%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD019-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:21:54 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.48s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 9 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 108 ( 62 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] :
( ~ defined(X)
| equalish(add(additive_identity,X),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| equalish(add(X,additive_inverse(X)),additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y] :
( ~ equalish(Y,X)
| equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Z,Y] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X,Z,Y] :
( ~ equalish(X,Y)
| ~ defined(Z)
| equalish(add(X,Z),add(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
equalish(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,plain,
! [X0] :
( ~ defined(X0)
| equalish(add(additive_identity,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f34,plain,
! [X0] :
( ~ defined(X0)
| equalish(add(X0,additive_inverse(X0)),additive_identity) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f36,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| equalish(add(X0,X1),add(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f48,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f63,plain,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f64,plain,
! [Z,Y] :
( ~ equalish(Y,Z)
| ! [X] :
( ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X,Y] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ defined(Z)
| equalish(add(X,Z),add(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(add(X0,X1),add(X2,X1)) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f73,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f74,plain,
equalish(additive_inverse(a),additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f75,plain,
~ equalish(a,additive_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f76,plain,
~ equalish(additive_identity,a),
inference(resolution,[status(thm)],[f63,f75]) ).
fof(f78,plain,
! [X0] :
( ~ equalish(X0,a)
| ~ equalish(additive_identity,X0) ),
inference(resolution,[status(thm)],[f65,f76]) ).
fof(f83,plain,
! [X0] :
( ~ equalish(X0,additive_identity)
| ~ equalish(X0,a) ),
inference(resolution,[status(thm)],[f78,f63]) ).
fof(f89,plain,
! [X0,X1] :
( ~ equalish(X1,a)
| ~ equalish(X0,X1)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f83,f65]) ).
fof(f103,plain,
! [X0] :
( ~ defined(a)
| ~ equalish(X0,add(additive_identity,a))
| ~ equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f89,f33]) ).
fof(f107,plain,
! [X0] :
( ~ equalish(X0,add(additive_identity,a))
| ~ equalish(X0,additive_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f73]) ).
fof(f212,plain,
! [X0] :
( ~ equalish(add(X0,a),additive_identity)
| ~ equalish(X0,additive_identity)
| ~ defined(a) ),
inference(resolution,[status(thm)],[f67,f107]) ).
fof(f216,plain,
! [X0] :
( ~ equalish(add(X0,a),additive_identity)
| ~ equalish(X0,additive_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f212,f73]) ).
fof(f225,plain,
! [X0,X1] :
( ~ equalish(X1,additive_identity)
| ~ equalish(add(X0,a),X1)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f216,f65]) ).
fof(f433,plain,
! [X0] :
( ~ defined(a)
| ~ defined(X0)
| ~ equalish(add(a,X0),additive_identity)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f225,f36]) ).
fof(f438,plain,
! [X0] :
( ~ defined(X0)
| ~ equalish(add(a,X0),additive_identity)
| ~ equalish(X0,additive_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f433,f73]) ).
fof(f439,plain,
( ~ defined(a)
| ~ defined(additive_inverse(a))
| ~ equalish(additive_inverse(a),additive_identity) ),
inference(resolution,[status(thm)],[f438,f34]) ).
fof(f442,plain,
( ~ defined(a)
| ~ defined(additive_inverse(a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f439,f74]) ).
fof(f461,plain,
~ defined(a),
inference(forward_subsumption_resolution,[status(thm)],[f442,f48]) ).
fof(f462,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f73,f461]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD019-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 15:43:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.48 % Refutation found
% 0.13/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.50 % Elapsed time: 0.134483 seconds
% 0.13/0.50 % CPU time: 0.824036 seconds
% 0.13/0.50 % Total memory used: 27.522 MB
% 0.13/0.50 % Net memory used: 25.750 MB
%------------------------------------------------------------------------------