%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD071-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:22:09 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 15 unt; 4 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 64 ( 30 ~; 30 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| product(X,Y,multiply(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Z,X,Y] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ less_or_equal(additive_identity,multiply(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f69,plain,
! [X0,X1,X2] :
( ~ product(X1,X2,X0)
| ~ less_or_equal(additive_identity,X2)
| ~ less_or_equal(additive_identity,X1)
| less_or_equal(additive_identity,X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f71,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f72,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f73,plain,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f74,plain,
less_or_equal(additive_identity,b),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f75,plain,
~ less_or_equal(additive_identity,multiply(a,b)),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f82,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| ~ less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,X0)
| less_or_equal(additive_identity,multiply(X0,X1)) ),
inference(resolution,[status(thm)],[f69,f61]) ).
fof(f104,definition,
( sQ5_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( sQ5_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,definition,
( sQ6_spl
<=> defined(b) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f109,plain,
( sQ6_spl
| ~ defined(b) ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f111,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f109,f72]) ).
fof(f112,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f111]) ).
fof(f113,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f71]) ).
fof(f114,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f113]) ).
fof(f115,plain,
( ~ defined(b)
| ~ defined(a)
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ),
inference(resolution,[status(thm)],[f82,f75]) ).
fof(f118,definition,
( sQ7_spl
<=> less_or_equal(additive_identity,a) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( sQ7_spl
| ~ less_or_equal(additive_identity,a) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
( sQ8_spl
<=> less_or_equal(additive_identity,b) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( sQ8_spl
| ~ less_or_equal(additive_identity,b) ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f115,f118,f121,f104,f107]) ).
fof(f130,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f73]) ).
fof(f131,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f132,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f123,f74]) ).
fof(f133,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f132]) ).
fof(f134,plain,
$false,
inference(sat_refutation,[status(thm)],[f112,f114,f124,f131,f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD071-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n026.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 15:47:37 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.41 % Elapsed time: 0.045923 seconds
% 0.15/0.41 % CPU time: 0.117936 seconds
% 0.15/0.41 % Total memory used: 13.403 MB
% 0.15/0.41 % Net memory used: 13.206 MB
%------------------------------------------------------------------------------