%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX204+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 : 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 03:13:26 PM UTC 2026
% Result : Theorem 0.08s 0.35s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 30 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 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 : 26 ( 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : proj1S(s(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : z != s(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Y] : x2(z,Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Y,N] : x2(s(N),Y) = s(x2(N,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y] : x22(z,Y) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Y,N] : x22(s(N),Y) = x2(Y,x22(N,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
? [X] : x22(X,X) != X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ? [X] : x22(X,X) != X,
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0] : proj1S(s(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0] : z != s(X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0] : x2(z,X0) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1] : x2(s(X0),X1) = s(x2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0] : x22(z,X0) = z,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1] : x22(s(X0),X1) = x2(X1,x22(X0,X1)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,plain,
! [X] : x22(X,X) = X,
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f16,plain,
! [X0] : x22(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,plain,
! [X0] : x22(s(z),X0) = x2(X0,z),
inference(paramodulation,[status(thm)],[f13,f14]) ).
fof(f111,plain,
! [X0,X1] : s(x2(X0,x22(X1,s(X0)))) = x22(s(X1),s(X0)),
inference(paramodulation,[status(thm)],[f14,f12]) ).
fof(f161,plain,
! [X0,X1] : x22(s(X0),s(s(X1))) = s(s(x2(X1,x22(X0,s(s(X1)))))),
inference(paramodulation,[status(thm)],[f12,f111]) ).
fof(f214,plain,
! [X0] : x22(s(X0),s(s(z))) = s(s(x22(X0,s(s(z))))),
inference(paramodulation,[status(thm)],[f11,f161]) ).
fof(f1000,plain,
x22(s(s(z)),s(s(z))) = s(s(x2(s(s(z)),z))),
inference(paramodulation,[status(thm)],[f19,f214]) ).
fof(f1048,plain,
s(s(z)) = s(s(x2(s(s(z)),z))),
inference(forward_demodulation,[status(thm)],[f16,f1000]) ).
fof(f1049,plain,
s(s(z)) = s(s(s(x2(s(z),z)))),
inference(forward_demodulation,[status(thm)],[f12,f1048]) ).
fof(f1050,plain,
s(s(z)) = s(s(s(s(x2(z,z))))),
inference(forward_demodulation,[status(thm)],[f12,f1049]) ).
fof(f1051,plain,
s(s(z)) = s(s(s(s(z)))),
inference(forward_demodulation,[status(thm)],[f11,f1050]) ).
fof(f1136,plain,
s(s(s(z))) = proj1S(s(s(z))),
inference(paramodulation,[status(thm)],[f1051,f9]) ).
fof(f1216,plain,
s(s(s(z))) = s(z),
inference(forward_demodulation,[status(thm)],[f9,f1136]) ).
fof(f1267,plain,
s(s(z)) = proj1S(s(z)),
inference(paramodulation,[status(thm)],[f1216,f9]) ).
fof(f1415,plain,
s(s(z)) = z,
inference(forward_demodulation,[status(thm)],[f9,f1267]) ).
fof(f1416,plain,
$false,
inference(resolution,[status(thm)],[f1415,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX204+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n010.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Mon Sep 21 10:33:55 UTC 2026
% 0.08/0.33 % CPUTime :
% 0.08/0.34 % Drodi V4.1.1
% 0.08/0.35 % Refutation found
% 0.08/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.37 % Elapsed time: 0.032060 seconds
% 0.11/0.37 % CPU time: 0.103259 seconds
% 0.11/0.37 % Total memory used: 4.578 MB
% 0.11/0.37 % Net memory used: 4.511 MB
%------------------------------------------------------------------------------