%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD010-3 : 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 12:21:51 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 9 unt; 2 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 13 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 8 ( 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ sum(additive_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f53,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f68,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f69,plain,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f162,plain,
( sum(additive_identity,multiplicative_identity,additive_identity)
| product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f41,f53]) ).
fof(f164,definition,
( sQ3_spl
<=> product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f165,plain,
( ~ sQ3_spl
| product(multiplicative_inverse(multiplicative_identity),multiplicative_identity,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,definition,
( sQ4_spl
<=> sum(additive_identity,multiplicative_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( ~ sQ4_spl
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f162,f164,f167]) ).
fof(f206,plain,
( ~ sQ3_spl
| product(multiplicative_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(resolution,[status(thm)],[f165,f42]) ).
fof(f207,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f69]) ).
fof(f208,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f207]) ).
fof(f209,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f68]) ).
fof(f210,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f209]) ).
fof(f211,plain,
$false,
inference(sat_refutation,[status(thm)],[f170,f208,f210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD010-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 15:36:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40 % Elapsed time: 0.033641 seconds
% 0.14/0.40 % CPU time: 0.084118 seconds
% 0.14/0.40 % Total memory used: 4.676 MB
% 0.14/0.40 % Net memory used: 4.635 MB
%------------------------------------------------------------------------------