%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD043-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 12:22:00 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.52s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 66 ( 34 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 56 ( 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,V,W,Y,U,Z] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
product(additive_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,plain,
! [W,U,Z] :
( ~ sum(U,Z,W)
| ! [V,Y] :
( ~ sum(Y,Z,V)
| ! [X] :
( ~ sum(X,Y,U)
| sum(X,V,W) ) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f36,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f45,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(f46,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)],[f45]) ).
fof(f51,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f71,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f72,plain,
product(additive_identity,a,b),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f73,plain,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( ~ sum(X2,X3,X1)
| ~ sum(X0,X2,X2)
| sum(X0,X1,X1) ),
inference(factoring,[status(thm)],[f32]) ).
fof(f79,plain,
! [X0] :
( ~ defined(X0)
| sum(X0,additive_identity,X0) ),
inference(resolution,[status(thm)],[f37,f35]) ).
fof(f82,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolution,[status(thm)],[f79,f51]) ).
fof(f130,plain,
sum(additive_inverse(b),b,additive_identity),
inference(resolution,[status(thm)],[f36,f71]) ).
fof(f137,plain,
( ~ sum(additive_identity,additive_identity,additive_identity)
| sum(b,b,b) ),
inference(resolution,[status(thm)],[f46,f72]) ).
fof(f164,plain,
sum(b,b,b),
inference(forward_subsumption_resolution,[status(thm)],[f137,f82]) ).
fof(f181,plain,
sum(b,additive_inverse(b),additive_identity),
inference(resolution,[status(thm)],[f130,f37]) ).
fof(f235,plain,
! [X0,X1] :
( ~ sum(b,X1,X0)
| sum(b,X0,X0) ),
inference(resolution,[status(thm)],[f74,f164]) ).
fof(f244,plain,
sum(b,additive_identity,additive_identity),
inference(resolution,[status(thm)],[f235,f181]) ).
fof(f254,plain,
sum(additive_identity,b,additive_identity),
inference(resolution,[status(thm)],[f244,f37]) ).
fof(f259,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f254,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD043-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n015.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 15:43:07 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.17/0.52 % Refutation found
% 0.17/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.56 % Elapsed time: 0.105935 seconds
% 0.17/0.56 % CPU time: 0.409488 seconds
% 0.17/0.56 % Total memory used: 16.467 MB
% 0.17/0.56 % Net memory used: 16.141 MB
%------------------------------------------------------------------------------