%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD025-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 12:21:56 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.43s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 16 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 80 ( 47 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 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(f10,axiom,
! [Y,X,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
defined(multiplicative_identity),
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(f29,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
product(multiplicative_identity,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ product(d,b,multiply(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,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(f42,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)],[f41]) ).
fof(f45,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f58,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f62,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| product(X,Y,multiply(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f63,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f73,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f75,plain,
defined(c),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f77,plain,
product(multiplicative_identity,a,b),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f78,plain,
product(multiplicative_identity,c,d),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f79,plain,
~ product(d,b,multiply(a,c)),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f81,plain,
~ product(b,d,multiply(a,c)),
inference(resolution,[status(thm)],[f47,f79]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ product(X1,X2,multiply(a,c))
| ~ product(X0,X2,d)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[f81,f42]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ product(X0,b,X2)
| ~ product(X2,X1,multiply(a,c))
| ~ product(X0,X1,d) ),
inference(resolution,[status(thm)],[f83,f47]) ).
fof(f174,plain,
! [X0] :
( ~ product(multiplicative_identity,b,X0)
| ~ product(X0,c,multiply(a,c)) ),
inference(resolution,[status(thm)],[f99,f78]) ).
fof(f180,plain,
( ~ defined(c)
| ~ defined(a)
| ~ product(multiplicative_identity,b,a) ),
inference(resolution,[status(thm)],[f174,f63]) ).
fof(f184,plain,
( ~ defined(c)
| ~ product(multiplicative_identity,b,a) ),
inference(forward_subsumption_resolution,[status(thm)],[f180,f73]) ).
fof(f185,plain,
~ product(multiplicative_identity,b,a),
inference(forward_subsumption_resolution,[status(thm)],[f184,f75]) ).
fof(f188,plain,
! [X0,X1,X2] :
( ~ product(X1,X2,a)
| ~ product(X0,X2,b)
| ~ product(multiplicative_identity,X0,X1) ),
inference(resolution,[status(thm)],[f185,f42]) ).
fof(f209,plain,
! [X0] :
( ~ defined(a)
| ~ product(X0,a,b)
| ~ product(multiplicative_identity,X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f188,f45]) ).
fof(f213,plain,
! [X0] :
( ~ product(X0,a,b)
| ~ product(multiplicative_identity,X0,multiplicative_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f209,f73]) ).
fof(f214,plain,
( ~ defined(multiplicative_identity)
| ~ product(multiplicative_identity,a,b) ),
inference(resolution,[status(thm)],[f213,f45]) ).
fof(f218,plain,
~ defined(multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[f214,f77]) ).
fof(f219,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f218,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD025-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n005.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 15:38:53 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.15/5.43 % Refutation found
% 0.15/5.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.45 % Elapsed time: 0.068549 seconds
% 0.15/5.45 % CPU time: 0.327331 seconds
% 0.15/5.45 % Total memory used: 19.439 MB
% 0.15/5.45 % Net memory used: 19.073 MB
%------------------------------------------------------------------------------