%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD041-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 4.66s 1.05s
% Output : CNFRefutation 4.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 25
% Syntax : Number of formulae : 80 ( 18 unt; 10 def)
% Number of atoms : 179 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 187 ( 88 ~; 89 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 11 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 87 ( 87 !; 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(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(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/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(f10,axiom,
! [Y,X,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
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,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
product(a,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,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(f33,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)],[f32]) ).
fof(f36,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f37,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f39,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(f40,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)],[f39]) ).
fof(f43,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f44,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f46,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(f47,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)],[f46]) ).
fof(f52,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f71,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f72,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f73,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f74,plain,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f75,plain,
product(a,b,additive_identity),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f80,plain,
! [X0] :
( ~ defined(X0)
| sum(X0,additive_identity,X0) ),
inference(resolution,[status(thm)],[f38,f36]) ).
fof(f93,definition,
( sQ1_spl
<=> defined(additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( sQ1_spl
| ~ defined(additive_identity) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f105,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f52]) ).
fof(f106,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f105]) ).
fof(f110,definition,
( sQ3_spl
<=> sum(additive_identity,additive_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ~ product(X2,b,X1)
| ~ product(X0,a,X2)
| product(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f40,f75]) ).
fof(f171,plain,
! [X0] :
( sum(X0,additive_inverse(X0),additive_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f37,f38]) ).
fof(f198,plain,
! [X0,X1] :
( ~ sum(X1,X0,X0)
| sum(X1,additive_identity,additive_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f171,f33]) ).
fof(f361,definition,
( sQ23_spl
<=> sum(b,b,b) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f362,plain,
( ~ sQ23_spl
| sum(b,b,b) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f373,definition,
( sQ26_spl
<=> defined(b) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f375,plain,
( sQ26_spl
| ~ defined(b) ),
inference(component_clause,[status(thm)],[f373]) ).
fof(f395,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f375,f72]) ).
fof(f396,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f395]) ).
fof(f432,definition,
( sQ27_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f434,plain,
( sQ27_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f437,plain,
! [X0] :
( ~ defined(b)
| ~ product(X0,a,multiplicative_identity)
| product(X0,additive_identity,b) ),
inference(resolution,[status(thm)],[f150,f43]) ).
fof(f442,definition,
( sQ29_spl
<=> sum(additive_identity,b,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ29_spl
| sum(additive_identity,b,additive_identity) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f446,definition,
! [X0] :
( sQ30_spl
<=> ( ~ product(X0,a,multiplicative_identity)
| product(X0,additive_identity,b) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f447,plain,
! [X0] :
( ~ sQ30_spl
| ~ product(X0,a,multiplicative_identity)
| product(X0,additive_identity,b) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( ~ sQ26_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f437,f446,f373]) ).
fof(f993,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f434,f71]) ).
fof(f994,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f993]) ).
fof(f1045,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f443,f74]) ).
fof(f1046,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f1045]) ).
fof(f1193,plain,
( ~ sQ30_spl
| ~ defined(a)
| sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),additive_identity,b) ),
inference(resolution,[status(thm)],[f447,f44]) ).
fof(f1194,definition,
( sQ82_spl
<=> product(multiplicative_inverse(a),additive_identity,b) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1195,plain,
( ~ sQ82_spl
| product(multiplicative_inverse(a),additive_identity,b) ),
inference(component_clause,[status(thm)],[f1194]) ).
fof(f1197,definition,
( sQ83_spl
<=> sum(additive_identity,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1198,plain,
( ~ sQ83_spl
| sum(additive_identity,a,additive_identity) ),
inference(component_clause,[status(thm)],[f1197]) ).
fof(f1200,plain,
( ~ sQ30_spl
| ~ sQ27_spl
| sQ83_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f1193,f1194,f1197,f432,f446]) ).
fof(f1217,plain,
( ~ sQ82_spl
| product(additive_identity,multiplicative_inverse(a),b) ),
inference(resolution,[status(thm)],[f1195,f45]) ).
fof(f1224,plain,
( ~ sQ83_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1198,f73]) ).
fof(f1225,plain,
~ sQ83_spl,
inference(contradiction_clause,[status(thm)],[f1224]) ).
fof(f1250,plain,
( ~ sQ82_spl
| ~ sum(additive_identity,additive_identity,additive_identity)
| sum(b,b,b) ),
inference(resolution,[status(thm)],[f1217,f47]) ).
fof(f1263,plain,
( ~ sQ82_spl
| ~ sQ3_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1250,f361,f110,f1194]) ).
fof(f3001,plain,
( ~ sQ23_spl
| sum(b,additive_identity,additive_identity)
| ~ defined(b) ),
inference(resolution,[status(thm)],[f198,f362]) ).
fof(f3017,plain,
( ~ defined(additive_identity)
| sum(additive_identity,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(resolution,[status(thm)],[f198,f80]) ).
fof(f3018,definition,
( sQ231_spl
<=> sum(b,additive_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f3019,plain,
( ~ sQ231_spl
| sum(b,additive_identity,additive_identity) ),
inference(component_clause,[status(thm)],[f3018]) ).
fof(f3021,plain,
( ~ sQ23_spl
| sQ231_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f3001,f373,f3018,f361]) ).
fof(f3046,plain,
( sQ3_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f3017,f93,f110]) ).
fof(f3060,plain,
( ~ sQ231_spl
| sum(additive_identity,b,additive_identity) ),
inference(resolution,[status(thm)],[f3019,f38]) ).
fof(f3066,plain,
( ~ sQ231_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f3060,f442,f3018]) ).
fof(f3067,plain,
$false,
inference(sat_refutation,[status(thm)],[f106,f396,f449,f994,f1046,f1200,f1225,f1263,f3021,f3046,f3066]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD041-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 15:37:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 4.66/1.05 % Refutation found
% 4.66/1.05 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.66/1.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.66/1.06 % Elapsed time: 0.690829 seconds
% 4.66/1.06 % CPU time: 5.209052 seconds
% 4.66/1.06 % Total memory used: 61.763 MB
% 4.66/1.06 % Net memory used: 56.798 MB
%------------------------------------------------------------------------------