%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD065-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 12:22:07 PM UTC 2026
% Result : Unsatisfiable 44.38s 6.04s
% Output : CNFRefutation 44.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 78 ( 15 unt; 0 def)
% Number of atoms : 178 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 199 ( 99 ~; 100 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 104 ( 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] :
( ~ defined(X)
| equalish(add(additive_identity,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| equalish(add(X,additive_inverse(X)),additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Z,Y] :
( ~ less_or_equal(Y,Z)
| ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Z,Y] :
( ~ less_or_equal(X,Y)
| ~ defined(Z)
| less_or_equal(add(X,Z),add(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y] :
( ~ equalish(Y,X)
| equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Z,Y] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X,Z,Y] :
( ~ equalish(X,Y)
| ~ defined(Z)
| equalish(add(X,Z),add(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [Y,Z,X] :
( ~ equalish(X,Y)
| ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
less_or_equal(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,plain,
! [X0] :
( ~ defined(X0)
| equalish(add(additive_identity,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f34,plain,
! [X0] :
( ~ defined(X0)
| equalish(add(X0,additive_inverse(X0)),additive_identity) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f36,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| equalish(add(X0,X1),add(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f47,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f48,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f54,plain,
! [Z,Y] :
( ~ less_or_equal(Y,Z)
| ! [X] :
( ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f57,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [X,Y] :
( ~ less_or_equal(X,Y)
| ! [Z] :
( ~ defined(Z)
| less_or_equal(add(X,Z),add(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X0,X2)
| ~ defined(X1)
| less_or_equal(add(X0,X1),add(X2,X1)) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f63,plain,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f64,plain,
! [Z,Y] :
( ~ equalish(Y,Z)
| ! [X] :
( ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X,Y] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ defined(Z)
| equalish(add(X,Z),add(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(add(X0,X1),add(X2,X1)) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f70,plain,
! [Y,X] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X0)
| ~ less_or_equal(X2,X1)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f74,plain,
less_or_equal(additive_inverse(a),additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f75,plain,
~ less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f81,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(a,X0)
| less_or_equal(X0,a) ),
inference(resolution,[status(thm)],[f57,f73]) ).
fof(f134,plain,
( less_or_equal(a,a)
| less_or_equal(a,a) ),
inference(resolution,[status(thm)],[f81,f73]) ).
fof(f136,plain,
less_or_equal(a,a),
inference(duplicate_literals_removal,[status(thm)],[f134]) ).
fof(f138,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(add(additive_inverse(a),X0),add(additive_identity,X0)) ),
inference(resolution,[status(thm)],[f59,f74]) ).
fof(f154,plain,
less_or_equal(add(additive_inverse(a),a),add(additive_identity,a)),
inference(resolution,[status(thm)],[f138,f73]) ).
fof(f406,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ equalish(X0,add(additive_identity,X1))
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f65,f33]) ).
fof(f408,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ equalish(X0,add(X1,additive_inverse(X1)))
| equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f65,f34]) ).
fof(f417,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| equalish(add(X0,a),add(X1,a)) ),
inference(resolution,[status(thm)],[f67,f73]) ).
fof(f418,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| equalish(add(X0,additive_identity),add(X1,additive_identity)) ),
inference(resolution,[status(thm)],[f67,f47]) ).
fof(f438,plain,
! [X0] :
( ~ equalish(X0,add(additive_identity,a))
| equalish(X0,a) ),
inference(resolution,[status(thm)],[f406,f73]) ).
fof(f439,plain,
! [X0] :
( ~ equalish(X0,add(additive_identity,additive_identity))
| equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f406,f47]) ).
fof(f572,plain,
! [X0] :
( ~ equalish(add(additive_inverse(a),a),X0)
| less_or_equal(X0,add(additive_identity,a)) ),
inference(resolution,[status(thm)],[f154,f71]) ).
fof(f606,plain,
( ~ defined(a)
| ~ defined(additive_inverse(a))
| less_or_equal(add(a,additive_inverse(a)),add(additive_identity,a)) ),
inference(resolution,[status(thm)],[f572,f36]) ).
fof(f610,plain,
( ~ defined(a)
| less_or_equal(add(a,additive_inverse(a)),add(additive_identity,a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f606,f48]) ).
fof(f614,plain,
less_or_equal(add(a,additive_inverse(a)),add(additive_identity,a)),
inference(forward_subsumption_resolution,[status(thm)],[f610,f73]) ).
fof(f621,plain,
! [X0] :
( ~ less_or_equal(add(additive_identity,a),X0)
| less_or_equal(add(a,additive_inverse(a)),X0) ),
inference(resolution,[status(thm)],[f614,f55]) ).
