%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD059-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:22:04 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 77 ( 40 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] :
( ~ defined(X)
| equalish(add(additive_identity,X),X) ),
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(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(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(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_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ less_or_equal(additive_identity,add(a,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(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(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(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(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_identity,a),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f75,plain,
~ less_or_equal(additive_identity,add(a,a)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f109,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(add(additive_identity,X0),add(a,X0)) ),
inference(resolution,[status(thm)],[f59,f74]) ).
fof(f114,plain,
! [X0,X1] :
( ~ equalish(add(additive_identity,X0),X1)
| less_or_equal(X1,add(a,X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f109,f71]) ).
fof(f164,plain,
! [X0] :
( ~ equalish(add(additive_identity,a),X0)
| less_or_equal(X0,add(a,a)) ),
inference(resolution,[status(thm)],[f114,f73]) ).
fof(f168,plain,
( ~ defined(a)
| ~ defined(additive_identity)
| less_or_equal(add(a,additive_identity),add(a,a)) ),
inference(resolution,[status(thm)],[f164,f36]) ).
fof(f174,plain,
( ~ defined(a)
| less_or_equal(add(a,additive_identity),add(a,a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f47]) ).
fof(f193,plain,
less_or_equal(add(a,additive_identity),add(a,a)),
inference(forward_subsumption_resolution,[status(thm)],[f174,f73]) ).
fof(f197,plain,
! [X0] :
( ~ less_or_equal(X0,add(a,additive_identity))
| less_or_equal(X0,add(a,a)) ),
inference(resolution,[status(thm)],[f193,f55]) ).
fof(f239,plain,
( ~ defined(additive_identity)
| less_or_equal(add(additive_identity,additive_identity),add(a,a)) ),
inference(resolution,[status(thm)],[f197,f109]) ).
fof(f241,plain,
less_or_equal(add(additive_identity,additive_identity),add(a,a)),
inference(forward_subsumption_resolution,[status(thm)],[f239,f47]) ).
fof(f245,plain,
! [X0] :
( ~ equalish(add(additive_identity,additive_identity),X0)
| less_or_equal(X0,add(a,a)) ),
inference(resolution,[status(thm)],[f241,f71]) ).
fof(f288,plain,
( ~ defined(additive_identity)
| less_or_equal(additive_identity,add(a,a)) ),
inference(resolution,[status(thm)],[f245,f33]) ).
fof(f294,plain,
~ defined(additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[f288,f75]) ).
fof(f297,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f294,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD059-1 : 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 : n009.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 15:43:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.37 % Drodi V4.1.1
% 0.15/0.44 % Refutation found
% 0.15/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.47 % Elapsed time: 0.083794 seconds
% 0.15/0.47 % CPU time: 0.488637 seconds
% 0.15/0.47 % Total memory used: 25.045 MB
% 0.15/0.47 % Net memory used: 24.231 MB
%------------------------------------------------------------------------------