%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD014-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:21:53 PM UTC 2026
% Result : Unsatisfiable 1.09s 0.71s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 58 ( 15 unt; 7 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 122 ( 60 ~; 55 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 8 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 44 ( 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
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,negated_conjecture,
sum(additive_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ sum(additive_identity,additive_inverse(a),additive_inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,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(f34,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)],[f33]) ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
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(f51,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f52,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
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,
sum(additive_identity,a,b),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f73,plain,
~ sum(additive_identity,additive_inverse(a),additive_inverse(b)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ~ sum(X0,X2,additive_inverse(b))
| ~ sum(X1,additive_inverse(a),X2)
| ~ sum(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f34,f73]) ).
fof(f87,definition,
( sQ1_spl
<=> defined(additive_inverse(b)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( sQ1_spl
| ~ defined(additive_inverse(b)) ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f104,definition,
( sQ3_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( sQ3_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f119,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f70]) ).
fof(f120,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f119]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ sum(X2,X0,additive_inverse(b))
| ~ sum(X1,additive_inverse(a),X2)
| ~ sum(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f79,f37]) ).
fof(f221,plain,
! [X0] :
( ~ defined(additive_inverse(b))
| ~ sum(X0,additive_inverse(a),additive_identity)
| ~ sum(additive_inverse(b),X0,additive_identity) ),
inference(resolution,[status(thm)],[f131,f35]) ).
fof(f225,definition,
! [X0] :
( sQ17_spl
<=> ( ~ sum(X0,additive_inverse(a),additive_identity)
| ~ sum(additive_inverse(b),X0,additive_identity) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f226,plain,
! [X0] :
( ~ sQ17_spl
| ~ sum(X0,additive_inverse(a),additive_identity)
| ~ sum(additive_inverse(b),X0,additive_identity) ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,plain,
( ~ sQ1_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f221,f225,f87]) ).
fof(f379,plain,
( sQ1_spl
| ~ defined(b) ),
inference(resolution,[status(thm)],[f89,f52]) ).
fof(f380,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f379,f71]) ).
fof(f381,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f380]) ).
fof(f449,plain,
( ~ sQ17_spl
| ~ defined(b)
| ~ sum(b,additive_inverse(a),additive_identity) ),
inference(resolution,[status(thm)],[f226,f36]) ).
fof(f453,definition,
( sQ41_spl
<=> sum(b,additive_inverse(a),additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( sQ41_spl
| ~ sum(b,additive_inverse(a),additive_identity) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,definition,
( sQ42_spl
<=> defined(b) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( sQ42_spl
| ~ defined(b) ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( ~ sQ17_spl
| ~ sQ42_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f449,f453,f456,f225]) ).
fof(f460,plain,
! [X0,X1,X2] :
( sQ41_spl
| ~ sum(X0,X2,additive_identity)
| ~ sum(X1,additive_inverse(a),X2)
| ~ sum(X0,X1,b) ),
inference(resolution,[status(thm)],[f455,f34]) ).
fof(f578,definition,
( sQ55_spl
<=> defined(additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f580,plain,
( sQ55_spl
| ~ defined(additive_identity) ),
inference(component_clause,[status(thm)],[f578]) ).
fof(f609,plain,
! [X0] :
( sQ41_spl
| ~ sum(additive_identity,X0,additive_identity)
| ~ sum(a,additive_inverse(a),X0) ),
inference(resolution,[status(thm)],[f460,f72]) ).
fof(f618,plain,
( sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f458,f71]) ).
fof(f619,plain,
sQ42_spl,
inference(contradiction_clause,[status(thm)],[f618]) ).
fof(f636,plain,
! [X0] :
( sQ41_spl
| ~ sum(additive_inverse(a),a,X0)
| ~ sum(additive_identity,X0,additive_identity) ),
inference(resolution,[status(thm)],[f609,f37]) ).
fof(f743,plain,
( sQ41_spl
| ~ defined(additive_identity)
| ~ sum(additive_inverse(a),a,additive_identity) ),
inference(resolution,[status(thm)],[f636,f35]) ).
fof(f747,definition,
( sQ74_spl
<=> sum(additive_inverse(a),a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f749,plain,
( sQ74_spl
| ~ sum(additive_inverse(a),a,additive_identity) ),
inference(component_clause,[status(thm)],[f747]) ).
fof(f750,plain,
( sQ41_spl
| ~ sQ55_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f743,f747,f578,f453]) ).
fof(f751,plain,
( sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f580,f51]) ).
fof(f752,plain,
sQ55_spl,
inference(contradiction_clause,[status(thm)],[f751]) ).
fof(f753,plain,
( sQ74_spl
| ~ defined(a) ),
inference(resolution,[status(thm)],[f749,f36]) ).
fof(f757,plain,
( sQ74_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f753,f104,f747]) ).
fof(f758,plain,
$false,
inference(sat_refutation,[status(thm)],[f120,f228,f381,f459,f619,f750,f752,f757]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD014-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n012.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 15:37:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 1.09/0.71 % Refutation found
% 1.09/0.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.09/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.76/0.73 % Elapsed time: 0.347394 seconds
% 1.76/0.73 % CPU time: 2.560440 seconds
% 1.76/0.73 % Total memory used: 46.275 MB
% 1.76/0.73 % Net memory used: 42.873 MB
%------------------------------------------------------------------------------