%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET222-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 02:09:40 PM UTC 2026
% Result : Unsatisfiable 126.33s 16.43s
% Output : CNFRefutation 126.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 23
% Syntax : Number of formulae : 85 ( 23 unt; 6 def)
% Number of atoms : 156 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 141 ( 70 ~; 65 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 145 ( 145 !; 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(f11,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox2/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/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(f16,axiom,
! [U,X,V,Y] :
( member(ordered_pair(U,V),cross_product(X,Y))
| ~ member(V,Y)
| ~ member(U,X) ),
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(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [Z,X,Y] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X] :
( member(null_class,X)
| ~ inductive(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
~ subclass(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z)),
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] :
( ~ subclass(X1,X2)
| member(X0,X2)
| ~ member(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(f128,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f129,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
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(ordered_pair(X0,X2),cross_product(X1,X3))
| member(X0,X1) ),
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(ordered_pair(X2,X0),cross_product(X3,X1))
| member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ 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] :
( ~ member(X0,cross_product(X1,X2))
| X0 = ordered_pair(first(X0),second(X0)) ),
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,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f143,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f144,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f145,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f150,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f169,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f172,plain,
inductive(omega),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f245,plain,
~ subclass(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f254,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[status(thm)],[f115,f118]) ).
fof(f257,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(ordered_pair(X0,X2),intersection(X3,cross_product(X1,X4)))
| member(X0,X1) ),
inference(resolution,[status(thm)],[f144,f132]) ).
fof(f290,plain,
~ subclass(restrict(cross_product(w,x),y,z),cross_product(w,z)),
inference(backward_demodulation,[status(thm)],[f150,f245]) ).
fof(f291,plain,
! [X0,X1,X2,X3] :
( member(X0,X1)
| ~ member(X0,restrict(X1,X2,X3)) ),
inference(paramodulation,[status(thm)],[f150,f142]) ).
fof(f296,plain,
! [X0,X1,X2,X3] :
( member(X0,restrict(X1,X2,X3))
| ~ member(X0,cross_product(X2,X3))
| ~ member(X0,X1) ),
inference(paramodulation,[status(thm)],[f150,f145]) ).
fof(f298,plain,
! [X0,X1,X2,X3] :
( member(X0,cross_product(X2,X3))
| ~ member(X0,restrict(X1,X2,X3)) ),
inference(paramodulation,[status(thm)],[f150,f144]) ).
fof(f306,plain,
! [X0] : member(singleton(X0),universal_class),
inference(paramodulation,[status(thm)],[f129,f128]) ).
fof(f316,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(ordered_pair(X0,X2),restrict(X3,X1,X4))
| member(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f150,f257]) ).
fof(f317,plain,
! [X0,X1,X2,X3] :
( member(not_subclass_element(restrict(X0,X1,X2),X3),X0)
| subclass(restrict(X0,X1,X2),X3) ),
inference(resolution,[status(thm)],[f291,f116]) ).
fof(f334,plain,
member(null_class,omega),
inference(resolution,[status(thm)],[f169,f172]) ).
fof(f337,plain,
! [X0,X1,X2,X3] :
( subclass(restrict(X0,X1,X2),X3)
| member(not_subclass_element(restrict(X0,X1,X2),X3),cross_product(X1,X2)) ),
inference(resolution,[status(thm)],[f298,f116]) ).
fof(f381,plain,
member(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)),cross_product(w,x)),
inference(resolution,[status(thm)],[f317,f290]) ).
fof(f426,plain,
! [X0] :
( ~ member(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)),X0)
| member(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)),restrict(X0,w,x)) ),
inference(resolution,[status(thm)],[f381,f296]) ).
fof(f438,definition,
! [X0] :
( sQ6_spl
<=> ~ member(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)),X0) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f439,plain,
! [X0] :
( ~ sQ6_spl
| ~ member(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)),X0) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f446,plain,
( ~ sQ6_spl
| subclass(restrict(cross_product(w,x),y,z),cross_product(w,z)) ),
inference(resolution,[status(thm)],[f439,f116]) ).
