%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD010-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 46.56s 6.71s
% Output : CNFRefutation 46.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 10 unt; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 134 ( 62 ~; 72 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 67 ( 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
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(f11,axiom,
! [C,D,B,X,Y,A,Z] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X] :
( sum(additive_identity,X,additive_identity)
| ~ defined(X)
| defined(multiplicative_inverse(X)) ),
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,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
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(f43,plain,
! [D,Y,Z] :
( ~ product(Y,Z,D)
| ! [C,X] :
( ~ product(X,Z,C)
| ! [B,A] :
( ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X4,X6,X1)
| ~ product(X3,X6,X0)
| ~ product(X5,X6,X2)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f49,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f53,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f54,plain,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f68,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f69,plain,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f73,plain,
! [X0] :
( ~ defined(X0)
| sum(X0,additive_identity,X0) ),
inference(resolution,[status(thm)],[f35,f33]) ).
fof(f222,plain,
! [X0] :
( sum(multiplicative_inverse(X0),additive_identity,multiplicative_inverse(X0))
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f54,f73]) ).
fof(f228,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X4,X0,X2)
| ~ product(X3,X0,X1)
| ~ sum(X3,X4,multiplicative_inverse(X0))
| sum(X1,X2,multiplicative_identity)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[status(thm)],[f41,f44]) ).
fof(f237,plain,
! [X0] :
( sum(additive_identity,multiplicative_inverse(X0),multiplicative_inverse(X0))
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f222,f35]) ).
fof(f344,plain,
! [X0,X1,X2] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| ~ product(multiplicative_inverse(X0),X0,X2)
| ~ product(additive_identity,X0,X1)
| sum(X1,X2,multiplicative_identity)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[status(thm)],[f228,f237]) ).
fof(f349,plain,
! [X0,X1,X2] :
( ~ product(multiplicative_inverse(X0),X0,X2)
| ~ product(additive_identity,X0,X1)
| sum(X1,X2,multiplicative_identity)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(duplicate_literals_removal,[status(thm)],[f344]) ).
fof(f421,plain,
! [X0,X1,X2] :
( ~ product(X0,additive_identity,X1)
| ~ product(multiplicative_inverse(X0),X0,X2)
| sum(X1,X2,multiplicative_identity)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[status(thm)],[f349,f42]) ).
fof(f443,plain,
! [X0,X1,X2] :
( ~ product(X0,multiplicative_inverse(X0),X2)
| ~ product(X0,additive_identity,X1)
| sum(X1,X2,multiplicative_identity)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[status(thm)],[f421,f42]) ).
fof(f458,plain,
! [X0] :
( ~ defined(multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_identity,additive_identity,X0)
| sum(X0,multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[f443,f40]) ).
fof(f462,plain,
! [X0] :
( ~ defined(multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_identity,additive_identity,X0)
| sum(X0,multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f458,f68]) ).
fof(f1101,plain,
! [X0] :
( ~ defined(multiplicative_inverse(multiplicative_identity))
| ~ product(multiplicative_identity,additive_identity,X0)
| sum(X0,multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f462,f53]) ).
fof(f1102,plain,
! [X0] :
( sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity)
| ~ product(multiplicative_identity,additive_identity,X0)
| sum(X0,multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(resolution,[status(thm)],[f1101,f54]) ).
fof(f1103,plain,
! [X0] :
( sum(additive_identity,multiplicative_identity,additive_identity)
| ~ product(multiplicative_identity,additive_identity,X0)
| sum(X0,multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f1102,f53]) ).
fof(f1457,plain,
! [X0] :
( ~ product(multiplicative_identity,additive_identity,X0)
| sum(X0,multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f1103,f68]) ).
fof(f1458,plain,
( ~ defined(additive_identity)
| sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity) ),
inference(resolution,[status(thm)],[f1457,f40]) ).
fof(f1463,plain,
~ defined(additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[f1458,f69]) ).
fof(f3336,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1463,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD010-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.60 % Computer : n020.cluster.edu
% 0.12/0.60 % Model : x86_64 x86_64
% 0.12/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.60 % Memory : 8046.5625MB
% 0.12/0.60 % OS : Linux 6.8.0-71-generic
% 0.12/0.60 % CPULimit : 300
% 0.12/0.60 % WCLimit : 300
% 0.12/0.60 % DateTime : Mon Sep 21 15:38:48 UTC 2026
% 0.12/0.61 % CPUTime :
% 0.18/0.63 % Drodi V4.1.1
% 46.56/6.71 % Refutation found
% 46.56/6.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 46.56/6.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 42.68/6.88 % Elapsed time: 6.209854 seconds
% 42.68/6.88 % CPU time: 48.500052 seconds
% 42.68/6.88 % Total memory used: 389.015 MB
% 42.68/6.88 % Net memory used: 344.107 MB
%------------------------------------------------------------------------------