%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD001-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 12:21:49 PM UTC 2026
% Result : Unsatisfiable 21.36s 3.13s
% Output : CNFRefutation 21.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 16 unt; 2 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 64 ( 32 ~; 30 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
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(f12,axiom,
! [A,Z,B,X,Y,C,D] :
( ~ sum(C,D,B)
| ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ sum(X,Y,A)
| product(A,Z,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
sum(additive_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f42,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f47,plain,
! [B,C,D] :
( ~ sum(C,D,B)
| ! [Z,Y] :
( ~ product(Y,Z,D)
| ! [X] :
( ~ product(X,Z,C)
| ! [A] :
( ~ sum(X,Y,A)
| product(A,Z,B) ) ) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f48,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sum(X5,X6,X2)
| ~ product(X4,X1,X6)
| ~ product(X3,X1,X5)
| ~ sum(X3,X4,X0)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f70,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f72,plain,
sum(additive_identity,a,b),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f73,plain,
~ product(multiplicative_identity,a,b),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f75,plain,
product(multiplicative_identity,a,a),
inference(resolution,[status(thm)],[f42,f70]) ).
fof(f77,plain,
product(multiplicative_identity,additive_identity,additive_identity),
inference(resolution,[status(thm)],[f51,f42]) ).
fof(f101,plain,
sum(additive_identity,a,a),
inference(resolution,[status(thm)],[f35,f70]) ).
fof(f544,plain,
product(a,multiplicative_identity,a),
inference(resolution,[status(thm)],[f75,f44]) ).
fof(f562,plain,
product(additive_identity,multiplicative_identity,additive_identity),
inference(resolution,[status(thm)],[f77,f44]) ).
fof(f786,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,X1,a)
| ~ product(X2,X1,additive_identity)
| ~ sum(X2,X3,X0)
| product(X0,X1,b) ),
inference(resolution,[status(thm)],[f48,f72]) ).
fof(f985,plain,
! [X0] :
( ~ product(a,X0,a)
| ~ product(additive_identity,X0,additive_identity)
| product(a,X0,b) ),
inference(resolution,[status(thm)],[f786,f101]) ).
fof(f36257,plain,
( ~ product(a,multiplicative_identity,a)
| product(a,multiplicative_identity,b) ),
inference(resolution,[status(thm)],[f985,f562]) ).
fof(f36258,definition,
( sQ6386_spl
<=> product(a,multiplicative_identity,b) ),
introduced(definition,[new_symbols(definition,[sQ6386_spl])],[split_symbol_definition]) ).
fof(f36259,plain,
( ~ sQ6386_spl
| product(a,multiplicative_identity,b) ),
inference(component_clause,[status(thm)],[f36258]) ).
fof(f36261,definition,
( sQ6387_spl
<=> product(a,multiplicative_identity,a) ),
introduced(definition,[new_symbols(definition,[sQ6387_spl])],[split_symbol_definition]) ).
fof(f36263,plain,
( sQ6387_spl
| ~ product(a,multiplicative_identity,a) ),
inference(component_clause,[status(thm)],[f36261]) ).
fof(f36264,plain,
( ~ sQ6387_spl
| sQ6386_spl ),
inference(split_clause,[status(thm)],[f36257,f36258,f36261]) ).
fof(f36267,plain,
( sQ6387_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f36263,f544]) ).
fof(f36268,plain,
sQ6387_spl,
inference(contradiction_clause,[status(thm)],[f36267]) ).
fof(f37253,plain,
( ~ sQ6386_spl
| product(multiplicative_identity,a,b) ),
inference(resolution,[status(thm)],[f36259,f44]) ).
fof(f37261,plain,
( ~ sQ6386_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f37253,f73]) ).
fof(f37262,plain,
~ sQ6386_spl,
inference(contradiction_clause,[status(thm)],[f37261]) ).
fof(f37263,plain,
$false,
inference(sat_refutation,[status(thm)],[f36264,f36268,f37262]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD001-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 15:38:29 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 21.36/3.13 % Refutation found
% 21.36/3.13 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 21.36/3.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 21.36/3.17 % Elapsed time: 2.803448 seconds
% 21.36/3.17 % CPU time: 21.809758 seconds
% 21.36/3.17 % Total memory used: 143.433 MB
% 21.36/3.17 % Net memory used: 130.651 MB
%------------------------------------------------------------------------------