%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD003-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:21:49 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 12 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 107 ( 62 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 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(f10,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ),
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,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ equalish(add(a,add(b,additive_inverse(b))),a),
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(f45,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| defined(add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f46,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| defined(add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
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,
defined(b),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f75,plain,
~ equalish(add(a,add(b,additive_inverse(b))),a),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
! [X0] :
( ~ equalish(X0,a)
| ~ equalish(add(a,add(b,additive_inverse(b))),X0) ),
inference(resolution,[status(thm)],[f65,f75]) ).
fof(f80,plain,
( ~ defined(a)
| ~ equalish(add(a,add(b,additive_inverse(b))),add(additive_identity,a)) ),
inference(resolution,[status(thm)],[f77,f33]) ).
fof(f84,plain,
~ equalish(add(a,add(b,additive_inverse(b))),add(additive_identity,a)),
inference(forward_subsumption_resolution,[status(thm)],[f80,f73]) ).
fof(f91,plain,
~ equalish(add(additive_identity,a),add(a,add(b,additive_inverse(b)))),
inference(resolution,[status(thm)],[f84,f63]) ).
fof(f111,plain,
! [X0] :
( ~ equalish(X0,add(a,add(b,additive_inverse(b))))
| ~ equalish(add(additive_identity,a),X0) ),
inference(resolution,[status(thm)],[f91,f65]) ).
fof(f148,plain,
! [X0] :
( ~ equalish(additive_identity,X0)
| ~ defined(a)
| ~ equalish(add(X0,a),add(a,add(b,additive_inverse(b)))) ),
inference(resolution,[status(thm)],[f111,f67]) ).
fof(f153,plain,
! [X0] :
( ~ equalish(additive_identity,X0)
| ~ equalish(add(X0,a),add(a,add(b,additive_inverse(b)))) ),
inference(forward_subsumption_resolution,[status(thm)],[f148,f73]) ).
fof(f202,plain,
( ~ defined(a)
| ~ defined(add(b,additive_inverse(b)))
| ~ equalish(additive_identity,add(b,additive_inverse(b))) ),
inference(resolution,[status(thm)],[f153,f36]) ).
fof(f205,plain,
( ~ defined(add(b,additive_inverse(b)))
| ~ equalish(additive_identity,add(b,additive_inverse(b))) ),
inference(forward_subsumption_resolution,[status(thm)],[f202,f73]) ).
fof(f206,plain,
( ~ defined(additive_inverse(b))
| ~ defined(b)
| ~ equalish(additive_identity,add(b,additive_inverse(b))) ),
inference(resolution,[status(thm)],[f205,f46]) ).
fof(f207,plain,
( ~ defined(additive_inverse(b))
| ~ equalish(additive_identity,add(b,additive_inverse(b))) ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f74]) ).
fof(f208,plain,
( ~ defined(b)
| ~ equalish(additive_identity,add(b,additive_inverse(b))) ),
inference(resolution,[status(thm)],[f207,f48]) ).
fof(f209,plain,
~ equalish(additive_identity,add(b,additive_inverse(b))),
inference(forward_subsumption_resolution,[status(thm)],[f208,f74]) ).
fof(f211,plain,
~ equalish(add(b,additive_inverse(b)),additive_identity),
inference(resolution,[status(thm)],[f209,f63]) ).
fof(f218,plain,
~ defined(b),
inference(resolution,[status(thm)],[f211,f34]) ).
fof(f221,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f218,f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD003-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 15:39:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.053794 seconds
% 0.13/0.43 % CPU time: 0.232423 seconds
% 0.13/0.43 % Total memory used: 19.642 MB
% 0.13/0.43 % Net memory used: 19.085 MB
%------------------------------------------------------------------------------