%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD067-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 0.15s 0.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 45 ( 12 unt; 5 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 102 ( 49 ~; 48 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f19,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
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,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f57,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| sum(X,Y,add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f58,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f66,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(f67,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)],[f66]) ).
fof(f70,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f71,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f72,plain,
less_or_equal(a,b),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f73,plain,
~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ~ sum(b,X2,X1)
| ~ sum(a,X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f67,f72]) ).
fof(f78,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(b)
| ~ sum(a,X1,X0)
| less_or_equal(X0,add(b,X1)) ),
inference(resolution,[status(thm)],[f77,f58]) ).
fof(f79,definition,
! [X0,X1] :
( sQ0_spl
<=> ( ~ defined(X1)
| ~ sum(a,X1,X0)
| less_or_equal(X0,add(b,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f80,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ defined(X1)
| ~ sum(a,X1,X0)
| less_or_equal(X0,add(b,X1)) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,definition,
( sQ1_spl
<=> defined(b) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( sQ1_spl
| ~ defined(b) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f78,f79,f82]) ).
fof(f90,definition,
( sQ3_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( sQ3_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f94,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f71]) ).
fof(f95,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f94]) ).
fof(f111,plain,
! [X0] :
( ~ defined(X0)
| sum(X0,additive_inverse(X0),additive_identity) ),
inference(resolution,[status(thm)],[f37,f36]) ).
fof(f130,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f92,f70]) ).
fof(f131,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f135,plain,
( ~ sQ0_spl
| ~ defined(additive_inverse(a))
| less_or_equal(additive_identity,add(b,additive_inverse(a)))
| ~ defined(a) ),
inference(resolution,[status(thm)],[f111,f80]) ).
fof(f138,definition,
( sQ9_spl
<=> less_or_equal(additive_identity,add(b,additive_inverse(a))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( ~ sQ9_spl
| less_or_equal(additive_identity,add(b,additive_inverse(a))) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,definition,
( sQ10_spl
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( sQ10_spl
| ~ defined(additive_inverse(a)) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| sQ9_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f135,f90,f138,f141,f79]) ).
fof(f149,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f139,f73]) ).
fof(f150,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f151,plain,
( sQ10_spl
| ~ defined(a) ),
inference(resolution,[status(thm)],[f143,f52]) ).
fof(f152,plain,
( sQ10_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f151,f90,f141]) ).
fof(f153,plain,
$false,
inference(sat_refutation,[status(thm)],[f85,f95,f131,f144,f150,f152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD067-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n003.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 21 15:46:01 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.44 % Drodi V4.1.1
% 0.15/0.47 % Refutation found
% 0.15/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.49 % Elapsed time: 0.053243 seconds
% 0.15/0.49 % CPU time: 0.139516 seconds
% 0.15/0.49 % Total memory used: 11.604 MB
% 0.15/0.49 % Net memory used: 11.471 MB
%------------------------------------------------------------------------------