%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD031-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:21:58 PM UTC 2026
% Result : Unsatisfiable 0.13s 5.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 43 ( 12 unt; 5 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 97 ( 47 ~; 45 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 37 ( 37 !; 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(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(f18,axiom,
! [X] :
( sum(additive_identity,X,additive_identity)
| ~ defined(X)
| defined(multiplicative_inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
product(multiplicative_identity,a,multiplicative_identity),
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,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,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(f39,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)],[f38]) ).
fof(f42,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,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,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f56,plain,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f70,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f71,plain,
product(multiplicative_identity,a,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f72,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f73,plain,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ product(X1,X2,multiplicative_inverse(a))
| ~ product(X0,X2,multiplicative_identity)
| ~ product(multiplicative_identity,X0,X1) ),
inference(resolution,[status(thm)],[f39,f73]) ).
fof(f181,plain,
( sum(additive_identity,a,additive_identity)
| defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[f56,f70]) ).
fof(f184,definition,
( sQ0_spl
<=> defined(multiplicative_inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f187,definition,
( sQ1_spl
<=> sum(additive_identity,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( ~ sQ1_spl
| sum(additive_identity,a,additive_identity) ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f181,f184,f187]) ).
fof(f220,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f72]) ).
fof(f221,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f222,plain,
! [X0] :
( ~ defined(multiplicative_inverse(a))
| ~ product(X0,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f92,f42]) ).
fof(f226,definition,
! [X0] :
( sQ9_spl
<=> ( ~ product(X0,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,X0,multiplicative_identity) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f227,plain,
! [X0] :
( ~ sQ9_spl
| ~ product(X0,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,X0,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,plain,
( ~ sQ0_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f222,f226,f184]) ).
fof(f232,plain,
! [X0] :
( ~ sQ9_spl
| ~ product(multiplicative_inverse(a),X0,multiplicative_identity)
| ~ product(multiplicative_identity,X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f227,f44]) ).
fof(f247,plain,
( ~ sQ9_spl
| ~ defined(a)
| sum(additive_identity,a,additive_identity)
| ~ product(multiplicative_identity,a,multiplicative_identity) ),
inference(resolution,[status(thm)],[f232,f43]) ).
fof(f251,definition,
( sQ12_spl
<=> product(multiplicative_identity,a,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( sQ12_spl
| ~ product(multiplicative_identity,a,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,definition,
( sQ13_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f256,plain,
( sQ13_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| sQ1_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f247,f251,f187,f254,f226]) ).
fof(f258,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f71]) ).
fof(f259,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f258]) ).
fof(f260,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f70]) ).
fof(f261,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f260]) ).
fof(f262,plain,
$false,
inference(sat_refutation,[status(thm)],[f190,f221,f229,f257,f259,f261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD031-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.36 % Computer : n019.cluster.edu
% 0.11/5.36 % Model : x86_64 x86_64
% 0.11/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.36 % Memory : 8046.5625MB
% 0.11/5.36 % OS : Linux 6.8.0-71-generic
% 0.11/5.36 % CPULimit : 300
% 0.11/5.36 % WCLimit : 300
% 0.11/5.36 % DateTime : Mon Sep 21 15:39:25 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.38 % Drodi V4.1.1
% 0.13/5.45 % Refutation found
% 0.13/5.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.46 % Elapsed time: 0.091251 seconds
% 0.13/5.46 % CPU time: 0.531099 seconds
% 0.13/5.46 % Total memory used: 23.008 MB
% 0.13/5.46 % Net memory used: 22.371 MB
%------------------------------------------------------------------------------