%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD064-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 12:22:07 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 9 unt; 3 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 73 ( 36 ~; 34 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U,V,X,Y,Z] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ less_or_equal(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f51,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f65,plain,
! [V,Y,Z] :
( ~ sum(Y,Z,V)
| ! [U,X] :
( ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f66,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ less_or_equal(X2,X3)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f70,plain,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f71,plain,
~ less_or_equal(additive_inverse(a),additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ sum(a,X2,X1)
| ~ sum(additive_identity,X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f66,f70]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ sum(additive_identity,X0,X2)
| less_or_equal(X2,X1)
| ~ sum(X0,a,X1) ),
inference(resolution,[status(thm)],[f36,f75]) ).
fof(f92,plain,
! [X0,X1] :
( ~ defined(X0)
| less_or_equal(X0,X1)
| ~ sum(X0,a,X1) ),
inference(resolution,[status(thm)],[f90,f34]) ).
fof(f107,plain,
( ~ defined(a)
| ~ defined(additive_inverse(a))
| less_or_equal(additive_inverse(a),additive_identity) ),
inference(resolution,[status(thm)],[f92,f35]) ).
fof(f111,definition,
( sQ5_spl
<=> less_or_equal(additive_inverse(a),additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ5_spl
| less_or_equal(additive_inverse(a),additive_identity) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,definition,
( sQ6_spl
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( sQ6_spl
| ~ defined(additive_inverse(a)) ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,definition,
( sQ7_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( sQ7_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f107,f111,f114,f117]) ).
fof(f134,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f69]) ).
fof(f135,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f134]) ).
fof(f136,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f112,f71]) ).
fof(f137,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f136]) ).
fof(f138,plain,
( sQ6_spl
| ~ defined(a) ),
inference(resolution,[status(thm)],[f116,f51]) ).
fof(f139,plain,
( sQ6_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f138,f117,f114]) ).
fof(f140,plain,
$false,
inference(sat_refutation,[status(thm)],[f120,f135,f137,f139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD064-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 15:43:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.042690 seconds
% 0.13/0.41 % CPU time: 0.114527 seconds
% 0.13/0.41 % Total memory used: 17.405 MB
% 0.13/0.41 % Net memory used: 17.153 MB
%------------------------------------------------------------------------------