fof(f748,plain,
! [X0] :
( ~ equalish(X0,add(additive_identity,additive_inverse(additive_identity)))
| equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f408,f47]) ).
fof(f799,plain,
( ~ defined(additive_identity)
| ~ defined(additive_inverse(additive_identity))
| equalish(add(additive_inverse(additive_identity),additive_identity),additive_identity) ),
inference(resolution,[status(thm)],[f748,f36]) ).
fof(f803,plain,
( ~ defined(additive_identity)
| equalish(add(additive_inverse(additive_identity),additive_identity),additive_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f799,f48]) ).
fof(f813,plain,
equalish(add(additive_inverse(additive_identity),additive_identity),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[f803,f47]) ).
fof(f928,plain,
! [X0] :
( equalish(add(X0,a),a)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f417,f438]) ).
fof(f1114,plain,
! [X0] :
( equalish(add(X0,additive_identity),additive_identity)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f418,f439]) ).
fof(f1138,plain,
! [X0,X1] :
( ~ equalish(X1,add(X0,additive_identity))
| equalish(X1,additive_identity)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f1114,f65]) ).
fof(f1440,plain,
! [X0] :
( ~ equalish(a,X0)
| less_or_equal(X0,a) ),
inference(resolution,[status(thm)],[f136,f71]) ).
fof(f1447,plain,
! [X0] :
( ~ equalish(X0,a)
| less_or_equal(X0,a) ),
inference(resolution,[status(thm)],[f1440,f63]) ).
fof(f1575,plain,
! [X0] :
( ~ equalish(X0,additive_identity)
| less_or_equal(add(X0,a),a) ),
inference(resolution,[status(thm)],[f1447,f928]) ).
fof(f1590,plain,
! [X0,X1] :
( ~ equalish(add(X0,a),X1)
| less_or_equal(X1,a)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f1575,f71]) ).
fof(f2303,plain,
! [X0,X1] :
( ~ equalish(add(X0,additive_identity),X1)
| equalish(X1,additive_identity)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f1138,f63]) ).
fof(f2526,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| less_or_equal(add(X1,a),a)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f1590,f417]) ).
fof(f3029,plain,
! [X0] :
( ~ equalish(add(add(additive_inverse(additive_identity),additive_identity),additive_identity),X0)
| equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f2303,f813]) ).
fof(f3047,plain,
! [X0] :
( less_or_equal(add(a,additive_inverse(a)),a)
| ~ equalish(X0,additive_identity)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f2526,f621]) ).
fof(f3059,plain,
! [X0] :
( less_or_equal(add(a,additive_inverse(a)),a)
| ~ equalish(X0,additive_identity) ),
inference(duplicate_literals_removal,[status(thm)],[f3047]) ).
fof(f3114,plain,
! [X0,X1] :
( ~ equalish(add(a,additive_inverse(a)),X1)
| less_or_equal(X1,a)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f3059,f71]) ).
fof(f5943,plain,
! [X0] :
( ~ equalish(add(additive_inverse(additive_identity),additive_identity),X0)
| equalish(add(X0,additive_identity),additive_identity) ),
inference(resolution,[status(thm)],[f3029,f418]) ).
fof(f6510,plain,
( ~ defined(additive_identity)
| ~ defined(additive_inverse(additive_identity))
| equalish(add(add(additive_identity,additive_inverse(additive_identity)),additive_identity),additive_identity) ),
inference(resolution,[status(thm)],[f5943,f36]) ).
fof(f6514,plain,
( ~ defined(additive_identity)
| equalish(add(add(additive_identity,additive_inverse(additive_identity)),additive_identity),additive_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f6510,f48]) ).
fof(f6689,plain,
equalish(add(add(additive_identity,additive_inverse(additive_identity)),additive_identity),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[f6514,f47]) ).
fof(f7019,plain,
! [X0] :
( ~ defined(a)
| less_or_equal(additive_identity,a)
| ~ equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f3114,f34]) ).
fof(f7024,plain,
! [X0] :
( ~ defined(a)
| ~ equalish(X0,additive_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f7019,f75]) ).
fof(f7112,plain,
! [X0] : ~ equalish(X0,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[f7024,f73]) ).
fof(f7113,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f6689,f7112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD065-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.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 15:42:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 44.38/6.04 % Refutation found
% 44.38/6.04 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 44.38/6.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 42.35/6.12 % Elapsed time: 5.737377 seconds
% 42.35/6.12 % CPU time: 44.959343 seconds
% 42.35/6.12 % Total memory used: 238.971 MB
% 42.35/6.12 % Net memory used: 212.168 MB
%------------------------------------------------------------------------------