%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD025-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 0.26s 0.61s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 41 ( 19 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 100 ( 58 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 66 ( 66 !; 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(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
product(multiplicative_identity,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
product(a,c,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
product(d,b,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ product(multiplicative_identity,u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,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(f46,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)],[f45]) ).
fof(f47,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(f48,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)],[f47]) ).
fof(f49,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f62,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f77,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f79,plain,
defined(c),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f83,plain,
product(multiplicative_identity,a,b),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f84,plain,
product(multiplicative_identity,c,d),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f85,plain,
product(a,c,u),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f86,plain,
product(d,b,v),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f87,plain,
~ product(multiplicative_identity,u,v),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ product(X1,X2,v)
| ~ product(X0,X2,u)
| ~ product(multiplicative_identity,X0,X1) ),
inference(resolution,[status(thm)],[f46,f87]) ).
fof(f91,plain,
! [X0] :
( ~ product(X0,b,u)
| ~ product(multiplicative_identity,X0,d) ),
inference(resolution,[status(thm)],[f88,f86]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( ~ product(X1,X3,u)
| ~ product(X2,b,X3)
| ~ product(X1,X2,X0)
| ~ product(multiplicative_identity,X0,d) ),
inference(resolution,[status(thm)],[f91,f48]) ).
fof(f351,plain,
! [X0,X1,X2] :
( ~ product(X0,X2,u)
| ~ product(X1,b,X2)
| ~ product(X0,X1,c) ),
inference(resolution,[status(thm)],[f100,f84]) ).
fof(f359,plain,
! [X0,X1,X2] :
( ~ product(X0,X2,c)
| ~ product(X2,X1,u)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[f351,f51]) ).
fof(f453,plain,
! [X0] :
( ~ defined(c)
| ~ product(c,X0,u)
| ~ product(multiplicative_identity,b,X0) ),
inference(resolution,[status(thm)],[f359,f49]) ).
fof(f457,plain,
! [X0] :
( ~ product(c,X0,u)
| ~ product(multiplicative_identity,b,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f453,f79]) ).
fof(f459,plain,
! [X0] :
( ~ product(X0,c,u)
| ~ product(multiplicative_identity,b,X0) ),
inference(resolution,[status(thm)],[f457,f51]) ).
fof(f461,plain,
~ product(multiplicative_identity,b,a),
inference(resolution,[status(thm)],[f459,f85]) ).
fof(f467,plain,
! [X0,X1,X2] :
( ~ product(X1,X2,a)
| ~ product(X0,X2,b)
| ~ product(multiplicative_identity,X0,X1) ),
inference(resolution,[status(thm)],[f461,f46]) ).
fof(f526,plain,
! [X0] :
( ~ defined(a)
| ~ product(X0,a,b)
| ~ product(multiplicative_identity,X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f467,f49]) ).
fof(f530,plain,
! [X0] :
( ~ product(X0,a,b)
| ~ product(multiplicative_identity,X0,multiplicative_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f77]) ).
fof(f531,plain,
( ~ defined(multiplicative_identity)
| ~ product(multiplicative_identity,a,b) ),
inference(resolution,[status(thm)],[f530,f49]) ).
fof(f535,plain,
~ defined(multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[f531,f83]) ).
fof(f536,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f535,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD025-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n007.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 15:36:50 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.46 % Drodi V4.1.1
% 0.26/0.61 % Refutation found
% 0.26/0.61 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.26/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.66 % Elapsed time: 0.197706 seconds
% 0.26/0.66 % CPU time: 1.053052 seconds
% 0.26/0.66 % Total memory used: 23.778 MB
% 0.26/0.66 % Net memory used: 23.103 MB
%------------------------------------------------------------------------------