : opt(d(E)) != opt(d(opt(E))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
~ ? [E] : opt(d(E)) != opt(d(opt(E))),
inference(negated_conjecture,[status(cth)],[f54]) ).
fof(f63,plain,
! [X0,X1,X2] : n(X0) != x(X1,X2),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f113,plain,
! [X0] : d(n(X0)) = n(z),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f114,plain,
! [X0,X1] : d(x(X0,X1)) = x(d(X0),d(X1)),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f127,plain,
! [X0] : opt(x(n(z),X0)) = X0,
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f133,plain,
! [E] : opt(d(E)) = opt(d(opt(E))),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f134,plain,
! [X0] : opt(d(X0)) = opt(d(opt(X0))),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f190,plain,
! [X0] : opt(d(x(n(z),X0))) = opt(d(X0)),
inference(paramodulation,[status(thm)],[f127,f134]) ).
fof(f212,plain,
! [X0,X1] : d(x(n(X0),X1)) = x(n(z),d(X1)),
inference(paramodulation,[status(thm)],[f113,f114]) ).
fof(f213,plain,
! [X0,X1] : d(x(X0,n(X1))) = x(d(X0),n(z)),
inference(paramodulation,[status(thm)],[f113,f114]) ).
fof(f257,plain,
! [X0,X1] : opt(d(x(n(X0),X1))) = d(X1),
inference(paramodulation,[status(thm)],[f212,f127]) ).
fof(f258,plain,
! [X0] : d(X0) = opt(d(X0)),
inference(backward_demodulation,[status(thm)],[f257,f190]) ).
fof(f267,plain,
! [X0,X1] : d(x(n(X0),X1)) = d(X1),
inference(backward_demodulation,[status(thm)],[f258,f257]) ).
fof(f384,plain,
! [X0,X1] : x(d(n(X0)),n(z)) = d(n(X1)),
inference(paramodulation,[status(thm)],[f213,f267]) ).
fof(f392,plain,
! [X0] : x(n(z),n(z)) = d(n(X0)),
inference(forward_demodulation,[status(thm)],[f113,f384]) ).
fof(f393,plain,
x(n(z),n(z)) = n(z),
inference(forward_demodulation,[status(thm)],[f113,f392]) ).
fof(f394,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f393,f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX190+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.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 10:26:28 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.054148 seconds
% 0.13/0.41 % CPU time: 0.166892 seconds
% 0.13/0.41 % Total memory used: 103.432 MB
% 0.13/0.41 % Net memory used: 103.392 MB
%------------------------------------------------------------------------------