%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD068-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 12:22:08 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.65s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 17 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 32 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 51 ( 51 !; 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(f24,axiom,
! [U,V,X,Y,Z] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
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,negated_conjecture,
sum(b,additive_inverse(a),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
less_or_equal(additive_identity,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,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(f36,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)],[f35]) ).
fof(f37,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f68,plain,
! [V,Y,Z] :
( ~ sum(Y,Z,V)
| ! [U,X] :
( ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ less_or_equal(X2,X3)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f72,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f73,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
sum(b,additive_inverse(a),u),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f76,plain,
less_or_equal(additive_identity,u),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f77,plain,
~ less_or_equal(a,b),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ sum(b,X2,X1)
| ~ sum(additive_inverse(a),X0,X2)
| sum(u,X0,X1) ),
inference(resolution,[status(thm)],[f36,f75]) ).
fof(f95,plain,
sum(additive_identity,b,b),
inference(resolution,[status(thm)],[f37,f73]) ).
fof(f96,plain,
sum(additive_identity,a,a),
inference(resolution,[status(thm)],[f37,f72]) ).
fof(f158,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolution,[status(thm)],[f38,f72]) ).
fof(f162,plain,
sum(b,additive_identity,b),
inference(resolution,[status(thm)],[f39,f95]) ).
fof(f788,plain,
! [X0,X1,X2] :
( ~ sum(u,X2,X1)
| ~ sum(additive_identity,X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f69,f76]) ).
fof(f1294,plain,
! [X0] :
( ~ sum(b,additive_identity,X0)
| sum(u,a,X0) ),
inference(resolution,[status(thm)],[f158,f89]) ).
fof(f1307,plain,
sum(u,a,b),
inference(resolution,[status(thm)],[f1294,f162]) ).
fof(f1312,plain,
! [X0] :
( ~ sum(additive_identity,a,X0)
| less_or_equal(X0,b) ),
inference(resolution,[status(thm)],[f1307,f788]) ).
fof(f1344,plain,
less_or_equal(a,b),
inference(resolution,[status(thm)],[f1312,f96]) ).
fof(f1345,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1344,f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD068-4 : 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 : n015.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 15:47:51 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.24/0.65 % Refutation found
% 0.24/0.65 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.24/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.64/0.66 % Elapsed time: 0.205580 seconds
% 0.64/0.66 % CPU time: 1.286446 seconds
% 0.64/0.66 % Total memory used: 27.530 MB
% 0.64/0.66 % Net memory used: 26.437 MB
%------------------------------------------------------------------------------