%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD009-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 4.80s 1.04s
% Output : CNFRefutation 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 114 ( 60 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X,Y,Z] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( equalish(X,additive_identity)
| ~ defined(X)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] :
( equalish(X,additive_identity)
| ~ defined(X)
| defined(multiplicative_inverse(X)) ),
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(f25,axiom,
! [X,Z,Y] :
( ~ equalish(X,Y)
| ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
! [X] : ~ equalish(multiply(a,X),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,plain,
! [Z] :
( ~ defined(Z)
| ! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| equalish(multiply(X,multiply(Y,Z)),multiply(multiply(X,Y),Z)) ) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ defined(X2)
| ~ defined(X1)
| ~ defined(X0)
| equalish(multiply(X0,multiply(X1,X2)),multiply(multiply(X0,X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0] :
( ~ defined(X0)
| equalish(multiply(multiplicative_identity,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
! [X0] :
( equalish(X0,additive_identity)
| ~ defined(X0)
| equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f53,plain,
! [X0] :
( equalish(X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f65,plain,
! [Z,Y] :
( ~ equalish(Y,Z)
| ! [X] :
( ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,plain,
! [X,Y] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(multiply(X0,X1),multiply(X2,X1)) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f74,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
~ equalish(a,additive_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
! [X0] : ~ equalish(multiply(a,X0),b),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( ~ equalish(multiply(multiply(X0,X1),X2),X3)
| equalish(multiply(X0,multiply(X1,X2)),X3)
| ~ defined(X2)
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f39,f66]) ).
fof(f210,plain,
! [X0,X1] :
( ~ equalish(X1,multiply(multiplicative_identity,X0))
| equalish(X1,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f40,f66]) ).
fof(f543,plain,
! [X0,X1] :
( ~ equalish(multiply(multiply(a,X0),X1),b)
| ~ defined(X1)
| ~ defined(X0)
| ~ defined(a) ),
inference(resolution,[status(thm)],[f124,f77]) ).
fof(f551,plain,
! [X0,X1] :
( ~ equalish(multiply(multiply(a,X0),X1),b)
| ~ defined(X1)
| ~ defined(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f543,f74]) ).
fof(f1459,plain,
! [X0] :
( ~ equalish(X0,multiply(multiplicative_identity,b))
| equalish(X0,b) ),
inference(resolution,[status(thm)],[f210,f75]) ).
fof(f1472,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| ~ equalish(multiply(multiply(a,X0),X1),multiply(multiplicative_identity,b)) ),
inference(resolution,[status(thm)],[f1459,f551]) ).
fof(f1767,plain,
! [X0] :
( ~ equalish(multiply(a,X0),multiplicative_identity)
| ~ defined(b)
| ~ defined(b)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f1472,f70]) ).
fof(f1771,plain,
! [X0] :
( ~ equalish(multiply(a,X0),multiplicative_identity)
| ~ defined(b)
| ~ defined(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1767]) ).
fof(f1772,plain,
! [X0] :
( ~ equalish(multiply(a,X0),multiplicative_identity)
| ~ defined(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1771,f75]) ).
fof(f1773,plain,
( equalish(a,additive_identity)
| ~ defined(a)
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[f1772,f41]) ).
fof(f1775,plain,
( equalish(a,additive_identity)
| ~ defined(a) ),
inference(forward_subsumption_resolution,[status(thm)],[f1773,f53]) ).
fof(f1778,plain,
equalish(a,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[f1775,f74]) ).
fof(f1779,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f76,f1778]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD009-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 15:37:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 4.80/1.04 % Refutation found
% 4.80/1.04 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.80/1.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.80/1.07 % Elapsed time: 0.689565 seconds
% 4.80/1.07 % CPU time: 5.206742 seconds
% 4.80/1.07 % Total memory used: 76.751 MB
% 4.80/1.07 % Net memory used: 67.166 MB
%------------------------------------------------------------------------------