fof(f457,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f446,f290]) ).
fof(f458,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f704,definition,
( sQ22_spl
<=> member(null_class,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f706,plain,
( sQ22_spl
| ~ member(null_class,universal_class) ),
inference(component_clause,[status(thm)],[f704]) ).
fof(f732,plain,
! [X0] :
( sQ22_spl
| ~ member(null_class,X0) ),
inference(resolution,[status(thm)],[f706,f254]) ).
fof(f774,definition,
! [X0] :
( sQ29_spl
<=> ~ member(X0,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f775,plain,
! [X0] :
( ~ sQ29_spl
| ~ member(X0,universal_class) ),
inference(component_clause,[status(thm)],[f774]) ).
fof(f817,plain,
not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)) = ordered_pair(first(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),second(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)))),
inference(resolution,[status(thm)],[f137,f381]) ).
fof(f840,plain,
! [X0,X1,X2] :
( ~ member(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)),restrict(X1,X0,X2))
| member(first(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),X0) ),
inference(paramodulation,[status(thm)],[f817,f316]) ).
fof(f845,plain,
! [X0,X1] :
( member(second(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),X1)
| ~ member(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f817,f134]) ).
fof(f846,plain,
! [X0,X1] :
( ~ member(first(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),X1)
| member(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)),cross_product(X1,X0))
| ~ member(second(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),X0) ),
inference(paramodulation,[status(thm)],[f817,f135]) ).
fof(f1026,definition,
( sQ47_spl
<=> member(first(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),w) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1029,definition,
( sQ48_spl
<=> subclass(restrict(cross_product(w,x),y,z),cross_product(w,z)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1030,plain,
( ~ sQ48_spl
| subclass(restrict(cross_product(w,x),y,z),cross_product(w,z)) ),
inference(component_clause,[status(thm)],[f1029]) ).
fof(f1033,plain,
( ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1030,f290]) ).
fof(f1034,plain,
~ sQ48_spl,
inference(contradiction_clause,[status(thm)],[f1033]) ).
fof(f1149,plain,
~ member(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)),cross_product(w,z)),
inference(resolution,[status(thm)],[f117,f290]) ).
fof(f1376,plain,
( ~ member(first(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),w)
| ~ member(second(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),z) ),
inference(resolution,[status(thm)],[f846,f1149]) ).
fof(f1392,definition,
( sQ77_spl
<=> member(second(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),z) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1395,plain,
( ~ sQ47_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f1376,f1392,f1026]) ).
fof(f1399,plain,
! [X0] :
( ~ member(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)),X0)
| member(first(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),w) ),
inference(resolution,[status(thm)],[f840,f426]) ).
fof(f1401,plain,
( sQ6_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f1399,f1026,f438]) ).
fof(f1574,plain,
( ~ sQ29_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f306,f775]) ).
fof(f1586,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f1574]) ).
fof(f1624,plain,
( sQ22_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f334,f732]) ).
fof(f1634,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f1624]) ).
fof(f1646,plain,
( subclass(restrict(cross_product(w,x),y,z),cross_product(w,z))
| member(second(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),z) ),
inference(resolution,[status(thm)],[f845,f337]) ).
fof(f1678,plain,
( sQ48_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f1646,f1392,f1029]) ).
fof(f1679,plain,
$false,
inference(sat_refutation,[status(thm)],[f458,f1034,f1395,f1401,f1586,f1634,f1678]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET222-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n026.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Mon Sep 21 05:05:07 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 126.33/16.43 % Refutation found
% 126.33/16.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 126.33/16.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 20.48/16.53 % Elapsed time: 16.090074 seconds
% 20.48/16.53 % CPU time: 127.066678 seconds
% 20.48/16.53 % Total memory used: 658.671 MB
% 20.48/16.53 % Net memory used: 587.525 MB
%------------------------------------------------------------------------------