%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD070-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 4.78s 1.09s
% Output : CNFRefutation 4.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 66 ( 17 unt; 6 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 156 ( 75 ~; 75 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] :
( ~ defined(X)
| equalish(add(additive_identity,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Z,Y] :
( ~ less_or_equal(Y,Z)
| ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Z,Y] :
( ~ less_or_equal(X,Y)
| ~ defined(Z)
| less_or_equal(add(X,Z),add(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y] :
( ~ equalish(Y,X)
| equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [Y,Z,X] :
( ~ equalish(X,Y)
| ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
equalish(add(a,b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ less_or_equal(additive_identity,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,plain,
! [X0] :
( ~ defined(X0)
| equalish(add(additive_identity,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f58,plain,
! [Z,Y] :
( ~ less_or_equal(Y,Z)
| ! [X] :
( ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f61,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
! [X,Y] :
( ~ less_or_equal(X,Y)
| ! [Z] :
( ~ defined(Z)
| less_or_equal(add(X,Z),add(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X0,X2)
| ~ defined(X1)
| less_or_equal(add(X0,X1),add(X2,X1)) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f67,plain,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f74,plain,
! [Y,X] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X0)
| ~ less_or_equal(X2,X1)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f78,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f79,plain,
defined(c),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f80,plain,
equalish(add(a,b),c),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f81,plain,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f82,plain,
less_or_equal(additive_identity,b),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f83,plain,
~ less_or_equal(additive_identity,c),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f84,plain,
! [X0] :
( ~ less_or_equal(X0,c)
| ~ less_or_equal(additive_identity,X0) ),
inference(resolution,[status(thm)],[f59,f83]) ).
fof(f95,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(c,X0)
| less_or_equal(X0,c) ),
inference(resolution,[status(thm)],[f61,f79]) ).
fof(f104,definition,
( sQ0_spl
<=> less_or_equal(c,c) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( ~ sQ0_spl
| less_or_equal(c,c) ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f106,plain,
( sQ0_spl
| ~ less_or_equal(c,c) ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,definition,
( sQ1_spl
<=> defined(c) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f109,plain,
( sQ1_spl
| ~ defined(c) ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f126,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f109,f79]) ).
fof(f127,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f126]) ).
fof(f132,plain,
! [X0] :
( ~ sQ0_spl
| ~ equalish(c,X0)
| less_or_equal(X0,c) ),
inference(resolution,[status(thm)],[f105,f75]) ).
fof(f135,plain,
! [X0] :
( ~ sQ0_spl
| ~ equalish(X0,c)
| less_or_equal(X0,c) ),
inference(resolution,[status(thm)],[f132,f67]) ).
fof(f194,definition,
( sQ13_spl
<=> less_or_equal(b,c) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( ~ sQ13_spl
| less_or_equal(b,c) ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f196,plain,
( sQ13_spl
| ~ less_or_equal(b,c) ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f216,plain,
! [X0,X1,X2,X3] :
( ~ equalish(add(X1,X0),X3)
| less_or_equal(X3,add(X2,X0))
| ~ less_or_equal(X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f63,f75]) ).
fof(f222,plain,
! [X0] :
( sQ13_spl
| ~ less_or_equal(X0,c)
| ~ less_or_equal(b,X0) ),
inference(resolution,[status(thm)],[f196,f59]) ).
fof(f227,definition,
( sQ17_spl
<=> defined(b) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f229,plain,
( sQ17_spl
| ~ defined(b) ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f231,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f229,f78]) ).
fof(f232,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f231]) ).
fof(f266,plain,
( sQ0_spl
| ~ defined(c)
| less_or_equal(c,c) ),
inference(resolution,[status(thm)],[f106,f95]) ).
fof(f268,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f266,f104,f107]) ).
fof(f352,plain,
( ~ sQ0_spl
| less_or_equal(add(a,b),c) ),
inference(resolution,[status(thm)],[f135,f80]) ).
fof(f471,plain,
( sQ13_spl
| ~ sQ0_spl
| ~ less_or_equal(b,add(a,b)) ),
inference(resolution,[status(thm)],[f352,f222]) ).
fof(f641,plain,
! [X0] :
( sQ13_spl
| ~ sQ0_spl
| ~ equalish(add(X0,b),b)
| ~ less_or_equal(X0,a)
| ~ defined(b) ),
inference(resolution,[status(thm)],[f471,f216]) ).
fof(f650,definition,
! [X0] :
( sQ51_spl
<=> ( ~ equalish(add(X0,b),b)
| ~ less_or_equal(X0,a) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f651,plain,
! [X0] :
( ~ sQ51_spl
| ~ equalish(add(X0,b),b)
| ~ less_or_equal(X0,a) ),
inference(component_clause,[status(thm)],[f650]) ).
fof(f653,plain,
( sQ13_spl
| ~ sQ0_spl
| sQ51_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f641,f227,f650,f104,f194]) ).
fof(f753,plain,
( ~ sQ13_spl
| ~ less_or_equal(additive_identity,b) ),
inference(resolution,[status(thm)],[f195,f84]) ).
fof(f755,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f753,f82]) ).
fof(f756,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f755]) ).
fof(f1958,plain,
( ~ sQ51_spl
| ~ defined(b)
| ~ less_or_equal(additive_identity,a) ),
inference(resolution,[status(thm)],[f651,f37]) ).
fof(f1962,definition,
( sQ195_spl
<=> less_or_equal(additive_identity,a) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f1964,plain,
( sQ195_spl
| ~ less_or_equal(additive_identity,a) ),
inference(component_clause,[status(thm)],[f1962]) ).
fof(f1965,plain,
( ~ sQ51_spl
| ~ sQ17_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f1958,f1962,f227,f650]) ).
fof(f1966,plain,
( sQ195_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1964,f81]) ).
fof(f1967,plain,
sQ195_spl,
inference(contradiction_clause,[status(thm)],[f1966]) ).
fof(f1968,plain,
$false,
inference(sat_refutation,[status(thm)],[f127,f232,f268,f653,f756,f1965,f1967]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD070-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.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 15:45:32 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 4.78/1.09 % Refutation found
% 4.78/1.09 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.78/1.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.78/1.12 % Elapsed time: 0.755796 seconds
% 4.78/1.12 % CPU time: 5.726002 seconds
% 4.78/1.12 % Total memory used: 81.947 MB
% 4.78/1.12 % Net memory used: 73.333 MB
%------------------------------------------------------------------------------