%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD037-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 12:21:59 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 45 ( 16 unt; 5 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 93 ( 47 ~; 41 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 35 ( 35 !; 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(f8,axiom,
! [X] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
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,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ product(b,multiplicative_inverse(a),multiplicative_identity),
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(f43,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f44,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f56,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f71,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f73,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f74,plain,
product(multiplicative_identity,a,b),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f75,plain,
~ product(b,multiplicative_inverse(a),multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f102,plain,
~ product(multiplicative_inverse(a),b,multiplicative_identity),
inference(resolution,[status(thm)],[f45,f75]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ~ product(X1,X2,multiplicative_identity)
| ~ product(X0,X2,b)
| ~ product(multiplicative_inverse(a),X0,X1) ),
inference(resolution,[status(thm)],[f102,f40]) ).
fof(f194,plain,
! [X0] :
( ~ defined(a)
| sum(additive_identity,a,additive_identity)
| ~ product(multiplicative_identity,X0,multiplicative_identity)
| ~ product(a,X0,b) ),
inference(resolution,[status(thm)],[f104,f44]) ).
fof(f199,definition,
! [X0] :
( sQ7_spl
<=> ( ~ product(multiplicative_identity,X0,multiplicative_identity)
| ~ product(a,X0,b) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f200,plain,
! [X0] :
( ~ sQ7_spl
| ~ product(multiplicative_identity,X0,multiplicative_identity)
| ~ product(a,X0,b) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,definition,
( sQ8_spl
<=> sum(additive_identity,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( ~ sQ8_spl
| sum(additive_identity,a,additive_identity) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
( sQ9_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( sQ9_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( ~ sQ9_spl
| sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f194,f199,f202,f205]) ).
fof(f216,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f71]) ).
fof(f217,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f216]) ).
fof(f219,plain,
! [X0] :
( ~ sQ7_spl
| ~ product(X0,a,b)
| ~ product(multiplicative_identity,X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f200,f45]) ).
fof(f221,plain,
( ~ sQ7_spl
| ~ defined(multiplicative_identity)
| ~ product(multiplicative_identity,a,b) ),
inference(resolution,[status(thm)],[f219,f43]) ).
fof(f225,definition,
( sQ12_spl
<=> product(multiplicative_identity,a,b) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( sQ12_spl
| ~ product(multiplicative_identity,a,b) ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,definition,
( sQ13_spl
<=> defined(multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( sQ13_spl
| ~ defined(multiplicative_identity) ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f221,f225,f228,f199]) ).
fof(f232,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f203,f73]) ).
fof(f233,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f232]) ).
fof(f234,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f227,f74]) ).
fof(f235,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f234]) ).
fof(f236,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f230,f56]) ).
fof(f237,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f238,plain,
$false,
inference(sat_refutation,[status(thm)],[f208,f217,f231,f233,f235,f237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD037-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n017.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 15:34:58 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.07/0.37 % Refutation found
% 0.07/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.39 % Elapsed time: 0.038219 seconds
% 0.12/0.39 % CPU time: 0.104285 seconds
% 0.12/0.39 % Total memory used: 4.994 MB
% 0.12/0.39 % Net memory used: 4.934 MB
%------------------------------------------------------------------------------