%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD016-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:21:53 PM UTC 2026
% Result : Unsatisfiable 8.32s 1.47s
% Output : CNFRefutation 8.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 15 unt; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 113 ( 64 ~; 49 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 69 ( 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,V,W,Y,U,Z] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [U,Z,W,X,Y,V] :
( ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(U,Z,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
defined(v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
sum(a,u,q),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
sum(a,v,r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
sum(additive_identity,q,r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
~ sum(additive_identity,u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,plain,
! [W,U,Z] :
( ~ sum(U,Z,W)
| ! [V,Y] :
( ~ sum(Y,Z,V)
| ! [X] :
( ~ sum(X,Y,U)
| sum(X,V,W) ) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [W,X,V] :
( ~ sum(X,V,W)
| ! [Z,Y] :
( ~ sum(Y,Z,V)
| ! [U] :
( ~ sum(X,Y,U)
| sum(U,Z,W) ) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f41,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f75,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f77,plain,
defined(v),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f80,plain,
sum(a,u,q),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f81,plain,
sum(a,v,r),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f82,plain,
sum(additive_identity,q,r),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f83,plain,
~ sum(additive_identity,u,v),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ~ sum(X0,X2,v)
| ~ sum(X1,u,X2)
| ~ sum(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f39,f83]) ).
fof(f101,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X4,X5,v)
| ~ sum(X3,X5,X2)
| ~ sum(X0,X3,X4)
| ~ sum(X1,u,X2)
| ~ sum(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f95,f37]) ).
fof(f216,plain,
! [X0,X1,X2,X3] :
( ~ defined(v)
| ~ sum(X3,v,X2)
| ~ sum(X0,X3,additive_identity)
| ~ sum(X1,u,X2)
| ~ sum(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f101,f40]) ).
fof(f220,plain,
! [X0,X1,X2,X3] :
( ~ sum(X3,v,X2)
| ~ sum(X0,X3,additive_identity)
| ~ sum(X1,u,X2)
| ~ sum(X0,X1,additive_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f77]) ).
fof(f899,plain,
! [X0,X1,X2] :
( ~ defined(X0)
| ~ sum(X0,v,X2)
| ~ sum(X1,u,X2)
| ~ sum(additive_inverse(X0),X1,additive_identity) ),
inference(resolution,[status(thm)],[f220,f41]) ).
fof(f1034,plain,
! [X0,X1] :
( ~ defined(X0)
| ~ defined(X0)
| ~ sum(X0,v,X1)
| ~ sum(X0,u,X1) ),
inference(resolution,[status(thm)],[f899,f41]) ).
fof(f1038,plain,
! [X0,X1] :
( ~ defined(X0)
| ~ sum(X0,v,X1)
| ~ sum(X0,u,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f1034]) ).
fof(f1042,plain,
( ~ defined(a)
| ~ sum(a,u,r) ),
inference(resolution,[status(thm)],[f1038,f81]) ).
fof(f1048,plain,
~ sum(a,u,r),
inference(forward_subsumption_resolution,[status(thm)],[f1042,f75]) ).
fof(f1051,plain,
! [X0,X1,X2] :
( ~ sum(X0,X2,r)
| ~ sum(X1,u,X2)
| ~ sum(X0,X1,a) ),
inference(resolution,[status(thm)],[f1048,f39]) ).
fof(f1075,plain,
! [X0] :
( ~ defined(a)
| ~ sum(additive_identity,X0,r)
| ~ sum(a,u,X0) ),
inference(resolution,[status(thm)],[f1051,f40]) ).
fof(f1079,plain,
! [X0] :
( ~ sum(additive_identity,X0,r)
| ~ sum(a,u,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1075,f75]) ).
fof(f1080,plain,
~ sum(additive_identity,q,r),
inference(resolution,[status(thm)],[f1079,f80]) ).
fof(f1085,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1080,f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD016-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 15:39:14 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 8.32/1.47 % Refutation found
% 8.32/1.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.32/1.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.32/1.50 % Elapsed time: 1.121842 seconds
% 8.32/1.50 % CPU time: 8.621507 seconds
% 8.32/1.50 % Total memory used: 81.140 MB
% 8.32/1.50 % Net memory used: 74.032 MB
%------------------------------------------------------------------------------