%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD059-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:22:05 PM UTC 2026
% Result : Unsatisfiable 0.13s 6.07s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 77 ( 23 unt; 9 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 154 ( 68 ~; 77 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] :
( ~ defined(X)
| equalish(add(additive_identity,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
defined(multiplicative_identity),
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(f29,hypothesis,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
equalish(add(a,a),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
~ less_or_equal(additive_identity,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| equalish(add(additive_identity,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f49,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f53,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f56,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(f57,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f59,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,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(f61,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)],[f60]) ).
fof(f65,plain,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f72,plain,
! [Y,X] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X0)
| ~ less_or_equal(X2,X1)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f76,plain,
defined(u),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f77,plain,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f78,plain,
equalish(add(a,a),u),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f79,plain,
~ less_or_equal(additive_identity,u),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f80,plain,
! [X0] :
( ~ less_or_equal(a,X0)
| less_or_equal(additive_identity,X0) ),
inference(resolution,[status(thm)],[f57,f77]) ).
fof(f92,definition,
( sQ1_spl
<=> less_or_equal(additive_identity,a) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( sQ1_spl
| ~ less_or_equal(additive_identity,a) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f116,definition,
( sQ4_spl
<=> defined(additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( sQ4_spl
| ~ defined(additive_identity) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f127,definition,
( sQ6_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( sQ6_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f146,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f75]) ).
fof(f147,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f146]) ).
fof(f178,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(u,X0)
| less_or_equal(X0,u) ),
inference(resolution,[status(thm)],[f59,f76]) ).
fof(f180,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(additive_identity,X0)
| less_or_equal(X0,additive_identity) ),
inference(resolution,[status(thm)],[f59,f49]) ).
fof(f181,plain,
( less_or_equal(u,u)
| less_or_equal(u,u) ),
inference(resolution,[status(thm)],[f178,f76]) ).
fof(f184,definition,
( sQ11_spl
<=> less_or_equal(u,u) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ11_spl
| less_or_equal(u,u) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,plain,
sQ11_spl,
inference(split_clause,[status(thm)],[f181,f184]) ).
fof(f195,definition,
( sQ14_spl
<=> less_or_equal(additive_identity,u) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( ~ sQ14_spl
| less_or_equal(additive_identity,u) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f202,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f79]) ).
fof(f203,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f204,plain,
! [X0] :
( ~ sQ11_spl
| ~ equalish(u,X0)
| less_or_equal(X0,u) ),
inference(resolution,[status(thm)],[f185,f73]) ).
fof(f211,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)],[f61,f73]) ).
fof(f230,plain,
! [X0] :
( ~ sQ11_spl
| ~ equalish(X0,u)
| less_or_equal(X0,u) ),
inference(resolution,[status(thm)],[f204,f65]) ).
fof(f232,definition,
( sQ16_spl
<=> defined(u) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f234,plain,
( sQ16_spl
| ~ defined(u) ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f289,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f77]) ).
fof(f290,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f289]) ).
fof(f317,plain,
( ~ sQ11_spl
| less_or_equal(add(a,a),u) ),
inference(resolution,[status(thm)],[f230,f78]) ).
fof(f331,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f234,f76]) ).
fof(f332,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f331]) ).
fof(f399,plain,
! [X0] :
( ~ sQ11_spl
| ~ less_or_equal(X0,add(a,a))
| less_or_equal(X0,u) ),
inference(resolution,[status(thm)],[f317,f57]) ).
fof(f420,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f49]) ).
fof(f421,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f463,plain,
( less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f180,f49]) ).
fof(f473,definition,
( sQ33_spl
<=> less_or_equal(additive_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f476,plain,
sQ33_spl,
inference(split_clause,[status(thm)],[f463,f473]) ).
fof(f593,plain,
! [X0,X1,X2] :
( less_or_equal(additive_identity,add(X2,X0))
| ~ equalish(add(X1,X0),a)
| ~ less_or_equal(X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f211,f80]) ).
fof(f735,definition,
! [X0] :
( sQ52_spl
<=> ( less_or_equal(additive_identity,add(X0,a))
| ~ less_or_equal(additive_identity,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f736,plain,
! [X0] :
( ~ sQ52_spl
| less_or_equal(additive_identity,add(X0,a))
| ~ less_or_equal(additive_identity,X0) ),
inference(component_clause,[status(thm)],[f735]) ).
fof(f838,definition,
( sQ60_spl
<=> defined(multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f840,plain,
( sQ60_spl
| ~ defined(multiplicative_identity) ),
inference(component_clause,[status(thm)],[f838]) ).
fof(f878,plain,
! [X0] :
( ~ defined(a)
| less_or_equal(additive_identity,add(X0,a))
| ~ less_or_equal(additive_identity,X0)
| ~ defined(a) ),
inference(resolution,[status(thm)],[f593,f35]) ).
fof(f882,plain,
( sQ52_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f878,f127,f735]) ).
fof(f1681,plain,
( sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f840,f53]) ).
fof(f1682,plain,
sQ60_spl,
inference(contradiction_clause,[status(thm)],[f1681]) ).
fof(f2251,plain,
( ~ sQ11_spl
| ~ sQ52_spl
| less_or_equal(additive_identity,u)
| ~ less_or_equal(additive_identity,a) ),
inference(resolution,[status(thm)],[f736,f399]) ).
fof(f2260,plain,
( ~ sQ11_spl
| ~ sQ52_spl
| sQ14_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f2251,f92,f195,f735,f184]) ).
fof(f2265,plain,
$false,
inference(sat_refutation,[status(thm)],[f147,f187,f203,f290,f332,f421,f476,f882,f1682,f2260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD059-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n002.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Mon Sep 21 15:46:09 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.38 % Drodi V4.1.1
% 0.13/6.07 % Refutation found
% 0.13/6.07 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/6.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/6.09 % Elapsed time: 0.710765 seconds
% 0.13/6.09 % CPU time: 5.390091 seconds
% 0.13/6.09 % Total memory used: 82.847 MB
% 0.13/6.09 % Net memory used: 74.494 MB
%------------------------------------------------------------------------------