%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD067-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 9.58s 1.67s
% Output : CNFRefutation 9.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 57 ( 19 unt; 3 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 110 ( 52 ~; 55 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( ~ defined(X)
| equalish(add(X,additive_inverse(X)),additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( ~ defined(X)
| defined(additive_inverse(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(f28,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
equalish(add(b,additive_inverse(a)),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ less_or_equal(additive_identity,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,plain,
! [X0] :
( ~ defined(X0)
| equalish(add(X0,additive_inverse(X0)),additive_identity) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f51,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f57,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(f58,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f60,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,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(f62,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)],[f61]) ).
fof(f66,plain,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f73,plain,
! [Y,X] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X0)
| ~ less_or_equal(X2,X1)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f76,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f78,plain,
defined(u),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f79,plain,
less_or_equal(a,b),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f80,plain,
equalish(add(b,additive_inverse(a)),u),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f81,plain,
~ less_or_equal(additive_identity,u),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f111,plain,
equalish(add(a,additive_inverse(a)),additive_identity),
inference(resolution,[status(thm)],[f37,f76]) ).
fof(f134,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(u,X0)
| less_or_equal(X0,u) ),
inference(resolution,[status(thm)],[f60,f78]) ).
fof(f176,plain,
( less_or_equal(u,u)
| less_or_equal(u,u) ),
inference(resolution,[status(thm)],[f134,f78]) ).
fof(f181,definition,
( sQ9_spl
<=> less_or_equal(u,u) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( ~ sQ9_spl
| less_or_equal(u,u) ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
sQ9_spl,
inference(split_clause,[status(thm)],[f176,f181]) ).
fof(f199,definition,
( sQ14_spl
<=> less_or_equal(additive_identity,u) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ14_spl
| less_or_equal(additive_identity,u) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f206,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f200,f81]) ).
fof(f207,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f206]) ).
fof(f338,plain,
defined(additive_inverse(a)),
inference(resolution,[status(thm)],[f51,f76]) ).
fof(f434,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(add(a,X0),add(b,X0)) ),
inference(resolution,[status(thm)],[f62,f79]) ).
fof(f709,plain,
equalish(u,add(b,additive_inverse(a))),
inference(resolution,[status(thm)],[f66,f80]) ).
fof(f940,plain,
less_or_equal(add(a,additive_inverse(a)),add(b,additive_inverse(a))),
inference(resolution,[status(thm)],[f338,f434]) ).
fof(f1985,plain,
! [X0] :
( ~ less_or_equal(u,X0)
| less_or_equal(add(b,additive_inverse(a)),X0) ),
inference(resolution,[status(thm)],[f74,f709]) ).
fof(f2269,plain,
( ~ sQ9_spl
| less_or_equal(add(b,additive_inverse(a)),u) ),
inference(resolution,[status(thm)],[f1985,f182]) ).
fof(f2311,plain,
! [X0] :
( ~ sQ9_spl
| ~ less_or_equal(X0,add(b,additive_inverse(a)))
| less_or_equal(X0,u) ),
inference(resolution,[status(thm)],[f2269,f58]) ).
fof(f3126,definition,
( sQ346_spl
<=> equalish(additive_identity,add(a,additive_inverse(a))) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f3127,plain,
( ~ sQ346_spl
| equalish(additive_identity,add(a,additive_inverse(a))) ),
inference(component_clause,[status(thm)],[f3126]) ).
fof(f3128,plain,
( sQ346_spl
| ~ equalish(additive_identity,add(a,additive_inverse(a))) ),
inference(component_clause,[status(thm)],[f3126]) ).
fof(f3137,plain,
( ~ sQ346_spl
| equalish(add(a,additive_inverse(a)),additive_identity) ),
inference(resolution,[status(thm)],[f3127,f66]) ).
fof(f3138,plain,
! [X0] :
( ~ sQ346_spl
| ~ less_or_equal(add(a,additive_inverse(a)),X0)
| less_or_equal(additive_identity,X0) ),
inference(resolution,[status(thm)],[f3137,f74]) ).
fof(f3143,plain,
( ~ sQ9_spl
| less_or_equal(add(a,additive_inverse(a)),u) ),
inference(resolution,[status(thm)],[f2311,f940]) ).
fof(f5964,plain,
( ~ sQ9_spl
| ~ sQ346_spl
| less_or_equal(additive_identity,u) ),
inference(resolution,[status(thm)],[f3138,f3143]) ).
fof(f5967,plain,
( ~ sQ9_spl
| ~ sQ346_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f5964,f199,f3126,f181]) ).
fof(f12362,plain,
equalish(additive_identity,add(a,additive_inverse(a))),
inference(resolution,[status(thm)],[f111,f66]) ).
fof(f12363,plain,
( sQ346_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12362,f3128]) ).
fof(f12364,plain,
sQ346_spl,
inference(contradiction_clause,[status(thm)],[f12363]) ).
fof(f12365,plain,
$false,
inference(sat_refutation,[status(thm)],[f184,f207,f5967,f12364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD067-2 : 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 : n018.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
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 15:46:30 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 9.58/1.67 % Refutation found
% 9.58/1.67 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 9.58/1.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.58/1.70 % Elapsed time: 1.321697 seconds
% 9.58/1.70 % CPU time: 10.303828 seconds
% 9.58/1.70 % Total memory used: 114.154 MB
% 9.58/1.70 % Net memory used: 100.665 MB
%------------------------------------------------------------------------------