%------------------------------------------------------------------------------
% 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/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Y] : x2(z,Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [N,Y] : x2(s(N),Y) = s(x2(N,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Y] : x22(z,Y) = z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [N,Y] : x22(s(N),Y) = x2(Y,x22(N,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : mul_idem(X) = eq(x22(X,X),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : eq(s(X),s(Y)) = eq(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] : eq(s(X),z) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : eq2(X,X) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
! [X] : eq2(mul_idem(X),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0] : x2(z,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [X0,X1] : x2(s(X0),X1) = s(x2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0] : x22(z,X0) = z,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
! [X0,X1] : x22(s(X0),X1) = x2(X1,x22(X0,X1)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
! [X0] : mul_idem(X0) = eq(x22(X0,X0),X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0,X1] : eq(s(X0),s(X1)) = eq(X0,X1),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
! [X0] : eq(s(X0),z) = bfalse,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
! [X0] : eq2(X0,X0) = btrue,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f26,plain,
! [X0] : eq2(mul_idem(X0),bfalse) != btrue,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f35,plain,
! [X0,X1] : x22(s(X0),s(X1)) = s(x2(X1,x22(X0,s(X1)))),
inference(paramodulation,[status(thm)],[f15,f17]) ).
fof(f37,plain,
! [X0] : x22(s(z),X0) = x2(X0,z),
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f45,plain,
! [X0,X1,X2] : eq(x22(s(X0),s(X1)),s(X2)) = eq(x2(X1,x22(X0,s(X1))),X2),
inference(paramodulation,[status(thm)],[f35,f21]) ).
fof(f327,plain,
! [X0] : mul_idem(s(X0)) = eq(x2(X0,x22(X0,s(X0))),X0),
inference(paramodulation,[status(thm)],[f18,f45]) ).
fof(f366,plain,
mul_idem(s(s(z))) = eq(x2(s(z),x2(s(s(z)),z)),s(z)),
inference(paramodulation,[status(thm)],[f37,f327]) ).
fof(f380,plain,
mul_idem(s(s(z))) = eq(s(x2(z,x2(s(s(z)),z))),s(z)),
inference(forward_demodulation,[status(thm)],[f15,f366]) ).
fof(f381,plain,
mul_idem(s(s(z))) = eq(x2(z,x2(s(s(z)),z)),z),
inference(forward_demodulation,[status(thm)],[f21,f380]) ).
fof(f382,plain,
mul_idem(s(s(z))) = eq(x2(s(s(z)),z),z),
inference(forward_demodulation,[status(thm)],[f14,f381]) ).
fof(f383,plain,
mul_idem(s(s(z))) = eq(s(x2(s(z),z)),z),
inference(forward_demodulation,[status(thm)],[f15,f382]) ).
fof(f384,plain,
mul_idem(s(s(z))) = bfalse,
inference(forward_demodulation,[status(thm)],[f23,f383]) ).
fof(f396,plain,
eq2(bfalse,bfalse) != btrue,
inference(paramodulation,[status(thm)],[f384,f26]) ).
fof(f397,plain,
btrue != btrue,
inference(forward_demodulation,[status(thm)],[f25,f396]) ).
fof(f398,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f397]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX204-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 10:35:44 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.46 % Elapsed time: 0.089533 seconds
% 0.14/0.46 % CPU time: 0.089080 seconds
% 0.14/0.46 % Total memory used: 2.489 MB
% 0.14/0.46 % Net memory used: 2.460 MB
%------------------------------------------------------------------------------