%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD008-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 12:21:51 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.73s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 21
% Syntax : Number of formulae : 72 ( 21 unt; 9 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 171 ( 85 ~; 77 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 10 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 66 ( 66 !; 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [U,Z,W,X,Y,V] :
( ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(U,Z,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
defined(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
sum(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
sum(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ sum(additive_identity,additive_inverse(c),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,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(f35,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)],[f34]) ).
fof(f36,plain,
! [W,X,V] :
( ~ sum(X,V,W)
| ! [Z,Y] :
( ~ sum(Y,Z,V)
| ! [U] :
( ~ sum(X,Y,U)
| sum(U,Z,W) ) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f39,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f73,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f74,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
defined(c),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
defined(d),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
sum(a,b,c),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f78,plain,
sum(additive_inverse(a),additive_inverse(b),d),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f79,plain,
~ sum(additive_identity,additive_inverse(c),d),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f81,plain,
~ sum(additive_inverse(c),additive_identity,d),
inference(resolution,[status(thm)],[f40,f79]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ sum(X1,X2,d)
| ~ sum(X0,X2,additive_identity)
| ~ sum(additive_inverse(c),X0,X1) ),
inference(resolution,[status(thm)],[f81,f35]) ).
fof(f112,plain,
! [X0] :
( ~ defined(c)
| ~ sum(additive_identity,X0,d)
| ~ sum(c,X0,additive_identity) ),
inference(resolution,[status(thm)],[f83,f39]) ).
fof(f116,definition,
! [X0] :
( sQ4_spl
<=> ( ~ sum(additive_identity,X0,d)
| ~ sum(c,X0,additive_identity) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f117,plain,
! [X0] :
( ~ sQ4_spl
| ~ sum(additive_identity,X0,d)
| ~ sum(c,X0,additive_identity) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,definition,
( sQ5_spl
<=> defined(c) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f121,plain,
( sQ5_spl
| ~ defined(c) ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f112,f116,f119]) ).
fof(f124,plain,
! [X0] :
( ~ sQ4_spl
| ~ sum(X0,c,additive_identity)
| ~ sum(additive_identity,X0,d) ),
inference(resolution,[status(thm)],[f117,f40]) ).
fof(f147,definition,
( sQ9_spl
<=> defined(d) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( sQ9_spl
| ~ defined(d) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f171,plain,
( ~ sQ4_spl
| ~ defined(d)
| ~ sum(d,c,additive_identity) ),
inference(resolution,[status(thm)],[f124,f38]) ).
fof(f175,definition,
( sQ13_spl
<=> sum(d,c,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( sQ13_spl
| ~ sum(d,c,additive_identity) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f171,f175,f147,f116]) ).
fof(f179,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f76]) ).
fof(f180,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f179]) ).
fof(f181,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f121,f75]) ).
fof(f182,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f181]) ).
fof(f183,plain,
! [X0,X1,X2] :
( sQ13_spl
| ~ sum(X0,X2,additive_identity)
| ~ sum(X1,c,X2)
| ~ sum(X0,X1,d) ),
inference(resolution,[status(thm)],[f177,f37]) ).
fof(f264,plain,
! [X0,X1,X2] :
( sQ13_spl
| ~ sum(X0,X2,d)
| ~ sum(X2,X1,additive_identity)
| ~ sum(X0,c,X1) ),
inference(resolution,[status(thm)],[f183,f40]) ).
fof(f341,definition,
( sQ31_spl
<=> defined(b) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( sQ31_spl
| ~ defined(b) ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f359,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f343,f74]) ).
fof(f360,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f359]) ).
fof(f431,plain,
! [X0] :
( sQ13_spl
| ~ sum(additive_inverse(b),X0,additive_identity)
| ~ sum(additive_inverse(a),c,X0) ),
inference(resolution,[status(thm)],[f264,f78]) ).
fof(f502,definition,
( sQ47_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f504,plain,
( sQ47_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f502]) ).
fof(f539,plain,
( sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f73]) ).
fof(f540,plain,
sQ47_spl,
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f585,plain,
( sQ13_spl
| ~ defined(b)
| ~ sum(additive_inverse(a),c,b) ),
inference(resolution,[status(thm)],[f431,f39]) ).
fof(f589,definition,
( sQ54_spl
<=> sum(additive_inverse(a),c,b) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f591,plain,
( sQ54_spl
| ~ sum(additive_inverse(a),c,b) ),
inference(component_clause,[status(thm)],[f589]) ).
fof(f592,plain,
( sQ13_spl
| ~ sQ31_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f585,f589,f341,f175]) ).
fof(f595,plain,
! [X0,X1,X2] :
( sQ54_spl
| ~ sum(X1,X2,b)
| ~ sum(X0,X2,c)
| ~ sum(additive_inverse(a),X0,X1) ),
inference(resolution,[status(thm)],[f591,f35]) ).
fof(f884,plain,
! [X0] :
( sQ54_spl
| ~ defined(b)
| ~ sum(X0,b,c)
| ~ sum(additive_inverse(a),X0,additive_identity) ),
inference(resolution,[status(thm)],[f595,f38]) ).
fof(f888,definition,
! [X0] :
( sQ85_spl
<=> ( ~ sum(X0,b,c)
| ~ sum(additive_inverse(a),X0,additive_identity) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f889,plain,
! [X0] :
( ~ sQ85_spl
| ~ sum(X0,b,c)
| ~ sum(additive_inverse(a),X0,additive_identity) ),
inference(component_clause,[status(thm)],[f888]) ).
fof(f891,plain,
( sQ54_spl
| ~ sQ31_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f884,f888,f341,f589]) ).
fof(f892,plain,
( ~ sQ85_spl
| ~ defined(a)
| ~ sum(a,b,c) ),
inference(resolution,[status(thm)],[f889,f39]) ).
fof(f896,definition,
( sQ86_spl
<=> sum(a,b,c) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f898,plain,
( sQ86_spl
| ~ sum(a,b,c) ),
inference(component_clause,[status(thm)],[f896]) ).
fof(f899,plain,
( ~ sQ85_spl
| ~ sQ47_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f892,f896,f502,f888]) ).
fof(f900,plain,
( sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f898,f77]) ).
fof(f901,plain,
sQ86_spl,
inference(contradiction_clause,[status(thm)],[f900]) ).
fof(f902,plain,
$false,
inference(sat_refutation,[status(thm)],[f122,f178,f180,f182,f360,f540,f592,f891,f899,f901]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD008-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n004.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Mon Sep 21 15:36:55 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.39 % Drodi V4.1.1
% 0.15/5.73 % Refutation found
% 0.15/5.73 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/5.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.76 % Elapsed time: 0.369200 seconds
% 0.15/5.76 % CPU time: 2.700683 seconds
% 0.15/5.76 % Total memory used: 35.282 MB
% 0.15/5.76 % Net memory used: 33.129 MB
%------------------------------------------------------------------------------