%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD013-2 : 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 12:21:52 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.51s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 17 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 87 ( 52 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y] :
( ~ equalish(Y,X)
| equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Z,Y] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X,Z,Y] :
( ~ equalish(X,Y)
| ~ defined(Z)
| equalish(add(X,Z),add(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
equalish(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
equalish(add(a,c),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ equalish(add(d,b),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f42,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| equalish(add(X0,X1),add(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f69,plain,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f70,plain,
! [Z,Y] :
( ~ equalish(Y,Z)
| ! [X] :
( ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [X,Y] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ defined(Z)
| equalish(add(X,Z),add(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(add(X0,X1),add(X2,X1)) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f80,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f81,plain,
defined(c),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f84,plain,
equalish(a,b),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f85,plain,
equalish(c,d),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f86,plain,
equalish(add(a,c),u),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f87,plain,
~ equalish(add(d,b),u),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f88,plain,
~ equalish(u,add(d,b)),
inference(resolution,[status(thm)],[f69,f87]) ).
fof(f90,plain,
! [X0] :
( ~ equalish(X0,add(d,b))
| ~ equalish(u,X0) ),
inference(resolution,[status(thm)],[f71,f88]) ).
fof(f93,plain,
! [X0] :
( ~ equalish(X0,u)
| ~ equalish(X0,add(d,b)) ),
inference(resolution,[status(thm)],[f90,f69]) ).
fof(f106,plain,
! [X0] :
( ~ equalish(add(X0,b),u)
| ~ equalish(X0,d)
| ~ defined(b) ),
inference(resolution,[status(thm)],[f73,f93]) ).
fof(f108,plain,
! [X0] :
( ~ equalish(add(X0,b),u)
| ~ equalish(X0,d) ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f80]) ).
fof(f124,plain,
! [X0,X1] :
( ~ equalish(X1,u)
| ~ equalish(add(X0,b),X1)
| ~ equalish(X0,d) ),
inference(resolution,[status(thm)],[f108,f71]) ).
fof(f176,plain,
! [X0] :
( ~ equalish(X0,u)
| ~ equalish(add(c,b),X0) ),
inference(resolution,[status(thm)],[f124,f85]) ).
fof(f182,plain,
( ~ defined(b)
| ~ defined(c)
| ~ equalish(add(b,c),u) ),
inference(resolution,[status(thm)],[f176,f42]) ).
fof(f187,plain,
( ~ defined(b)
| ~ equalish(add(b,c),u) ),
inference(forward_subsumption_resolution,[status(thm)],[f182,f81]) ).
fof(f190,plain,
~ equalish(add(b,c),u),
inference(forward_subsumption_resolution,[status(thm)],[f187,f80]) ).
fof(f191,plain,
! [X0] :
( ~ equalish(X0,u)
| ~ equalish(add(b,c),X0) ),
inference(resolution,[status(thm)],[f190,f71]) ).
fof(f208,plain,
! [X0] :
( ~ equalish(b,X0)
| ~ defined(c)
| ~ equalish(add(X0,c),u) ),
inference(resolution,[status(thm)],[f191,f73]) ).
fof(f213,plain,
! [X0] :
( ~ equalish(b,X0)
| ~ equalish(add(X0,c),u) ),
inference(forward_subsumption_resolution,[status(thm)],[f208,f81]) ).
fof(f258,plain,
~ equalish(b,a),
inference(resolution,[status(thm)],[f213,f86]) ).
fof(f262,plain,
~ equalish(a,b),
inference(resolution,[status(thm)],[f258,f69]) ).
fof(f263,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f262,f84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD013-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n005.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Mon Sep 21 15:37:17 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Drodi V4.1.1
% 0.13/0.51 % Refutation found
% 0.13/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.53 % Elapsed time: 0.175365 seconds
% 0.13/0.53 % CPU time: 1.219036 seconds
% 0.13/0.53 % Total memory used: 36.683 MB
% 0.13/0.53 % Net memory used: 33.674 MB
%------------------------------------------------------------------------------