%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD040-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:22:00 PM UTC 2026
% Result : Unsatisfiable 0.15s 1.00s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 70 ( 22 unt; 5 def)
% Number of atoms : 146 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 145 ( 69 ~; 71 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 86 ( 86 !; 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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f8,axiom,
! [X] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [C,D,B,X,Y,A,Z] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,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(f31,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)],[f30]) ).
fof(f32,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(f33,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)],[f32]) ).
fof(f34,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f41,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f42,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
! [D,Y,Z] :
( ~ product(Y,Z,D)
| ! [C,X] :
( ~ product(X,Z,C)
| ! [B,A] :
( ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X4,X6,X1)
| ~ product(X3,X6,X0)
| ~ product(X5,X6,X2)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f50,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f69,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f70,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f71,plain,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f74,plain,
! [X0] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(X0,multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[f31,f71]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ sum(X2,additive_identity,X1)
| ~ sum(X0,additive_identity,X2)
| sum(X0,multiplicative_inverse(a),X1) ),
inference(resolution,[status(thm)],[f31,f71]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ~ sum(X2,additive_identity,X1)
| ~ sum(X0,X2,additive_identity)
| sum(X0,X1,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[f31,f71]) ).
fof(f78,plain,
sum(additive_identity,a,a),
inference(resolution,[status(thm)],[f34,f69]) ).
fof(f79,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolution,[status(thm)],[f34,f50]) ).
fof(f91,plain,
sum(a,additive_identity,a),
inference(resolution,[status(thm)],[f36,f78]) ).
fof(f146,plain,
product(multiplicative_identity,a,a),
inference(resolution,[status(thm)],[f41,f69]) ).
fof(f150,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolution,[status(thm)],[f35,f69]) ).
fof(f185,definition,
( sQ3_spl
<=> sum(additive_identity,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ3_spl
| sum(additive_identity,a,additive_identity) ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f197,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolution,[status(thm)],[f42,f69]) ).
fof(f203,definition,
( sQ7_spl
<=> product(multiplicative_inverse(a),a,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( ~ sQ7_spl
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f197,f203,f185]) ).
fof(f211,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f186,f70]) ).
fof(f212,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f261,plain,
sum(additive_identity,multiplicative_inverse(a),multiplicative_inverse(a)),
inference(resolution,[status(thm)],[f74,f79]) ).
fof(f264,plain,
! [X0] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(X0,multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[f261,f33]) ).
fof(f287,plain,
sum(multiplicative_inverse(a),multiplicative_inverse(a),multiplicative_inverse(a)),
inference(resolution,[status(thm)],[f264,f71]) ).
fof(f307,plain,
! [X0] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(X0,multiplicative_inverse(a),additive_identity) ),
inference(resolution,[status(thm)],[f75,f79]) ).
fof(f311,plain,
! [X0] :
( ~ sum(X0,a,additive_identity)
| sum(X0,a,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[f76,f91]) ).
fof(f375,plain,
sum(additive_identity,multiplicative_inverse(a),additive_identity),
inference(resolution,[status(thm)],[f307,f79]) ).
fof(f379,plain,
! [X0,X1,X2] :
( ~ sum(X2,X1,multiplicative_inverse(a))
| ~ sum(additive_identity,X2,X0)
| sum(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f375,f33]) ).
fof(f638,plain,
sum(additive_inverse(a),a,multiplicative_inverse(a)),
inference(resolution,[status(thm)],[f150,f311]) ).
fof(f789,plain,
( ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| sum(a,a,a) ),
inference(resolution,[status(thm)],[f45,f146]) ).
fof(f798,definition,
( sQ43_spl
<=> sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f802,definition,
( sQ44_spl
<=> sum(a,a,a) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f803,plain,
( ~ sQ44_spl
| sum(a,a,a) ),
inference(component_clause,[status(thm)],[f802]) ).
fof(f805,plain,
( ~ sQ43_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f789,f802,f798]) ).
fof(f1054,plain,
sum(a,additive_inverse(a),multiplicative_inverse(a)),
inference(resolution,[status(thm)],[f638,f36]) ).
fof(f1381,plain,
! [X0] :
( ~ sum(additive_identity,a,X0)
| sum(X0,additive_inverse(a),additive_identity) ),
inference(resolution,[status(thm)],[f379,f1054]) ).
fof(f1511,plain,
( ~ sQ7_spl
| ~ sum(multiplicative_inverse(a),multiplicative_inverse(a),multiplicative_inverse(a))
| sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f204,f45]) ).
fof(f1528,definition,
( sQ53_spl
<=> sum(multiplicative_inverse(a),multiplicative_inverse(a),multiplicative_inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1530,plain,
( sQ53_spl
| ~ sum(multiplicative_inverse(a),multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(component_clause,[status(thm)],[f1528]) ).
fof(f1531,plain,
( ~ sQ7_spl
| ~ sQ53_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f1511,f798,f1528,f203]) ).
fof(f1562,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1530,f287]) ).
fof(f1563,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f1562]) ).
fof(f1806,plain,
sum(a,additive_inverse(a),additive_identity),
inference(resolution,[status(thm)],[f1381,f78]) ).
fof(f1815,plain,
! [X0] :
( ~ sum(X0,a,a)
| sum(X0,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f1806,f31]) ).
fof(f1822,plain,
( ~ sQ44_spl
| sum(a,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f1815,f803]) ).
fof(f1842,plain,
( ~ sQ44_spl
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[f1822,f36]) ).
fof(f1848,plain,
( ~ sQ44_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f1842,f185,f802]) ).
fof(f1849,plain,
$false,
inference(sat_refutation,[status(thm)],[f206,f212,f805,f1531,f1563,f1848]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD040-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n017.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Mon Sep 21 15:35:13 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.57 % Drodi V4.1.1
% 0.15/1.00 % Refutation found
% 0.15/1.00 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/1.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/1.02 % Elapsed time: 0.441462 seconds
% 0.15/1.02 % CPU time: 3.271483 seconds
% 0.15/1.02 % Total memory used: 50.167 MB
% 0.15/1.02 % Net memory used: 46.588 MB
%------------------------------------------------------------------------------