%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET347-6 : 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 02:09:50 PM UTC 2026
% Result : Unsatisfiable 245.70s 36.43s
% Output : CNFRefutation 145.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 20
% Syntax : Number of formulae : 100 ( 23 unt; 0 def)
% Number of atoms : 199 ( 69 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 189 ( 90 ~; 99 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 6 con; 0-3 aty)
% Number of variables : 178 ( 178 !; 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(f4,axiom,
! [X] : subclass(X,universal_class),
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(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(f22,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X,Y,Xr] : intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X] :
( member(null_class,X)
| ~ inductive(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [X] :
( inductive(X)
| ~ subclass(image(successor_relation,X),X)
| ~ member(null_class,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [X] : domain_of(restrict(element_relation,universal_class,X)) = sum_class(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [X] :
( member(sum_class(X),universal_class)
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [X] :
( intersection(X,regular(X)) = null_class
| X = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f70,axiom,
! [Y] :
( member(apply(choice,Y),Y)
| Y = null_class
| ~ member(Y,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
sum_class(null_class) != null_class,
file('/export/starexec/sandbox/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(f118,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
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(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] :
( ordered_pair(first(X0),second(X0)) = 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(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(f146,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f150,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f151,plain,
! [X0,X1,X2] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f152,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f169,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f171,plain,
! [X0] :
( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f172,plain,
inductive(omega),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f175,plain,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f176,plain,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f188,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f189,plain,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f192,plain,
! [X0] :
( member(apply(choice,X0),X0)
| X0 = null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f245,plain,
sum_class(null_class) != null_class,
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f287,plain,
! [X0,X1] :
( ordered_pair(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))) = regular(cross_product(X0,X1))
| cross_product(X0,X1) = null_class ),
inference(resolution,[status(thm)],[f188,f137]) ).
fof(f292,plain,
! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f146,f188]) ).
fof(f294,plain,
! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[f146,f116]) ).
fof(f295,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ subclass(X2,complement(X1))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f146,f115]) ).
fof(f299,plain,
! [X0,X1] :
( intersection(X0,X1) = null_class
| member(regular(intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f142,f188]) ).
fof(f301,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f142,f116]) ).
fof(f304,plain,
! [X0,X1] :
( intersection(X0,X1) = null_class
| member(regular(intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f144,f188]) ).
fof(f315,plain,
! [X0,X1] :
( X1 = null_class
| member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f189,f142]) ).
fof(f351,plain,
! [X0,X1,X2,X3] :
( member(X0,X1)
| ~ member(X0,restrict(X1,X2,X3)) ),
inference(paramodulation,[status(thm)],[f150,f142]) ).
fof(f410,plain,
! [X0,X1,X2] :
( ~ member(X1,X2)
| ~ subclass(X2,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(resolution,[status(thm)],[f152,f115]) ).
fof(f413,plain,
! [X0,X1] :
( ~ member(X1,sum_class(X0))
| restrict(restrict(element_relation,universal_class,X0),singleton(X1),universal_class) != null_class ),
inference(paramodulation,[status(thm)],[f175,f152]) ).
fof(f546,plain,
! [X0,X1] :
( subclass(null_class,X0)
| X1 = null_class
| member(not_subclass_element(null_class,X0),X1) ),
inference(resolution,[status(thm)],[f315,f116]) ).
fof(f616,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(X0,X2)
| ~ subclass(X2,restrict(X1,X3,X4))
| member(X0,X1) ),
inference(resolution,[status(thm)],[f351,f115]) ).
fof(f624,plain,
( inductive(universal_class)
| ~ member(null_class,universal_class) ),
inference(resolution,[status(thm)],[f171,f118]) ).
fof(f700,plain,
! [X0] :
( restrict(restrict(element_relation,universal_class,X0),singleton(apply(choice,sum_class(X0))),universal_class) != null_class
| sum_class(X0) = null_class
| ~ member(sum_class(X0),universal_class) ),
inference(resolution,[status(thm)],[f192,f413]) ).
