%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET183-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:09:35 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 9 unt; 3 def)
% Number of atoms : 84 ( 7 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 78 ( 35 ~; 40 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [Z,X,Y] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
subclass(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
intersection(x,y) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f116,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f118,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f122,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f142,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f143,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f146,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f246,plain,
subclass(x,y),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f247,plain,
intersection(x,y) != x,
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f252,plain,
! [X0] :
( member(X0,y)
| ~ member(X0,x) ),
inference(resolution,[status(thm)],[f116,f246]) ).
fof(f271,plain,
! [X0,X1,X2] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f117,f143]) ).
fof(f272,plain,
! [X0] :
( member(not_subclass_element(x,X0),y)
| subclass(x,X0) ),
inference(resolution,[status(thm)],[f117,f252]) ).
fof(f307,plain,
! [X0,X1,X2] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) ),
inference(resolution,[status(thm)],[f118,f146]) ).
fof(f361,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f271,f118]) ).
fof(f369,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f361]) ).
fof(f370,plain,
! [X0] :
( subclass(x,intersection(X0,y))
| ~ member(not_subclass_element(x,intersection(X0,y)),X0)
| subclass(x,intersection(X0,y)) ),
inference(resolution,[status(thm)],[f307,f272]) ).
fof(f377,plain,
! [X0] :
( ~ member(not_subclass_element(x,intersection(X0,y)),X0)
| subclass(x,intersection(X0,y)) ),
inference(duplicate_literals_removal,[status(thm)],[f370]) ).
fof(f573,plain,
( subclass(x,intersection(x,y))
| subclass(x,intersection(x,y)) ),
inference(resolution,[status(thm)],[f377,f117]) ).
fof(f583,definition,
( sQ25_spl
<=> subclass(x,intersection(x,y)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f584,plain,
( ~ sQ25_spl
| subclass(x,intersection(x,y)) ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,plain,
sQ25_spl,
inference(split_clause,[status(thm)],[f573,f583]) ).
fof(f608,plain,
( ~ sQ25_spl
| intersection(x,y) = x
| ~ subclass(intersection(x,y),x) ),
inference(resolution,[status(thm)],[f584,f122]) ).
fof(f610,definition,
( sQ28_spl
<=> subclass(intersection(x,y),x) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f612,plain,
( sQ28_spl
| ~ subclass(intersection(x,y),x) ),
inference(component_clause,[status(thm)],[f610]) ).
fof(f613,definition,
( sQ29_spl
<=> intersection(x,y) = x ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f614,plain,
( ~ sQ29_spl
| intersection(x,y) = x ),
inference(component_clause,[status(thm)],[f613]) ).
fof(f616,plain,
( ~ sQ25_spl
| sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f608,f610,f613,f583]) ).
fof(f617,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f612,f369]) ).
fof(f618,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f617]) ).
fof(f619,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f614,f247]) ).
fof(f620,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f619]) ).
fof(f621,plain,
$false,
inference(sat_refutation,[status(thm)],[f586,f616,f618,f620]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET183-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.42 % Computer : n009.cluster.edu
% 0.08/0.42 % Model : x86_64 x86_64
% 0.08/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.42 % Memory : 8046.5625MB
% 0.08/0.42 % OS : Linux 6.8.0-71-generic
% 0.08/0.42 % CPULimit : 300
% 0.08/0.42 % WCLimit : 300
% 0.08/0.42 % DateTime : Mon Sep 21 04:59:42 UTC 2026
% 0.08/0.42 % CPUTime :
% 0.08/0.44 % Drodi V4.1.1
% 0.13/0.46 % Refutation found
% 0.13/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.49 % Elapsed time: 0.055420 seconds
% 0.13/0.49 % CPU time: 0.166758 seconds
% 0.13/0.49 % Total memory used: 89.752 MB
% 0.13/0.49 % Net memory used: 89.668 MB
%------------------------------------------------------------------------------