%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD015-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 0.17s 0.59s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 20 unt; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 35 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 54 ( 54 !; 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(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
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(f29,negated_conjecture,
sum(additive_identity,additive_inverse(a),additive_inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ sum(additive_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,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(f32,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)],[f31]) ).
fof(f33,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(f34,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)],[f33]) ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f36,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f70,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f71,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f72,plain,
sum(additive_identity,additive_inverse(a),additive_inverse(b)),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f73,plain,
~ sum(additive_identity,a,b),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ sum(X2,additive_inverse(a),X1)
| ~ sum(X0,additive_identity,X2)
| sum(X0,additive_inverse(b),X1) ),
inference(resolution,[status(thm)],[f32,f72]) ).
fof(f78,plain,
sum(additive_identity,b,b),
inference(resolution,[status(thm)],[f35,f71]) ).
fof(f79,plain,
sum(additive_identity,a,a),
inference(resolution,[status(thm)],[f35,f70]) ).
fof(f98,plain,
sum(a,additive_identity,a),
inference(resolution,[status(thm)],[f37,f79]) ).
fof(f99,plain,
sum(b,additive_identity,b),
inference(resolution,[status(thm)],[f37,f78]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ~ sum(X0,X2,b)
| ~ sum(X1,a,X2)
| ~ sum(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f34,f73]) ).
fof(f123,plain,
sum(additive_inverse(b),b,additive_identity),
inference(resolution,[status(thm)],[f36,f71]) ).
fof(f124,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolution,[status(thm)],[f36,f70]) ).
fof(f127,plain,
sum(b,additive_inverse(b),additive_identity),
inference(resolution,[status(thm)],[f123,f37]) ).
fof(f133,plain,
sum(a,additive_inverse(a),additive_identity),
inference(resolution,[status(thm)],[f124,f37]) ).
fof(f276,plain,
! [X0] :
( ~ sum(X0,additive_identity,a)
| sum(X0,additive_inverse(b),additive_identity) ),
inference(resolution,[status(thm)],[f76,f133]) ).
fof(f286,plain,
sum(a,additive_inverse(b),additive_identity),
inference(resolution,[status(thm)],[f276,f98]) ).
fof(f288,plain,
sum(additive_inverse(b),a,additive_identity),
inference(resolution,[status(thm)],[f286,f37]) ).
fof(f295,plain,
! [X0] :
( ~ sum(X0,additive_identity,b)
| ~ sum(X0,additive_inverse(b),additive_identity) ),
inference(resolution,[status(thm)],[f288,f115]) ).
fof(f307,plain,
~ sum(b,additive_inverse(b),additive_identity),
inference(resolution,[status(thm)],[f295,f99]) ).
fof(f309,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f307,f127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD015-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n003.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 15:39:01 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.59 % Refutation found
% 0.17/0.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.60 % Elapsed time: 0.149446 seconds
% 0.17/0.60 % CPU time: 0.952693 seconds
% 0.17/0.60 % Total memory used: 26.112 MB
% 0.17/0.60 % Net memory used: 25.368 MB
%------------------------------------------------------------------------------