fof(f733,plain,
! [X0] :
( ~ member(X0,universal_class)
| restrict(restrict(element_relation,universal_class,X0),singleton(apply(choice,sum_class(X0))),universal_class) != null_class
| sum_class(X0) = null_class ),
inference(resolution,[status(thm)],[f700,f176]) ).
fof(f794,plain,
( ~ inductive(universal_class)
| restrict(restrict(element_relation,universal_class,null_class),singleton(apply(choice,sum_class(null_class))),universal_class) != null_class
| sum_class(null_class) = null_class ),
inference(resolution,[status(thm)],[f733,f169]) ).
fof(f810,plain,
( ~ inductive(universal_class)
| restrict(restrict(element_relation,universal_class,null_class),singleton(apply(choice,sum_class(null_class))),universal_class) != null_class ),
inference(forward_subsumption_resolution,[status(thm)],[f794,f245]) ).
fof(f863,plain,
! [X0,X1] :
( ~ member(regular(complement(X0)),X1)
| ~ subclass(X1,X0)
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f292,f115]) ).
fof(f893,plain,
( ~ member(null_class,universal_class)
| restrict(restrict(element_relation,universal_class,null_class),singleton(apply(choice,sum_class(null_class))),universal_class) != null_class ),
inference(resolution,[status(thm)],[f810,f624]) ).
fof(f900,plain,
! [X0] :
( ~ member(null_class,X0)
| ~ subclass(X0,universal_class)
| restrict(restrict(element_relation,universal_class,null_class),singleton(apply(choice,sum_class(null_class))),universal_class) != null_class ),
inference(resolution,[status(thm)],[f893,f115]) ).
fof(f901,plain,
! [X0] :
( ~ member(null_class,X0)
| restrict(restrict(element_relation,universal_class,null_class),singleton(apply(choice,sum_class(null_class))),universal_class) != null_class ),
inference(forward_subsumption_resolution,[status(thm)],[f900,f118]) ).
fof(f971,plain,
! [X0] :
( ~ inductive(X0)
| restrict(restrict(element_relation,universal_class,null_class),singleton(apply(choice,sum_class(null_class))),universal_class) != null_class ),
inference(resolution,[status(thm)],[f901,f169]) ).
fof(f987,plain,
restrict(restrict(element_relation,universal_class,null_class),singleton(apply(choice,sum_class(null_class))),universal_class) != null_class,
inference(resolution,[status(thm)],[f971,f172]) ).
fof(f1439,plain,
! [X0,X1,X2] :
( intersection(cross_product(X1,X2),X0) = null_class
| member(regular(restrict(X0,X1,X2)),cross_product(X1,X2)) ),
inference(paramodulation,[status(thm)],[f151,f299]) ).
fof(f1452,plain,
! [X0,X1,X2] :
( restrict(X0,X1,X2) = null_class
| member(regular(restrict(X0,X1,X2)),cross_product(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f151,f1439]) ).
fof(f2000,plain,
! [X0,X1,X2,X3] :
( cross_product(X0,X1) = null_class
| member(second(regular(cross_product(X0,X1))),X3)
| ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3)) ),
inference(paramodulation,[status(thm)],[f287,f134]) ).
fof(f6096,plain,
! [X0] :
( ~ member(regular(complement(universal_class)),X0)
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f863,f118]) ).
fof(f6099,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f6096,f188]) ).
fof(f6148,plain,
complement(universal_class) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f6099]) ).
fof(f6160,plain,
! [X0] :
( subclass(null_class,X0)
| ~ member(not_subclass_element(complement(universal_class),X0),universal_class) ),
inference(paramodulation,[status(thm)],[f6148,f294]) ).
fof(f6173,plain,
! [X0] :
( subclass(null_class,X0)
| ~ member(not_subclass_element(null_class,X0),universal_class) ),
inference(forward_demodulation,[status(thm)],[f6148,f6160]) ).
fof(f6908,plain,
! [X0,X1] :
( ~ member(not_subclass_element(null_class,X0),X1)
| ~ subclass(X1,universal_class)
| subclass(null_class,X0) ),
inference(resolution,[status(thm)],[f6173,f115]) ).
fof(f6909,plain,
! [X0,X1] :
( ~ member(not_subclass_element(null_class,X0),X1)
| subclass(null_class,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f6908,f118]) ).
