%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD066-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.12s 0.53s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 51 ( 26 unt; 2 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 80 ( 40 ~; 38 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 53 ( 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,V,W,Y,U,Z] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(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,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
sum(a,c,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
sum(b,c,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
less_or_equal(u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,plain,
! [W,U,Z] :
( ~ sum(U,Z,W)
| ! [V,Y] :
( ~ sum(Y,Z,V)
| ! [X] :
( ~ sum(X,Y,U)
| sum(X,V,W) ) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f40,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f41,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f71,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(f72,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)],[f71]) ).
fof(f75,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f76,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f77,plain,
defined(c),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f80,plain,
sum(a,c,u),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f81,plain,
sum(b,c,v),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f82,plain,
less_or_equal(u,v),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f83,plain,
~ less_or_equal(a,b),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f105,plain,
sum(additive_identity,b,b),
inference(resolution,[status(thm)],[f40,f76]) ).
fof(f106,plain,
sum(additive_identity,a,a),
inference(resolution,[status(thm)],[f40,f75]) ).
fof(f113,plain,
sum(additive_inverse(c),c,additive_identity),
inference(resolution,[status(thm)],[f41,f77]) ).
fof(f116,plain,
sum(c,a,u),
inference(resolution,[status(thm)],[f42,f80]) ).
fof(f167,definition,
( sQ9_spl
<=> less_or_equal(u,v) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( sQ9_spl
| ~ less_or_equal(u,v) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f443,definition,
( sQ70_spl
<=> less_or_equal(a,b) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( ~ sQ70_spl
| less_or_equal(a,b) ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f450,plain,
( ~ sQ70_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f444,f83]) ).
fof(f451,plain,
~ sQ70_spl,
inference(contradiction_clause,[status(thm)],[f450]) ).
fof(f650,plain,
sum(c,b,v),
inference(resolution,[status(thm)],[f81,f42]) ).
fof(f663,plain,
! [X0,X1,X2] :
( ~ sum(X2,a,X1)
| ~ sum(X0,c,X2)
| sum(X0,u,X1) ),
inference(resolution,[status(thm)],[f116,f37]) ).
fof(f670,plain,
! [X0,X1,X2] :
( ~ sum(X2,b,X1)
| ~ sum(X0,c,X2)
| sum(X0,v,X1) ),
inference(resolution,[status(thm)],[f650,f37]) ).
fof(f1680,plain,
! [X0] :
( ~ sum(additive_identity,b,X0)
| sum(additive_inverse(c),v,X0) ),
inference(resolution,[status(thm)],[f113,f670]) ).
fof(f1681,plain,
! [X0] :
( ~ sum(additive_identity,a,X0)
| sum(additive_inverse(c),u,X0) ),
inference(resolution,[status(thm)],[f113,f663]) ).
fof(f1696,plain,
sum(additive_inverse(c),v,b),
inference(resolution,[status(thm)],[f1680,f105]) ).
fof(f1700,plain,
sum(v,additive_inverse(c),b),
inference(resolution,[status(thm)],[f1696,f42]) ).
fof(f1708,plain,
! [X0,X1] :
( ~ sum(X1,additive_inverse(c),X0)
| ~ less_or_equal(X1,v)
| less_or_equal(X0,b) ),
inference(resolution,[status(thm)],[f1700,f72]) ).
fof(f1725,plain,
sum(additive_inverse(c),u,a),
inference(resolution,[status(thm)],[f1681,f106]) ).
fof(f1729,plain,
sum(u,additive_inverse(c),a),
inference(resolution,[status(thm)],[f1725,f42]) ).
fof(f1770,plain,
( ~ less_or_equal(u,v)
| less_or_equal(a,b) ),
inference(resolution,[status(thm)],[f1708,f1729]) ).
fof(f1772,plain,
( ~ sQ9_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f1770,f443,f167]) ).
fof(f1774,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f169,f82]) ).
fof(f1775,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f1774]) ).
fof(f1776,plain,
$false,
inference(sat_refutation,[status(thm)],[f451,f1772,f1775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD066-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 15:44:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.12/0.53 % Refutation found
% 0.12/0.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.71/0.54 % Elapsed time: 0.187729 seconds
% 0.71/0.54 % CPU time: 1.303926 seconds
% 0.71/0.54 % Total memory used: 29.917 MB
% 0.71/0.54 % Net memory used: 28.550 MB
%------------------------------------------------------------------------------