%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD029-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:21:57 PM UTC 2026
% Result : Unsatisfiable 174.25s 22.51s
% Output : CNFRefutation 174.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 76 ( 20 unt; 5 def)
% Number of atoms : 174 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 192 ( 94 ~; 93 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 120 ( 120 !; 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(f6,axiom,
! [X,V,W,Y,U,Z] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U,Z,W,X,Y,V] :
( ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(U,Z,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
file('/export/starexec/sandbox2/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/sandbox2/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/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(f30,hypothesis,
defined(v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
product(a,u,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
product(a,v,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ product(multiplicative_identity,u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,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(f36,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)],[f35]) ).
fof(f37,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(f38,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)],[f37]) ).
fof(f39,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f40,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f42,plain,
! [W,U,Z] :
( ~ product(U,Z,W)
| ! [V,Y] :
( ~ product(Y,Z,V)
| ! [X] :
( ~ product(X,Y,U)
| product(X,V,W) ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [W,X,V] :
( ~ product(X,V,W)
| ! [Z,Y] :
( ~ product(Y,Z,V)
| ! [U] :
( ~ product(X,Y,U)
| product(U,Z,W) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f47,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f49,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(f50,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)],[f49]) ).
fof(f74,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f75,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f77,plain,
defined(v),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f78,plain,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f79,plain,
product(a,u,b),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f80,plain,
product(a,v,b),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f81,plain,
~ product(multiplicative_identity,u,v),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f84,plain,
sum(additive_identity,a,a),
inference(resolution,[status(thm)],[f39,f74]) ).
fof(f88,plain,
sum(additive_inverse(b),b,additive_identity),
inference(resolution,[status(thm)],[f40,f75]) ).
fof(f224,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolution,[status(thm)],[f47,f74]) ).
fof(f237,definition,
( sQ28_spl
<=> sum(additive_identity,b,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( ~ sQ28_spl
| sum(additive_identity,b,additive_identity) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f241,definition,
( sQ29_spl
<=> product(multiplicative_inverse(a),a,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f242,plain,
( ~ sQ29_spl
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,definition,
( sQ30_spl
<=> sum(additive_identity,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( ~ sQ30_spl
| sum(additive_identity,a,additive_identity) ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( sQ30_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f224,f241,f244]) ).
fof(f287,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f78]) ).
fof(f288,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f361,plain,
! [X0,X1,X2] :
( ~ product(X2,v,X1)
| ~ product(X0,a,X2)
| product(X0,b,X1) ),
inference(resolution,[status(thm)],[f43,f80]) ).
fof(f371,plain,
! [X0,X1,X2] :
( ~ product(X2,b,X1)
| ~ product(X2,a,X0)
| product(X0,u,X1) ),
inference(resolution,[status(thm)],[f45,f79]) ).
fof(f378,plain,
product(multiplicative_identity,v,v),
inference(resolution,[status(thm)],[f46,f77]) ).
fof(f413,plain,
( ~ sum(a,a,a)
| sum(b,b,b) ),
inference(resolution,[status(thm)],[f50,f80]) ).
fof(f429,definition,
( sQ54_spl
<=> sum(b,b,b) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( ~ sQ54_spl
| sum(b,b,b) ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f440,definition,
( sQ57_spl
<=> sum(a,a,a) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( sQ57_spl
| ~ sum(a,a,a) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,plain,
( ~ sQ57_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f413,f429,f440]) ).
fof(f480,plain,
! [X0,X1,X2] :
( ~ sQ54_spl
| ~ sum(X2,b,X1)
| ~ sum(X2,b,X0)
| sum(X0,b,X1) ),
inference(resolution,[status(thm)],[f430,f38]) ).
fof(f1352,plain,
! [X0] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(X0,a,a) ),
inference(resolution,[status(thm)],[f84,f36]) ).
fof(f1389,plain,
! [X0] :
( ~ sQ54_spl
| ~ sum(additive_inverse(b),b,X0)
| sum(X0,b,additive_identity) ),
inference(resolution,[status(thm)],[f88,f480]) ).
fof(f1398,plain,
( ~ sQ54_spl
| sum(additive_identity,b,additive_identity) ),
inference(resolution,[status(thm)],[f1389,f88]) ).
fof(f1399,plain,
( ~ sQ54_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f1398,f237,f429]) ).
fof(f1645,plain,
( ~ sQ30_spl
| sum(a,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f245,f41]) ).
fof(f1871,plain,
! [X0] :
( ~ product(X0,a,multiplicative_identity)
| product(X0,b,v) ),
inference(resolution,[status(thm)],[f378,f361]) ).
fof(f6523,plain,
( ~ sQ30_spl
| sum(a,a,a) ),
inference(resolution,[status(thm)],[f1645,f1352]) ).
fof(f6537,plain,
( ~ sQ30_spl
| sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6523,f442]) ).
fof(f6538,plain,
( ~ sQ30_spl
| sQ57_spl ),
inference(contradiction_clause,[status(thm)],[f6537]) ).
fof(f6956,plain,
( ~ sQ29_spl
| product(multiplicative_inverse(a),b,v) ),
inference(resolution,[status(thm)],[f242,f1871]) ).
fof(f7641,plain,
! [X0] :
( ~ sQ29_spl
| ~ product(multiplicative_inverse(a),a,X0)
| product(X0,u,v) ),
inference(resolution,[status(thm)],[f6956,f371]) ).
fof(f8739,plain,
( ~ sQ29_spl
| product(multiplicative_identity,u,v) ),
inference(resolution,[status(thm)],[f7641,f242]) ).
fof(f8740,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8739,f81]) ).
fof(f8741,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f8740]) ).
fof(f8742,plain,
$false,
inference(sat_refutation,[status(thm)],[f247,f288,f443,f1399,f6538,f8741]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD029-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 15:40:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 174.25/22.51 % Refutation found
% 174.25/22.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 174.25/22.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.69/22.65 % Elapsed time: 22.288378 seconds
% 5.69/22.65 % CPU time: 175.542382 seconds
% 5.69/22.65 % Total memory used: 490.486 MB
% 5.69/22.65 % Net memory used: 442.375 MB
%------------------------------------------------------------------------------