fof(f6910,plain,
! [X0,X1] :
( subclass(null_class,X1)
| X0 = null_class ),
inference(backward_subsumption_resolution,[status(thm)],[f546,f6909]) ).
fof(f6957,plain,
! [X0,X1,X2] :
( ~ member(X1,null_class)
| member(X1,X2)
| X0 = null_class ),
inference(resolution,[status(thm)],[f6910,f616]) ).
fof(f6970,plain,
! [X0,X1,X2] :
( ~ member(X1,null_class)
| ~ member(X1,X2)
| X0 = null_class ),
inference(resolution,[status(thm)],[f6910,f295]) ).
fof(f7094,plain,
! [X0,X1] :
( ~ member(X1,null_class)
| X0 = null_class ),
inference(forward_subsumption_resolution,[status(thm)],[f6970,f6957]) ).
fof(f7096,plain,
! [X0,X1] :
( intersection(X1,null_class) = null_class
| X0 = null_class ),
inference(resolution,[status(thm)],[f7094,f304]) ).
fof(f7239,plain,
! [X0] :
( intersection(X0,null_class) = null_class
| null_class != null_class ),
inference(equality_factoring,[status(thm)],[f7096]) ).
fof(f7240,plain,
! [X0] : intersection(X0,null_class) = null_class,
inference(trivial_equality_resolution,[status(thm)],[f7239]) ).
fof(f7242,plain,
! [X0,X1] : restrict(null_class,X0,X1) = null_class,
inference(paramodulation,[status(thm)],[f151,f7240]) ).
fof(f7253,plain,
! [X0,X1] :
( subclass(null_class,X1)
| member(not_subclass_element(intersection(X0,null_class),X1),X0) ),
inference(paramodulation,[status(thm)],[f7240,f301]) ).
fof(f7265,plain,
! [X0,X1] :
( subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),X1) ),
inference(forward_demodulation,[status(thm)],[f7240,f7253]) ).
fof(f7266,plain,
! [X0] : subclass(null_class,X0),
inference(forward_subsumption_resolution,[status(thm)],[f7265,f6909]) ).
fof(f7275,plain,
! [X0,X1] :
( ~ member(X1,null_class)
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(resolution,[status(thm)],[f7266,f410]) ).
fof(f7312,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f7275,f7094]) ).
fof(f29890,plain,
! [X0,X1] :
( cross_product(X0,X1) = null_class
| cross_product(X0,X1) = null_class
| member(second(regular(cross_product(X0,X1))),X1) ),
inference(resolution,[status(thm)],[f2000,f188]) ).
fof(f29893,plain,
! [X0,X1] :
( cross_product(X0,X1) = null_class
| member(second(regular(cross_product(X0,X1))),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f29890]) ).
fof(f105104,plain,
! [X0] : cross_product(X0,null_class) = null_class,
inference(resolution,[status(thm)],[f29893,f7312]) ).
fof(f105309,plain,
! [X0,X1] :
( restrict(X0,X1,null_class) = null_class
| member(regular(restrict(X0,X1,null_class)),null_class) ),
inference(paramodulation,[status(thm)],[f105104,f1452]) ).
fof(f105512,plain,
! [X0,X1] : restrict(X0,X1,null_class) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[f105309,f7312]) ).
fof(f105591,plain,
restrict(null_class,singleton(apply(choice,sum_class(null_class))),universal_class) != null_class,
inference(backward_demodulation,[status(thm)],[f105512,f987]) ).
fof(f106055,plain,
null_class != null_class,
inference(forward_demodulation,[status(thm)],[f7242,f105591]) ).
fof(f106056,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f106055]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET347-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n012.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 05:10:14 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 245.70/36.43 % Refutation found
% 245.70/36.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 245.70/36.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 18.95/36.74 % Elapsed time: 31.358337 seconds
% 18.95/36.74 % CPU time: 247.671523 seconds
% 18.95/36.74 % Total memory used: 1.277 GB
% 18.95/36.74 % Net memory used: 1.169 GB
%------------------------------------------------------------------------------