%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD018-1 : 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 12:21:54 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 48 ( 9 unt; 5 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 108 ( 55 ~; 48 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 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(f12,axiom,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
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(f28,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
equalish(a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ equalish(additive_inverse(a),additive_identity),
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(f48,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
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(f73,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f74,plain,
equalish(a,additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f75,plain,
~ equalish(additive_inverse(a),additive_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f78,plain,
! [X0] :
( equalish(add(additive_identity,additive_inverse(X0)),additive_inverse(X0))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f48,f33]) ).
fof(f82,plain,
! [X0] :
( ~ equalish(X0,additive_identity)
| ~ equalish(additive_inverse(a),X0) ),
inference(resolution,[status(thm)],[f65,f75]) ).
fof(f84,plain,
! [X0] :
( ~ equalish(X0,additive_inverse(a))
| ~ equalish(X0,additive_identity) ),
inference(resolution,[status(thm)],[f82,f63]) ).
fof(f89,definition,
( sQ1_spl
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( sQ1_spl
| ~ defined(additive_inverse(a)) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f112,plain,
( ~ equalish(add(additive_identity,additive_inverse(a)),additive_identity)
| ~ defined(a) ),
inference(resolution,[status(thm)],[f78,f84]) ).
fof(f113,definition,
( sQ5_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( sQ5_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,definition,
( sQ6_spl
<=> equalish(add(additive_identity,additive_inverse(a)),additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( sQ6_spl
| ~ equalish(add(additive_identity,additive_inverse(a)),additive_identity) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f112,f113,f116]) ).
fof(f120,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f73]) ).
fof(f121,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f120]) ).
fof(f129,plain,
( sQ1_spl
| ~ defined(a) ),
inference(resolution,[status(thm)],[f91,f48]) ).
fof(f130,plain,
( sQ1_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f129,f113,f89]) ).
fof(f174,plain,
! [X0] :
( sQ6_spl
| ~ equalish(X0,additive_identity)
| ~ equalish(add(additive_identity,additive_inverse(a)),X0) ),
inference(resolution,[status(thm)],[f118,f65]) ).
fof(f230,plain,
! [X0] :
( sQ6_spl
| ~ equalish(add(X0,additive_inverse(a)),additive_identity)
| ~ equalish(additive_identity,X0)
| ~ defined(additive_inverse(a)) ),
inference(resolution,[status(thm)],[f67,f174]) ).
fof(f232,definition,
! [X0] :
( sQ18_spl
<=> ( ~ equalish(add(X0,additive_inverse(a)),additive_identity)
| ~ equalish(additive_identity,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f233,plain,
! [X0] :
( ~ sQ18_spl
| ~ equalish(add(X0,additive_inverse(a)),additive_identity)
| ~ equalish(additive_identity,X0) ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( sQ6_spl
| sQ18_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f230,f89,f232,f116]) ).
fof(f247,plain,
( ~ sQ18_spl
| ~ defined(a)
| ~ equalish(additive_identity,a) ),
inference(resolution,[status(thm)],[f233,f34]) ).
fof(f250,definition,
( sQ20_spl
<=> equalish(additive_identity,a) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f252,plain,
( sQ20_spl
| ~ equalish(additive_identity,a) ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,plain,
( ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f247,f250,f113,f232]) ).
fof(f275,plain,
( sQ20_spl
| ~ equalish(a,additive_identity) ),
inference(resolution,[status(thm)],[f252,f63]) ).
fof(f276,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f275,f74]) ).
fof(f277,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f276]) ).
fof(f278,plain,
$false,
inference(sat_refutation,[status(thm)],[f119,f121,f130,f235,f253,f277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD018-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n009.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 21 15:38:27 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.41 % Drodi V4.1.1
% 0.17/0.49 % Refutation found
% 0.17/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.54 % Elapsed time: 0.128547 seconds
% 0.17/0.54 % CPU time: 0.505318 seconds
% 0.17/0.54 % Total memory used: 21.600 MB
% 0.17/0.54 % Net memory used: 20.920 MB
%------------------------------------------------------------------------------