%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD006-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:21:50 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 7 unt; 2 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 27 ~; 24 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] :
( ~ defined(X)
| equalish(add(additive_identity,X),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| equalish(add(X,additive_inverse(X)),additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( ~ defined(X)
| defined(additive_inverse(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(f28,negated_conjecture,
~ equalish(additive_inverse(additive_identity),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,plain,
! [X0] :
( ~ defined(X0)
| equalish(add(additive_identity,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f32,plain,
! [X0] :
( ~ defined(X0)
| equalish(add(X0,additive_inverse(X0)),additive_identity) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f45,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f61,plain,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f62,plain,
! [Z,Y] :
( ~ equalish(Y,Z)
| ! [X] :
( ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f71,plain,
~ equalish(additive_inverse(additive_identity),additive_identity),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f73,plain,
! [X0] :
( equalish(X0,add(additive_identity,X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f31,f61]) ).
fof(f76,plain,
! [X0] :
( ~ equalish(X0,additive_identity)
| ~ equalish(additive_inverse(additive_identity),X0) ),
inference(resolution,[status(thm)],[f63,f71]) ).
fof(f78,plain,
( ~ defined(additive_inverse(additive_identity))
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity) ),
inference(resolution,[status(thm)],[f76,f73]) ).
fof(f81,definition,
( sQ0_spl
<=> equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( sQ0_spl
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,definition,
( sQ1_spl
<=> defined(additive_inverse(additive_identity)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( sQ1_spl
| ~ defined(additive_inverse(additive_identity)) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f78,f81,f84]) ).
fof(f92,plain,
( sQ1_spl
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[f86,f46]) ).
fof(f93,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f92,f45]) ).
fof(f94,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f93]) ).
fof(f98,plain,
( sQ0_spl
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[f83,f32]) ).
fof(f101,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f98,f45]) ).
fof(f102,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f101]) ).
fof(f103,plain,
$false,
inference(sat_refutation,[status(thm)],[f87,f94,f102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD006-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 15:31:42 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.048962 seconds
% 0.13/0.42 % CPU time: 0.125641 seconds
% 0.13/0.42 % Total memory used: 17.332 MB
% 0.13/0.42 % Net memory used: 17.058 MB
%------------------------------------------------------------------------------