%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET214-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 02:09:39 PM UTC 2026
% Result : Unsatisfiable 116.43s 20.40s
% Output : CNFRefutation 116.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 9 unt; 3 def)
% Number of atoms : 78 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 69 ( 32 ~; 34 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f14,axiom,
! [U,V,X,Y] :
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U,X,V,Y] :
( member(ordered_pair(U,V),cross_product(X,Y))
| ~ member(V,Y)
| ~ member(U,X) ),
file('/export/starexec/sandbox/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/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(f113,negated_conjecture,
~ subclass(cross_product(intersection(x,y),z),cross_product(x,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f117,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f131,plain,
! [U,X] :
( member(U,X)
| ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f132,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X2,X0),cross_product(X3,X1))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f136,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f137,plain,
! [X0,X1,X2] :
( X0 = ordered_pair(first(X0),second(X0))
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f141,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f142,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f245,plain,
~ subclass(cross_product(intersection(x,y),z),cross_product(x,z)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f463,plain,
member(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z)),cross_product(intersection(x,y),z)),
inference(resolution,[status(thm)],[f116,f245]) ).
fof(f836,plain,
not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z)) = ordered_pair(first(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z))),second(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z)))),
inference(resolution,[status(thm)],[f137,f463]) ).
fof(f841,plain,
! [X0,X1] :
( ~ member(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z)),cross_product(X0,X1))
| member(first(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z))),X0) ),
inference(paramodulation,[status(thm)],[f836,f132]) ).
fof(f842,plain,
! [X0,X1] :
( ~ member(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z)),cross_product(X1,X0))
| member(second(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z))),X0) ),
inference(paramodulation,[status(thm)],[f836,f134]) ).
fof(f843,plain,
! [X0,X1] :
( ~ member(first(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z))),X1)
| member(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z)),cross_product(X1,X0))
| ~ member(second(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z))),X0) ),
inference(paramodulation,[status(thm)],[f836,f135]) ).
fof(f906,plain,
member(first(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z))),intersection(x,y)),
inference(resolution,[status(thm)],[f841,f463]) ).
fof(f952,definition,
( sQ51_spl
<=> member(second(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z))),z) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1052,plain,
member(first(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z))),x),
inference(resolution,[status(thm)],[f906,f142]) ).
fof(f1648,plain,
( subclass(cross_product(intersection(x,y),z),cross_product(x,z))
| ~ member(first(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z))),x)
| ~ member(second(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z))),z) ),
inference(resolution,[status(thm)],[f843,f117]) ).
fof(f1650,definition,
( sQ96_spl
<=> member(first(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z))),x) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1652,plain,
( sQ96_spl
| ~ member(first(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z))),x) ),
inference(component_clause,[status(thm)],[f1650]) ).
fof(f1653,definition,
( sQ97_spl
<=> subclass(cross_product(intersection(x,y),z),cross_product(x,z)) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1654,plain,
( ~ sQ97_spl
| subclass(cross_product(intersection(x,y),z),cross_product(x,z)) ),
inference(component_clause,[status(thm)],[f1653]) ).
fof(f1656,plain,
( sQ97_spl
| ~ sQ96_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f1648,f952,f1650,f1653]) ).
fof(f1667,plain,
( ~ sQ97_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1654,f245]) ).
fof(f1668,plain,
~ sQ97_spl,
inference(contradiction_clause,[status(thm)],[f1667]) ).
fof(f1681,plain,
( subclass(cross_product(intersection(x,y),z),cross_product(x,z))
| member(second(not_subclass_element(cross_product(intersection(x,y),z),cross_product(x,z))),z) ),
inference(resolution,[status(thm)],[f842,f116]) ).
fof(f1688,plain,
( sQ97_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f1681,f952,f1653]) ).
fof(f2170,plain,
( sQ96_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1652,f1052]) ).
fof(f2171,plain,
sQ96_spl,
inference(contradiction_clause,[status(thm)],[f2170]) ).
fof(f2172,plain,
$false,
inference(sat_refutation,[status(thm)],[f1656,f1668,f1688,f2171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET214-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/5.50 % Computer : n012.cluster.edu
% 0.05/5.50 % Model : x86_64 x86_64
% 0.05/5.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.50 % Memory : 8046.5625MB
% 0.05/5.50 % OS : Linux 6.8.0-71-generic
% 0.05/5.50 % CPULimit : 300
% 0.05/5.50 % WCLimit : 300
% 0.05/5.50 % DateTime : Mon Sep 21 05:00:58 UTC 2026
% 0.05/5.50 % CPUTime :
% 0.05/5.52 % Drodi V4.1.1
% 116.43/20.40 % Refutation found
% 116.43/20.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 116.43/20.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 59.56/20.49 % Elapsed time: 14.965409 seconds
% 59.56/20.49 % CPU time: 118.507907 seconds
% 59.56/20.49 % Total memory used: 697.603 MB
% 59.56/20.49 % Net memory used: 616.449 MB
%------------------------------------------------------------------------------