%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ROB016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 02:06:32 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 11 unt; 0 def)
% Number of atoms : 21 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y] : negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
negate(add(d,e)) = negate(e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
positive_integer(k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y,X,Vk] :
( negate(add(Y,multiply(Vk,add(X,negate(add(X,negate(Y))))))) = negate(Y)
| ~ positive_integer(Vk)
| negate(add(negate(Y),negate(add(X,negate(Y))))) != X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0,X1] : negate(add(negate(add(X0,X1)),negate(add(X0,negate(X1))))) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
negate(add(d,e)) = negate(e),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f21,plain,
positive_integer(k),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,plain,
! [X0,X1,X2] :
( negate(add(X0,multiply(X2,add(X1,negate(add(X1,negate(X0))))))) = negate(X0)
| ~ positive_integer(X2)
| negate(add(negate(X0),negate(add(X1,negate(X0))))) != X1 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f23,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f40,plain,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
inference(paramodulation,[status(thm)],[f20,f14]) ).
fof(f52,plain,
( ~ positive_integer(k)
| negate(add(negate(e),negate(add(d,negate(e))))) != d ),
inference(resolution,[status(thm)],[f22,f23]) ).
fof(f61,plain,
( ~ positive_integer(k)
| d != d ),
inference(forward_demodulation,[status(thm)],[f40,f52]) ).
fof(f62,plain,
~ positive_integer(k),
inference(trivial_equality_resolution,[status(thm)],[f61]) ).
fof(f63,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f62,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:21:35 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.058083 seconds
% 0.14/0.44 % CPU time: 0.195911 seconds
% 0.14/0.44 % Total memory used: 32.216 MB
% 0.14/0.44 % Net memory used: 32.141 MB
%------------------------------------------------------------------------------