%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD009-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 0.08s 0.43s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 88 ( 48 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 49 !; 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/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y,X,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X] :
( sum(additive_identity,X,additive_identity)
| ~ defined(X)
| defined(multiplicative_inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| product(X,Y,multiply(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
! [X] : ~ product(a,X,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,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(f39,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)],[f38]) ).
fof(f42,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f56,plain,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f59,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| product(X,Y,multiply(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f60,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f70,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f71,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f72,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f73,plain,
! [X0] : ~ product(a,X0,b),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( ~ product(X1,X2,b)
| ~ product(X0,X2,X3)
| ~ product(a,X0,X1) ),
inference(resolution,[status(thm)],[f39,f73]) ).
fof(f277,plain,
! [X0,X1] :
( ~ defined(b)
| ~ product(X0,b,X1)
| ~ product(a,X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f107,f42]) ).
fof(f286,plain,
! [X0,X1] :
( ~ product(X0,b,X1)
| ~ product(a,X0,multiplicative_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f277,f71]) ).
fof(f355,plain,
! [X0] :
( ~ defined(b)
| ~ defined(X0)
| ~ product(a,X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f286,f60]) ).
fof(f361,plain,
! [X0] :
( ~ defined(X0)
| ~ product(a,X0,multiplicative_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f355,f71]) ).
fof(f365,plain,
! [X0] :
( ~ product(X0,a,multiplicative_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f361,f44]) ).
fof(f366,plain,
( ~ defined(a)
| sum(additive_identity,a,additive_identity)
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[f365,f43]) ).
fof(f371,plain,
( ~ defined(a)
| ~ defined(multiplicative_inverse(a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f366,f72]) ).
fof(f374,plain,
( ~ defined(a)
| defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[f56,f72]) ).
fof(f390,plain,
defined(multiplicative_inverse(a)),
inference(forward_subsumption_resolution,[status(thm)],[f374,f70]) ).
fof(f405,plain,
~ defined(a),
inference(forward_subsumption_resolution,[status(thm)],[f371,f390]) ).
fof(f406,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f70,f405]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD009-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n018.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Mon Sep 21 15:38:59 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Drodi V4.1.1
% 0.08/0.43 % Refutation found
% 0.08/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.45 % Elapsed time: 0.107770 seconds
% 0.08/0.45 % CPU time: 0.708077 seconds
% 0.08/0.45 % Total memory used: 25.080 MB
% 0.08/0.45 % Net memory used: 24.246 MB
%------------------------------------------------------------------------------