%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD018-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 13 unt; 4 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 81 ( 42 ~; 35 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,V,W,Y,U,Z] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ sum(additive_identity,additive_inverse(a),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,plain,
! [W,U,Z] :
( ~ sum(U,Z,W)
| ! [V,Y] :
( ~ sum(Y,Z,V)
| ! [X] :
( ~ sum(X,Y,U)
| sum(X,V,W) ) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f31,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f34,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f50,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f69,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f70,plain,
sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f71,plain,
~ sum(additive_identity,additive_inverse(a),additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f73,plain,
~ sum(additive_inverse(a),additive_identity,additive_identity),
inference(resolution,[status(thm)],[f36,f71]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ sum(X1,X2,additive_identity)
| ~ sum(X0,X2,additive_identity)
| ~ sum(additive_inverse(a),X0,X1) ),
inference(resolution,[status(thm)],[f73,f31]) ).
fof(f96,definition,
( sQ3_spl
<=> defined(additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( sQ3_spl
| ~ defined(additive_identity) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f100,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f98,f50]) ).
fof(f101,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f100]) ).
fof(f110,plain,
! [X0] :
( ~ defined(a)
| ~ sum(additive_identity,X0,additive_identity)
| ~ sum(a,X0,additive_identity) ),
inference(resolution,[status(thm)],[f75,f35]) ).
fof(f114,definition,
! [X0] :
( sQ4_spl
<=> ( ~ sum(additive_identity,X0,additive_identity)
| ~ sum(a,X0,additive_identity) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f115,plain,
! [X0] :
( ~ sQ4_spl
| ~ sum(additive_identity,X0,additive_identity)
| ~ sum(a,X0,additive_identity) ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,definition,
( sQ5_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( sQ5_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f110,f114,f117]) ).
fof(f122,plain,
! [X0] :
( ~ sQ4_spl
| ~ sum(X0,a,additive_identity)
| ~ sum(additive_identity,X0,additive_identity) ),
inference(resolution,[status(thm)],[f115,f36]) ).
fof(f125,plain,
( ~ sQ4_spl
| ~ defined(additive_identity)
| ~ sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[f122,f34]) ).
fof(f129,definition,
( sQ6_spl
<=> sum(additive_identity,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( sQ6_spl
| ~ sum(additive_identity,a,additive_identity) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f125,f129,f96,f114]) ).
fof(f133,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f70]) ).
fof(f134,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f133]) ).
fof(f135,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f69]) ).
fof(f136,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f135]) ).
fof(f137,plain,
$false,
inference(sat_refutation,[status(thm)],[f101,f120,f132,f134,f136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD018-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 15:37:56 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.42 % Elapsed time: 0.043154 seconds
% 0.11/0.42 % CPU time: 0.134969 seconds
% 0.11/0.42 % Total memory used: 17.644 MB
% 0.11/0.42 % Net memory used: 17.392 MB
%------------------------------------------------------------------------------