%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD032-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 12 unt; 4 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 85 ( 43 ~; 38 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ product(multiplicative_identity,a,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,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(f41,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)],[f40]) ).
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(f70,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f71,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f72,plain,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f73,plain,
~ product(multiplicative_identity,a,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f136,plain,
! [X0,X1,X2] :
( ~ product(X0,X2,multiplicative_identity)
| ~ product(X1,a,X2)
| ~ product(X0,X1,multiplicative_identity) ),
inference(resolution,[status(thm)],[f41,f73]) ).
fof(f147,definition,
( sQ1_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( sQ1_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f154,plain,
! [X0] :
( ~ defined(a)
| ~ product(X0,a,multiplicative_identity)
| ~ product(X0,multiplicative_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f136,f42]) ).
fof(f158,definition,
! [X0] :
( sQ2_spl
<=> ( ~ product(X0,a,multiplicative_identity)
| ~ product(X0,multiplicative_identity,multiplicative_identity) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f159,plain,
! [X0] :
( ~ sQ2_spl
| ~ product(X0,a,multiplicative_identity)
| ~ product(X0,multiplicative_identity,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f154,f158,f147]) ).
fof(f162,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f70]) ).
fof(f163,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f209,definition,
( sQ3_spl
<=> sum(additive_identity,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( ~ sQ3_spl
| sum(additive_identity,a,additive_identity) ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f216,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f71]) ).
fof(f217,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f216]) ).
fof(f490,plain,
( ~ sQ2_spl
| ~ defined(a)
| sum(additive_identity,a,additive_identity)
| ~ product(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f159,f43]) ).
fof(f495,definition,
( sQ29_spl
<=> product(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( sQ29_spl
| ~ product(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f498,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ3_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f490,f495,f209,f147,f158]) ).
fof(f502,plain,
( sQ29_spl
| ~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity) ),
inference(resolution,[status(thm)],[f497,f44]) ).
fof(f503,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f72]) ).
fof(f504,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f505,plain,
$false,
inference(sat_refutation,[status(thm)],[f161,f163,f217,f498,f504]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD032-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n004.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 15:39:06 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.51 % Refutation found
% 0.17/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.57 % Elapsed time: 0.120747 seconds
% 0.17/0.57 % CPU time: 0.400084 seconds
% 0.17/0.57 % Total memory used: 18.548 MB
% 0.17/0.57 % Net memory used: 18.310 MB
%------------------------------------------------------------------------------