%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD016-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 1.58s 0.64s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 23 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 36 ~; 34 |; 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 : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 59 ( 59 !; 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(f29,hypothesis,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
defined(v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
sum(a,u,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
sum(a,v,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ sum(additive_identity,u,v),
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(f39,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f73,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f75,plain,
defined(u),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
defined(v),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
sum(a,u,b),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f78,plain,
sum(a,v,b),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f79,plain,
~ sum(additive_identity,u,v),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ sum(X2,v,X1)
| ~ sum(X0,a,X2)
| sum(X0,b,X1) ),
inference(resolution,[status(thm)],[f35,f78]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ sum(X2,u,X1)
| ~ sum(X0,a,X2)
| sum(X0,b,X1) ),
inference(resolution,[status(thm)],[f35,f77]) ).
fof(f102,plain,
sum(additive_identity,v,v),
inference(resolution,[status(thm)],[f38,f76]) ).
fof(f104,plain,
sum(additive_identity,u,u),
inference(resolution,[status(thm)],[f38,f75]) ).
fof(f115,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolution,[status(thm)],[f39,f73]) ).
fof(f117,plain,
sum(v,a,b),
inference(resolution,[status(thm)],[f40,f78]) ).
fof(f653,plain,
! [X0] :
( ~ sum(X0,v,v)
| sum(X0,b,b) ),
inference(resolution,[status(thm)],[f117,f35]) ).
fof(f1048,plain,
sum(additive_identity,b,b),
inference(resolution,[status(thm)],[f102,f653]) ).
fof(f1052,plain,
! [X0] :
( ~ sum(X0,a,additive_identity)
| sum(X0,b,v) ),
inference(resolution,[status(thm)],[f102,f81]) ).
fof(f1064,plain,
sum(b,additive_identity,b),
inference(resolution,[status(thm)],[f1048,f40]) ).
fof(f1077,plain,
! [X0,X1,X2] :
( ~ sum(X2,b,X1)
| ~ sum(X2,b,X0)
| sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f1064,f37]) ).
fof(f1100,plain,
! [X0] :
( ~ sum(X0,a,additive_identity)
| sum(X0,b,u) ),
inference(resolution,[status(thm)],[f104,f83]) ).
fof(f1586,plain,
sum(additive_inverse(a),b,u),
inference(resolution,[status(thm)],[f115,f1100]) ).
fof(f1587,plain,
sum(additive_inverse(a),b,v),
inference(resolution,[status(thm)],[f115,f1052]) ).
fof(f1816,plain,
! [X0] :
( ~ sum(additive_inverse(a),b,X0)
| sum(X0,additive_identity,v) ),
inference(resolution,[status(thm)],[f1587,f1077]) ).
fof(f2028,plain,
sum(u,additive_identity,v),
inference(resolution,[status(thm)],[f1816,f1586]) ).
fof(f2066,plain,
sum(additive_identity,u,v),
inference(resolution,[status(thm)],[f2028,f40]) ).
fof(f2073,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2066,f79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD016-3 : 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 : n005.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 15:37:02 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 1.58/0.64 % Refutation found
% 1.58/0.64 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.58/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.58/0.66 % Elapsed time: 0.293788 seconds
% 1.58/0.66 % CPU time: 2.099560 seconds
% 1.58/0.66 % Total memory used: 31.733 MB
% 1.58/0.66 % Net memory used: 29.960 MB
%------------------------------------------------------------------------------