%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET468-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 02:09:58 PM UTC 2026
% Result : Unsatisfiable 16.59s 2.60s
% Output : CNFRefutation 16.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 11 unt; 4 def)
% Number of atoms : 100 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 95 ( 47 ~; 44 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 55 !; 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(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U,V,X,Y] :
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(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(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
x = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
~ subclass(cross_product(x,x),identity_relation),
file('/export/starexec/sandbox2/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(f119,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f134,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f137,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f147,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f189,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f246,plain,
x = null_class,
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f247,plain,
~ subclass(cross_product(x,x),identity_relation),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f252,plain,
~ subclass(cross_product(null_class,x),identity_relation),
inference(forward_demodulation,[status(thm)],[f246,f247]) ).
fof(f253,plain,
~ subclass(cross_product(null_class,null_class),identity_relation),
inference(forward_demodulation,[status(thm)],[f246,f252]) ).
fof(f255,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f119,f116]) ).
fof(f630,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f189,f147]) ).
fof(f1309,plain,
! [X0,X1,X2] :
( ordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))) = not_subclass_element(cross_product(X0,X1),X2)
| subclass(cross_product(X0,X1),X2) ),
inference(resolution,[status(thm)],[f117,f138]) ).
fof(f2536,plain,
! [X0] :
( ~ member(regular(complement(universal_class)),X0)
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f630,f255]) ).
fof(f2545,definition,
( sQ90_spl
<=> complement(universal_class) = null_class ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f2546,plain,
( ~ sQ90_spl
| complement(universal_class) = null_class ),
inference(component_clause,[status(thm)],[f2545]) ).
fof(f2547,plain,
( sQ90_spl
| complement(universal_class) != null_class ),
inference(component_clause,[status(thm)],[f2545]) ).
fof(f2548,definition,
! [X0] :
( sQ91_spl
<=> ~ member(regular(complement(universal_class)),X0) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f2549,plain,
! [X0] :
( ~ sQ91_spl
| ~ member(regular(complement(universal_class)),X0) ),
inference(component_clause,[status(thm)],[f2548]) ).
fof(f2551,plain,
( sQ91_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f2536,f2545,f2548]) ).
fof(f2680,plain,
! [X0] :
( ~ sQ90_spl
| ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f2546,f147]) ).
fof(f2690,plain,
! [X0] :
( ~ sQ90_spl
| ~ member(X0,null_class) ),
inference(forward_subsumption_resolution,[status(thm)],[f2680,f255]) ).
fof(f4287,plain,
( ~ sQ91_spl
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f2549,f189]) ).
fof(f4417,plain,
( sQ90_spl
| ~ sQ91_spl
| null_class != null_class ),
inference(forward_demodulation,[status(thm)],[f4287,f2547]) ).
fof(f4418,plain,
( sQ90_spl
| ~ sQ91_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f4417]) ).
fof(f4419,plain,
( sQ90_spl
| ~ sQ91_spl ),
inference(contradiction_clause,[status(thm)],[f4418]) ).
fof(f5118,plain,
ordered_pair(first(not_subclass_element(cross_product(null_class,null_class),identity_relation)),second(not_subclass_element(cross_product(null_class,null_class),identity_relation))) = not_subclass_element(cross_product(null_class,null_class),identity_relation),
inference(resolution,[status(thm)],[f1309,f253]) ).
fof(f5182,plain,
! [X0,X1] :
( member(second(not_subclass_element(cross_product(null_class,null_class),identity_relation)),X1)
| ~ member(not_subclass_element(cross_product(null_class,null_class),identity_relation),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f5118,f135]) ).
fof(f6890,plain,
( subclass(cross_product(null_class,null_class),identity_relation)
| member(second(not_subclass_element(cross_product(null_class,null_class),identity_relation)),null_class) ),
inference(resolution,[status(thm)],[f5182,f117]) ).
fof(f6898,definition,
( sQ311_spl
<=> member(second(not_subclass_element(cross_product(null_class,null_class),identity_relation)),null_class) ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f6899,plain,
( ~ sQ311_spl
| member(second(not_subclass_element(cross_product(null_class,null_class),identity_relation)),null_class) ),
inference(component_clause,[status(thm)],[f6898]) ).
fof(f6901,definition,
( sQ312_spl
<=> subclass(cross_product(null_class,null_class),identity_relation) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f6902,plain,
( ~ sQ312_spl
| subclass(cross_product(null_class,null_class),identity_relation) ),
inference(component_clause,[status(thm)],[f6901]) ).
fof(f6904,plain,
( sQ312_spl
| sQ311_spl ),
inference(split_clause,[status(thm)],[f6890,f6898,f6901]) ).
fof(f6907,plain,
( ~ sQ311_spl
| ~ sQ90_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6899,f2690]) ).
fof(f6908,plain,
( ~ sQ311_spl
| ~ sQ90_spl ),
inference(contradiction_clause,[status(thm)],[f6907]) ).
fof(f6909,plain,
( ~ sQ312_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6902,f253]) ).
fof(f6910,plain,
~ sQ312_spl,
inference(contradiction_clause,[status(thm)],[f6909]) ).
fof(f6911,plain,
$false,
inference(sat_refutation,[status(thm)],[f2551,f4419,f6904,f6908,f6910]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET468-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n010.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 05:19:40 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 16.59/2.60 % Refutation found
% 16.59/2.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 16.59/2.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.12/2.65 % Elapsed time: 2.283680 seconds
% 2.12/2.65 % CPU time: 17.672756 seconds
% 2.12/2.65 % Total memory used: 226.833 MB
% 2.12/2.65 % Net memory used: 209.807 MB
%------------------------------------------------------------------------------