%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD005-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 12:21:50 PM UTC 2026
% Result : Unsatisfiable 0.42s 0.46s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 56 ( 29 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f15,axiom,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
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(f29,negated_conjecture,
! [X] : ~ sum(a,X,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,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(f33,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)],[f32]) ).
fof(f34,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f51,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f56,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| sum(X,Y,add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f57,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f69,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f70,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f71,plain,
! [X0] : ~ sum(a,X0,b),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
! [X0] :
( ~ defined(X0)
| sum(X0,b,add(X0,b)) ),
inference(resolution,[status(thm)],[f57,f70]) ).
fof(f168,plain,
sum(additive_identity,b,b),
inference(resolution,[status(thm)],[f34,f70]) ).
fof(f173,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolution,[status(thm)],[f35,f69]) ).
fof(f184,plain,
sum(b,additive_identity,b),
inference(resolution,[status(thm)],[f168,f36]) ).
fof(f195,plain,
! [X0,X1,X2] :
( ~ sum(X2,X1,additive_identity)
| ~ sum(b,X2,X0)
| sum(X0,X1,b) ),
inference(resolution,[status(thm)],[f184,f33]) ).
fof(f506,plain,
! [X0] :
( ~ sum(b,additive_inverse(a),X0)
| sum(X0,a,b) ),
inference(resolution,[status(thm)],[f195,f173]) ).
fof(f609,plain,
defined(additive_inverse(a)),
inference(resolution,[status(thm)],[f51,f69]) ).
fof(f718,plain,
sum(additive_inverse(a),b,add(additive_inverse(a),b)),
inference(resolution,[status(thm)],[f609,f76]) ).
fof(f791,plain,
sum(b,additive_inverse(a),add(additive_inverse(a),b)),
inference(resolution,[status(thm)],[f718,f36]) ).
fof(f825,plain,
sum(add(additive_inverse(a),b),a,b),
inference(resolution,[status(thm)],[f791,f506]) ).
fof(f845,plain,
sum(a,add(additive_inverse(a),b),b),
inference(resolution,[status(thm)],[f825,f36]) ).
fof(f846,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f845,f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : FLD005-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 15:36:06 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.42/0.46 % Refutation found
% 0.42/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.42/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.42/0.48 % Elapsed time: 0.166278 seconds
% 0.42/0.48 % CPU time: 1.149511 seconds
% 0.42/0.48 % Total memory used: 33.660 MB
% 0.42/0.48 % Net memory used: 31.829 MB
%------------------------------------------------------------------------------