%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD013-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:21:52 PM UTC 2026
% Result : Unsatisfiable 1.23s 0.66s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 39 ( 15 unt; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 115 ( 65 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 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(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
defined(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
sum(additive_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
sum(additive_identity,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ sum(a,c,add(d,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,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(f35,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)],[f34]) ).
fof(f36,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(f37,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)],[f36]) ).
fof(f38,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f60,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| sum(X,Y,add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f61,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f73,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f74,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f76,plain,
defined(d),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
sum(additive_identity,a,b),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f78,plain,
sum(additive_identity,c,d),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f79,plain,
~ sum(a,c,add(d,b)),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f81,plain,
~ sum(c,a,add(d,b)),
inference(resolution,[status(thm)],[f40,f79]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ sum(X1,X2,add(d,b))
| ~ sum(X0,X2,a)
| ~ sum(c,X0,X1) ),
inference(resolution,[status(thm)],[f81,f35]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ sum(X0,c,X2)
| ~ sum(X2,X1,add(d,b))
| ~ sum(X0,X1,a) ),
inference(resolution,[status(thm)],[f83,f40]) ).
fof(f173,plain,
! [X0] :
( ~ defined(a)
| ~ sum(additive_identity,c,X0)
| ~ sum(X0,a,add(d,b)) ),
inference(resolution,[status(thm)],[f93,f38]) ).
fof(f177,plain,
! [X0] :
( ~ sum(additive_identity,c,X0)
| ~ sum(X0,a,add(d,b)) ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f73]) ).
fof(f178,plain,
! [X0,X1,X2,X3] :
( ~ sum(X1,X3,add(d,b))
| ~ sum(X2,a,X3)
| ~ sum(X1,X2,X0)
| ~ sum(additive_identity,c,X0) ),
inference(resolution,[status(thm)],[f177,f37]) ).
fof(f727,plain,
! [X0,X1] :
( ~ defined(b)
| ~ defined(d)
| ~ sum(X1,a,b)
| ~ sum(d,X1,X0)
| ~ sum(additive_identity,c,X0) ),
inference(resolution,[status(thm)],[f178,f61]) ).
fof(f731,plain,
! [X0,X1] :
( ~ defined(b)
| ~ sum(X1,a,b)
| ~ sum(d,X1,X0)
| ~ sum(additive_identity,c,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f727,f76]) ).
fof(f732,plain,
! [X0,X1] :
( ~ sum(X1,a,b)
| ~ sum(d,X1,X0)
| ~ sum(additive_identity,c,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f731,f74]) ).
fof(f733,plain,
! [X0] :
( ~ sum(d,additive_identity,X0)
| ~ sum(additive_identity,c,X0) ),
inference(resolution,[status(thm)],[f732,f77]) ).
fof(f739,plain,
! [X0] :
( ~ sum(additive_identity,d,X0)
| ~ sum(additive_identity,c,X0) ),
inference(resolution,[status(thm)],[f733,f40]) ).
fof(f743,plain,
( ~ defined(d)
| ~ sum(additive_identity,c,d) ),
inference(resolution,[status(thm)],[f739,f38]) ).
fof(f749,plain,
~ defined(d),
inference(forward_subsumption_resolution,[status(thm)],[f743,f78]) ).
fof(f751,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f749,f76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD013-3 : 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 : n009.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 15:37:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 1.23/0.66 % Refutation found
% 1.23/0.66 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.23/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.23/0.68 % Elapsed time: 0.307765 seconds
% 1.23/0.68 % CPU time: 2.219813 seconds
% 1.23/0.68 % Total memory used: 37.415 MB
% 1.23/0.68 % Net memory used: 34.743 MB
%------------------------------------------------------------------------------