%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD028-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 12:21:56 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.55s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 16 unt; 2 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 84 ( 42 ~; 40 |; 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 : 48 ( 48 !; 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(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
defined(v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
product(a,u,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
product(a,v,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ product(multiplicative_identity,u,v),
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(f74,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f77,plain,
defined(v),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f78,plain,
~ sum(additive_identity,a,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(f529,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolution,[status(thm)],[f47,f74]) ).
fof(f574,definition,
( sQ93_spl
<=> product(multiplicative_inverse(a),a,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( ~ sQ93_spl
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f574]) ).
fof(f577,definition,
( sQ94_spl
<=> sum(additive_identity,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f578,plain,
( ~ sQ94_spl
| sum(additive_identity,a,additive_identity) ),
inference(component_clause,[status(thm)],[f577]) ).
fof(f580,plain,
( sQ94_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f529,f574,f577]) ).
fof(f640,plain,
( ~ sQ94_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f578,f78]) ).
fof(f641,plain,
~ sQ94_spl,
inference(contradiction_clause,[status(thm)],[f640]) ).
fof(f1009,plain,
! [X0,X1,X2] :
( ~ product(X2,v,X1)
| ~ product(X0,a,X2)
| product(X0,b,X1) ),
inference(resolution,[status(thm)],[f43,f80]) ).
fof(f1017,plain,
! [X0,X1,X2] :
( ~ product(X2,b,X1)
| ~ product(X2,a,X0)
| product(X0,u,X1) ),
inference(resolution,[status(thm)],[f45,f79]) ).
fof(f1326,plain,
product(multiplicative_identity,v,v),
inference(resolution,[status(thm)],[f46,f77]) ).
fof(f2502,plain,
! [X0] :
( ~ sQ93_spl
| ~ product(multiplicative_inverse(a),b,X0)
| product(multiplicative_identity,u,X0) ),
inference(resolution,[status(thm)],[f575,f1017]) ).
fof(f2505,plain,
! [X0] :
( ~ sQ93_spl
| ~ product(multiplicative_identity,v,X0)
| product(multiplicative_inverse(a),b,X0) ),
inference(resolution,[status(thm)],[f575,f1009]) ).
fof(f2513,plain,
( ~ sQ93_spl
| product(multiplicative_inverse(a),b,v) ),
inference(resolution,[status(thm)],[f1326,f2505]) ).
fof(f2527,plain,
( ~ sQ93_spl
| product(multiplicative_identity,u,v) ),
inference(resolution,[status(thm)],[f2513,f2502]) ).
fof(f2535,plain,
( ~ sQ93_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2527,f81]) ).
fof(f2536,plain,
~ sQ93_spl,
inference(contradiction_clause,[status(thm)],[f2535]) ).
fof(f2537,plain,
$false,
inference(sat_refutation,[status(thm)],[f580,f641,f2536]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD028-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 15:38:32 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.55 % Refutation found
% 0.08/0.55 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.86/0.58 % Elapsed time: 0.199143 seconds
% 0.86/0.58 % CPU time: 1.324440 seconds
% 0.86/0.58 % Total memory used: 30.779 MB
% 0.86/0.58 % Net memory used: 29.105 MB
%------------------------------------------------------------------------------