%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET150-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:09:30 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 54 ( 5 unt; 6 def)
% Number of atoms : 119 ( 4 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 114 ( 49 ~; 59 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
complement(complement(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f115,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f117,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f118,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f121,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f146,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f147,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f245,plain,
complement(complement(x)) != x,
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f263,plain,
( ~ subclass(x,complement(complement(x)))
| ~ subclass(complement(complement(x)),x) ),
inference(resolution,[status(thm)],[f121,f245]) ).
fof(f265,definition,
( sQ0_spl
<=> subclass(complement(complement(x)),x) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( sQ0_spl
| ~ subclass(complement(complement(x)),x) ),
inference(component_clause,[status(thm)],[f265]) ).
fof(f268,definition,
( sQ1_spl
<=> subclass(x,complement(complement(x))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f270,plain,
( sQ1_spl
| ~ subclass(x,complement(complement(x))) ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f271,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f263,f265,f268]) ).
fof(f287,plain,
! [X0,X1] :
( ~ member(not_subclass_element(complement(X0),X1),X0)
| subclass(complement(X0),X1) ),
inference(resolution,[status(thm)],[f116,f146]) ).
fof(f329,definition,
( sQ3_spl
<=> member(not_subclass_element(complement(complement(x)),x),universal_class) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( sQ3_spl
| ~ member(not_subclass_element(complement(complement(x)),x),universal_class) ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f341,plain,
! [X0] :
( sQ3_spl
| ~ member(not_subclass_element(complement(complement(x)),x),X0)
| ~ subclass(X0,universal_class) ),
inference(resolution,[status(thm)],[f331,f115]) ).
fof(f342,plain,
! [X0] :
( sQ3_spl
| ~ member(not_subclass_element(complement(complement(x)),x),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f341,f118]) ).
fof(f343,plain,
( sQ3_spl
| subclass(complement(complement(x)),x) ),
inference(resolution,[status(thm)],[f342,f116]) ).
fof(f348,plain,
( sQ3_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f343,f267]) ).
fof(f349,plain,
( sQ3_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f348]) ).
fof(f352,plain,
( sQ1_spl
| ~ member(not_subclass_element(x,complement(complement(x))),complement(complement(x))) ),
inference(resolution,[status(thm)],[f270,f117]) ).
fof(f354,plain,
( sQ1_spl
| member(not_subclass_element(x,complement(complement(x))),complement(x))
| ~ member(not_subclass_element(x,complement(complement(x))),universal_class) ),
inference(resolution,[status(thm)],[f352,f147]) ).
fof(f356,definition,
( sQ6_spl
<=> member(not_subclass_element(x,complement(complement(x))),universal_class) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f358,plain,
( sQ6_spl
| ~ member(not_subclass_element(x,complement(complement(x))),universal_class) ),
inference(component_clause,[status(thm)],[f356]) ).
fof(f359,definition,
( sQ7_spl
<=> member(not_subclass_element(x,complement(complement(x))),complement(x)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f360,plain,
( ~ sQ7_spl
| member(not_subclass_element(x,complement(complement(x))),complement(x)) ),
inference(component_clause,[status(thm)],[f359]) ).
fof(f362,plain,
( sQ1_spl
| sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f354,f356,f359,f268]) ).
fof(f406,plain,
( ~ sQ7_spl
| ~ member(not_subclass_element(x,complement(complement(x))),x) ),
inference(resolution,[status(thm)],[f360,f146]) ).
fof(f412,plain,
( ~ sQ7_spl
| subclass(x,complement(complement(x))) ),
inference(resolution,[status(thm)],[f406,f116]) ).
fof(f457,definition,
( sQ16_spl
<=> member(not_subclass_element(complement(complement(x)),x),x) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( sQ0_spl
| ~ member(not_subclass_element(complement(complement(x)),x),x) ),
inference(resolution,[status(thm)],[f267,f117]) ).
fof(f493,plain,
! [X0] :
( sQ6_spl
| ~ member(not_subclass_element(x,complement(complement(x))),X0)
| ~ subclass(X0,universal_class) ),
inference(resolution,[status(thm)],[f358,f115]) ).
fof(f494,plain,
! [X0] :
( sQ6_spl
| ~ member(not_subclass_element(x,complement(complement(x))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f493,f118]) ).
fof(f515,plain,
( sQ0_spl
| ~ member(not_subclass_element(complement(complement(x)),x),complement(x)) ),
inference(resolution,[status(thm)],[f287,f267]) ).
fof(f554,plain,
( sQ0_spl
| member(not_subclass_element(complement(complement(x)),x),x)
| ~ member(not_subclass_element(complement(complement(x)),x),universal_class) ),
inference(resolution,[status(thm)],[f515,f147]) ).
fof(f556,plain,
( sQ0_spl
| sQ16_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f554,f329,f457,f265]) ).
fof(f557,plain,
( sQ0_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f492,f457,f265]) ).
fof(f560,plain,
( sQ6_spl
| subclass(x,complement(complement(x))) ),
inference(resolution,[status(thm)],[f494,f116]) ).
fof(f566,plain,
( sQ6_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f560,f270]) ).
fof(f567,plain,
( sQ6_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f566]) ).
fof(f568,plain,
( ~ sQ7_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f412,f270]) ).
fof(f569,plain,
( ~ sQ7_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f568]) ).
fof(f570,plain,
$false,
inference(sat_refutation,[status(thm)],[f271,f349,f362,f556,f557,f567,f569]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET150-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.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 04:57:14 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.066768 seconds
% 0.13/0.43 % CPU time: 0.294122 seconds
% 0.13/0.43 % Total memory used: 110.258 MB
% 0.13/0.43 % Net memory used: 109.660 MB
%------------------------------------------------------------------------------