%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD010-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 12:21:51 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 9 unt; 4 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 77 ( 36 ~; 37 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( equalish(X,additive_identity)
| ~ defined(X)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] :
( equalish(X,additive_identity)
| ~ defined(X)
| defined(multiplicative_inverse(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y] :
( ~ equalish(Y,X)
| equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Z,Y] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,plain,
! [X0] :
( ~ defined(X0)
| equalish(multiply(multiplicative_identity,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f38,plain,
! [X0] :
( equalish(X0,additive_identity)
| ~ defined(X0)
| equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f49,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f50,plain,
! [X0] :
( equalish(X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f61,plain,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f62,plain,
! [Z,Y] :
( ~ equalish(Y,Z)
| ! [X] :
( ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f70,plain,
~ equalish(additive_identity,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f71,plain,
~ equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f72,plain,
! [X0] :
( ~ defined(X0)
| equalish(X0,multiply(multiplicative_identity,X0)) ),
inference(resolution,[status(thm)],[f61,f37]) ).
fof(f79,plain,
! [X0] :
( ~ equalish(X0,multiplicative_identity)
| ~ equalish(multiplicative_inverse(multiplicative_identity),X0) ),
inference(resolution,[status(thm)],[f63,f71]) ).
fof(f107,plain,
( ~ defined(multiplicative_inverse(multiplicative_identity))
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity) ),
inference(resolution,[status(thm)],[f79,f72]) ).
fof(f113,definition,
( sQ5_spl
<=> defined(multiplicative_inverse(multiplicative_identity)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( sQ5_spl
| ~ defined(multiplicative_inverse(multiplicative_identity)) ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f117,definition,
( sQ6_spl
<=> equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( sQ6_spl
| ~ equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity) ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( ~ sQ5_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f107,f117,f113]) ).
fof(f141,plain,
( sQ5_spl
| equalish(multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[f115,f50]) ).
fof(f142,definition,
( sQ11_spl
<=> defined(multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( sQ11_spl
| ~ defined(multiplicative_identity) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,definition,
( sQ12_spl
<=> equalish(multiplicative_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ12_spl
| equalish(multiplicative_identity,additive_identity) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ5_spl
| sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f141,f142,f145,f113]) ).
fof(f149,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f49]) ).
fof(f150,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f158,plain,
( sQ6_spl
| equalish(multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(resolution,[status(thm)],[f119,f38]) ).
fof(f161,plain,
( sQ6_spl
| sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f158,f142,f145,f117]) ).
fof(f162,plain,
( ~ sQ12_spl
| equalish(additive_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f146,f61]) ).
fof(f163,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f70]) ).
fof(f164,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f163]) ).
fof(f165,plain,
$false,
inference(sat_refutation,[status(thm)],[f120,f148,f150,f161,f164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD010-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 15:38:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.044824 seconds
% 0.13/0.41 % CPU time: 0.124817 seconds
% 0.13/0.41 % Total memory used: 17.682 MB
% 0.13/0.41 % Net memory used: 17.388 MB
%------------------------------------------------------------------------------