%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET260-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 02:09:44 PM UTC 2026
% Result : Unsatisfiable 124.22s 16.14s
% Output : CNFRefutation 124.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 54 ( 24 unt; 0 def)
% Number of atoms : 93 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 77 ( 38 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 84 ( 84 !; 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(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
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(f23,axiom,
! [Z,X,Y] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
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(f29,axiom,
! [X,Y,Xr] : intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [Z,X] :
( member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) = null_class
| ~ member(Z,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(f113,negated_conjecture,
member(ordered_pair(x,y),xr),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,negated_conjecture,
~ member(x,domain_of(xr)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ~ member(X2,X0)
| member(X2,X1)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f120,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f126,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f127,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f131,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f133,plain,
! [U,X] :
( member(U,X)
| ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X2),cross_product(X1,X3))
| member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f136,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X2,X0),cross_product(X3,X1))
| member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X2)
| ~ member(X1,X3)
| member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f147,plain,
! [X0,X1,X2] :
( member(X0,intersection(X2,X1))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f148,plain,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f153,plain,
! [X0,X1,X2] : restrict(X0,X1,X2) = intersection(cross_product(X1,X2),X0),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f155,plain,
! [X0,X1] :
( restrict(X1,singleton(X0),universal_class) = null_class
| ~ member(X0,universal_class)
| member(X0,domain_of(X1)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f190,plain,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f247,plain,
member(ordered_pair(x,y),xr),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f248,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f249,plain,
~ member(x,domain_of(xr)),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f252,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[f248,f136]) ).
fof(f254,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[f134,f248]) ).
fof(f255,plain,
! [X0] :
( member(x,domain_of(X0))
| null_class = restrict(X0,singleton(x),universal_class) ),
inference(resolution,[status(thm)],[f254,f155]) ).
fof(f257,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(ordered_pair(X0,y),cross_product(X1,universal_class)) ),
inference(resolution,[status(thm)],[f137,f252]) ).
fof(f428,plain,
restrict(xr,singleton(x),universal_class) = null_class,
inference(resolution,[status(thm)],[f255,f249]) ).
fof(f492,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f117,f120]) ).
fof(f494,plain,
! [X0] :
( X0 = null_class
| member(regular(X0),universal_class) ),
inference(resolution,[status(thm)],[f492,f190]) ).
fof(f617,plain,
! [X0] :
( null_class = complement(X0)
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f148,f190]) ).
fof(f918,plain,
! [X0] : member(x,unordered_pair(x,X0)),
inference(resolution,[status(thm)],[f127,f254]) ).
fof(f1019,plain,
! [X0] :
( member(ordered_pair(x,y),intersection(X0,xr))
| ~ member(ordered_pair(x,y),X0) ),
inference(resolution,[status(thm)],[f147,f247]) ).
fof(f1094,plain,
member(x,singleton(x)),
inference(paramodulation,[status(thm)],[f131,f918]) ).
fof(f1105,plain,
member(ordered_pair(x,y),cross_product(singleton(x),universal_class)),
inference(resolution,[status(thm)],[f1094,f257]) ).
fof(f6652,plain,
( complement(universal_class) = null_class
| null_class = complement(universal_class) ),
inference(resolution,[status(thm)],[f617,f494]) ).
fof(f6659,plain,
complement(universal_class) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f6652]) ).
fof(f6689,plain,
! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f6659,f148]) ).
fof(f6690,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f6689,f492]) ).
fof(f10597,plain,
member(ordered_pair(x,y),intersection(cross_product(singleton(x),universal_class),xr)),
inference(resolution,[status(thm)],[f1105,f1019]) ).
fof(f10619,plain,
member(ordered_pair(x,y),restrict(xr,singleton(x),universal_class)),
inference(forward_demodulation,[status(thm)],[f153,f10597]) ).
fof(f10620,plain,
member(ordered_pair(x,y),null_class),
inference(forward_demodulation,[status(thm)],[f428,f10619]) ).
fof(f10621,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f10620,f6690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET260-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n004.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 05:03:34 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 124.22/16.14 % Refutation found
% 124.22/16.14 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 124.22/16.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 16.01/16.23 % Elapsed time: 15.793021 seconds
% 16.01/16.23 % CPU time: 124.976243 seconds
% 16.01/16.23 % Total memory used: 737.747 MB
% 16.01/16.23 % Net memory used: 644.194 MB
%------------------------------------------------------------------------------