%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD063-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 12:22:06 PM UTC 2026
% Result : Unsatisfiable 20.58s 3.06s
% Output : CNFRefutation 20.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 12 unt; 0 def)
% Number of atoms : 88 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 100 ( 51 ~; 49 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 68 !; 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
less_or_equal(additive_inverse(b),additive_inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox2/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(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(f57,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| sum(X,Y,add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f58,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f66,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(f67,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)],[f66]) ).
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,
less_or_equal(additive_inverse(b),additive_inverse(a)),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f73,plain,
~ less_or_equal(a,b),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ sum(additive_inverse(a),X2,X1)
| ~ sum(additive_inverse(b),X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f67,f72]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( ~ defined(X0)
| ~ sum(additive_identity,X3,X2)
| ~ sum(X0,X3,X1)
| sum(additive_inverse(X0),X1,X2) ),
inference(resolution,[status(thm)],[f32,f36]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ defined(X2)
| ~ defined(X0)
| ~ sum(X0,X2,X1)
| sum(additive_inverse(X0),X1,X2) ),
inference(resolution,[status(thm)],[f81,f35]) ).
fof(f94,plain,
! [X0] :
( ~ defined(X0)
| sum(X0,a,add(X0,a)) ),
inference(resolution,[status(thm)],[f58,f70]) ).
fof(f1778,plain,
! [X0,X1] :
( ~ defined(X0)
| ~ sum(X0,b,X1)
| sum(additive_inverse(X0),X1,b) ),
inference(resolution,[status(thm)],[f88,f71]) ).
fof(f1779,plain,
! [X0,X1] :
( ~ defined(X0)
| ~ sum(X0,a,X1)
| sum(additive_inverse(X0),X1,a) ),
inference(resolution,[status(thm)],[f88,f70]) ).
fof(f1785,plain,
! [X0] :
( ~ sum(a,b,X0)
| sum(additive_inverse(a),X0,b) ),
inference(resolution,[status(thm)],[f1778,f70]) ).
fof(f1804,plain,
! [X0] :
( ~ sum(b,a,X0)
| sum(additive_inverse(a),X0,b) ),
inference(resolution,[status(thm)],[f1785,f37]) ).
fof(f1811,plain,
( ~ defined(b)
| sum(additive_inverse(a),add(b,a),b) ),
inference(resolution,[status(thm)],[f1804,f94]) ).
fof(f1814,plain,
sum(additive_inverse(a),add(b,a),b),
inference(forward_subsumption_resolution,[status(thm)],[f1811,f71]) ).
fof(f1824,plain,
! [X0] :
( ~ sum(b,a,X0)
| sum(additive_inverse(b),X0,a) ),
inference(resolution,[status(thm)],[f1779,f71]) ).
fof(f1833,plain,
( ~ defined(b)
| sum(additive_inverse(b),add(b,a),a) ),
inference(resolution,[status(thm)],[f1824,f94]) ).
fof(f1836,plain,
sum(additive_inverse(b),add(b,a),a),
inference(forward_subsumption_resolution,[status(thm)],[f1833,f71]) ).
fof(f1838,plain,
! [X0] :
( ~ sum(additive_inverse(a),add(b,a),X0)
| less_or_equal(a,X0) ),
inference(resolution,[status(thm)],[f1836,f76]) ).
fof(f2606,plain,
less_or_equal(a,b),
inference(resolution,[status(thm)],[f1838,f1814]) ).
fof(f2609,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2606,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD063-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 15:45:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 20.58/3.06 % Refutation found
% 20.58/3.06 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 20.58/3.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 20.58/3.10 % Elapsed time: 2.721714 seconds
% 20.58/3.10 % CPU time: 21.309893 seconds
% 20.58/3.10 % Total memory used: 166.518 MB
% 20.58/3.10 % Net memory used: 149.223 MB
%------------------------------------------------------------------------------