%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD033-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 12:21:58 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.52s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 14 unt; 2 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 31 ~; 24 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X,V,W,Y,U,Z] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y,X,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
product(m,a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ product(multiplicative_identity,m,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,plain,
! [W,U,Z] :
( ~ product(U,Z,W)
| ! [V,Y] :
( ~ product(Y,Z,V)
| ! [X] :
( ~ product(X,Y,U)
| product(X,V,W) ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f40,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f44,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f71,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f73,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f74,plain,
product(m,a,a),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f75,plain,
~ product(multiplicative_identity,m,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f86,plain,
~ product(m,multiplicative_identity,multiplicative_identity),
inference(resolution,[status(thm)],[f45,f75]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ~ product(X1,X2,multiplicative_identity)
| ~ product(X0,X2,multiplicative_identity)
| ~ product(m,X0,X1) ),
inference(resolution,[status(thm)],[f40,f86]) ).
fof(f214,plain,
! [X0] :
( ~ product(a,X0,multiplicative_identity)
| ~ product(a,X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f110,f74]) ).
fof(f218,plain,
! [X0] : ~ product(a,X0,multiplicative_identity),
inference(duplicate_literals_removal,[status(thm)],[f214]) ).
fof(f221,plain,
! [X0] : ~ product(X0,a,multiplicative_identity),
inference(resolution,[status(thm)],[f218,f45]) ).
fof(f222,plain,
( ~ defined(a)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[f221,f44]) ).
fof(f226,definition,
( sQ3_spl
<=> sum(additive_identity,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( ~ sQ3_spl
| sum(additive_identity,a,additive_identity) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,definition,
( sQ4_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f231,plain,
( sQ4_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f232,plain,
( ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f222,f226,f229]) ).
fof(f233,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f227,f73]) ).
fof(f234,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f233]) ).
fof(f235,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f71]) ).
fof(f236,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f235]) ).
fof(f237,plain,
$false,
inference(sat_refutation,[status(thm)],[f232,f234,f236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD033-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n013.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 21 15:38:36 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.43 % Drodi V4.1.1
% 0.15/0.52 % Refutation found
% 0.15/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.56 % Elapsed time: 0.129227 seconds
% 0.15/0.56 % CPU time: 0.679516 seconds
% 0.15/0.56 % Total memory used: 22.561 MB
% 0.15/0.56 % Net memory used: 22.114 MB
%------------------------------------------------------------------------------