%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD030-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:21:57 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 34 ( 13 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 96 ( 55 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 60 !; 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U,Z,W,X,Y,V] :
( ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(U,Z,W) ),
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(f10,axiom,
! [Y,X,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| product(X,Y,multiply(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
product(multiplicative_identity,a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ product(d,b,multiply(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,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(f40,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)],[f39]) ).
fof(f41,plain,
! [W,X,V] :
( ~ product(X,V,W)
| ! [Z,Y] :
( ~ product(Y,Z,V)
| ! [U] :
( ~ product(X,Y,U)
| product(U,Z,W) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f60,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| product(X,Y,multiply(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f61,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f71,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f72,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f74,plain,
product(multiplicative_identity,a,d),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f75,plain,
~ product(d,b,multiply(a,b)),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ product(X1,X2,multiply(a,b))
| ~ product(X0,X2,b)
| ~ product(d,X0,X1) ),
inference(resolution,[status(thm)],[f40,f75]) ).
fof(f89,plain,
! [X0] :
( ~ defined(b)
| ~ product(X0,b,multiply(a,b))
| ~ product(d,multiplicative_identity,X0) ),
inference(resolution,[status(thm)],[f76,f43]) ).
fof(f100,plain,
! [X0] :
( ~ product(X0,b,multiply(a,b))
| ~ product(d,multiplicative_identity,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f72]) ).
fof(f102,plain,
( ~ defined(b)
| ~ defined(a)
| ~ product(d,multiplicative_identity,a) ),
inference(resolution,[status(thm)],[f100,f61]) ).
fof(f106,plain,
( ~ defined(b)
| ~ product(d,multiplicative_identity,a) ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f71]) ).
fof(f107,plain,
~ product(d,multiplicative_identity,a),
inference(forward_subsumption_resolution,[status(thm)],[f106,f72]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ~ product(X0,X2,a)
| ~ product(X1,multiplicative_identity,X2)
| ~ product(X0,X1,d) ),
inference(resolution,[status(thm)],[f107,f42]) ).
fof(f186,plain,
! [X0] :
( ~ defined(a)
| ~ product(X0,multiplicative_identity,a)
| ~ product(multiplicative_identity,X0,d) ),
inference(resolution,[status(thm)],[f108,f43]) ).
fof(f196,plain,
! [X0] :
( ~ product(X0,multiplicative_identity,a)
| ~ product(multiplicative_identity,X0,d) ),
inference(forward_subsumption_resolution,[status(thm)],[f186,f71]) ).
fof(f213,plain,
~ product(a,multiplicative_identity,a),
inference(resolution,[status(thm)],[f196,f74]) ).
fof(f254,plain,
~ product(multiplicative_identity,a,a),
inference(resolution,[status(thm)],[f213,f45]) ).
fof(f256,plain,
~ defined(a),
inference(resolution,[status(thm)],[f254,f43]) ).
fof(f261,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f256,f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD030-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n012.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 15:38:21 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.083106 seconds
% 0.11/0.44 % CPU time: 0.470565 seconds
% 0.11/0.44 % Total memory used: 23.159 MB
% 0.11/0.44 % Net memory used: 22.670 MB
%------------------------------------------------------------------------------