%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD036-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 12:21:59 PM UTC 2026
% Result : Unsatisfiable 0.19s 5.93s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 44 ( 18 unt; 2 def)
% Number of atoms : 88 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 88 ( 44 ~; 42 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 54 ( 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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/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(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
product(a,c,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
product(b,c,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ product(multiplicative_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ sum(additive_identity,c,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f48,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f75,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f76,plain,
defined(c),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f78,plain,
product(a,c,u),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f79,plain,
product(b,c,u),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f80,plain,
~ product(multiplicative_identity,a,b),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f81,plain,
~ sum(additive_identity,c,additive_identity),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f527,plain,
( sum(additive_identity,c,additive_identity)
| product(multiplicative_inverse(c),c,multiplicative_identity) ),
inference(resolution,[status(thm)],[f47,f76]) ).
fof(f560,definition,
( sQ89_spl
<=> product(multiplicative_inverse(c),c,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f561,plain,
( ~ sQ89_spl
| product(multiplicative_inverse(c),c,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f560]) ).
fof(f563,definition,
( sQ90_spl
<=> sum(additive_identity,c,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f564,plain,
( ~ sQ90_spl
| sum(additive_identity,c,additive_identity) ),
inference(component_clause,[status(thm)],[f563]) ).
fof(f566,plain,
( sQ90_spl
| sQ89_spl ),
inference(split_clause,[status(thm)],[f527,f560,f563]) ).
fof(f1511,plain,
product(multiplicative_identity,b,b),
inference(resolution,[status(thm)],[f46,f75]) ).
fof(f1515,plain,
product(c,b,u),
inference(resolution,[status(thm)],[f48,f79]) ).
fof(f1516,plain,
product(c,a,u),
inference(resolution,[status(thm)],[f48,f78]) ).
fof(f1523,plain,
! [X0,X1,X2] :
( ~ product(X2,b,X1)
| ~ product(X0,c,X2)
| product(X0,u,X1) ),
inference(resolution,[status(thm)],[f1515,f43]) ).
fof(f1526,plain,
! [X0,X1,X2] :
( ~ product(X2,u,X1)
| ~ product(X2,c,X0)
| product(X0,a,X1) ),
inference(resolution,[status(thm)],[f1516,f45]) ).
fof(f1721,plain,
( ~ sQ90_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f564,f81]) ).
fof(f1722,plain,
~ sQ90_spl,
inference(contradiction_clause,[status(thm)],[f1721]) ).
fof(f5682,plain,
! [X0] :
( ~ sQ89_spl
| ~ product(multiplicative_inverse(c),u,X0)
| product(multiplicative_identity,a,X0) ),
inference(resolution,[status(thm)],[f561,f1526]) ).
fof(f5683,plain,
! [X0] :
( ~ sQ89_spl
| ~ product(multiplicative_identity,b,X0)
| product(multiplicative_inverse(c),u,X0) ),
inference(resolution,[status(thm)],[f561,f1523]) ).
fof(f9497,plain,
( ~ sQ89_spl
| product(multiplicative_inverse(c),u,b) ),
inference(resolution,[status(thm)],[f5683,f1511]) ).
fof(f9526,plain,
( ~ sQ89_spl
| product(multiplicative_identity,a,b) ),
inference(resolution,[status(thm)],[f9497,f5682]) ).
fof(f9537,plain,
( ~ sQ89_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9526,f80]) ).
fof(f9538,plain,
~ sQ89_spl,
inference(contradiction_clause,[status(thm)],[f9537]) ).
fof(f9539,plain,
$false,
inference(sat_refutation,[status(thm)],[f566,f1722,f9538]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD036-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.41 % Computer : n008.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Mon Sep 21 15:40:28 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.43 % Drodi V4.1.1
% 0.19/5.93 % Refutation found
% 0.19/5.93 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/5.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/5.97 % Elapsed time: 0.535538 seconds
% 0.19/5.97 % CPU time: 3.947623 seconds
% 0.19/5.97 % Total memory used: 43.886 MB
% 0.19/5.97 % Net memory used: 40.931 MB
%------------------------------------------------------------------------------