%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET518-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:10:02 PM UTC 2026
% Result : Unsatisfiable 161.76s 20.98s
% Output : CNFRefutation 129.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 17
% Syntax : Number of formulae : 74 ( 15 unt; 0 def)
% Number of atoms : 166 ( 49 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 160 ( 68 ~; 92 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 126 ( 126 !; 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(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
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(f10,axiom,
! [Y,X] :
( member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
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(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(f55,axiom,
! [X] : complement(image(element_relation,complement(X))) = power_class(X),
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(f113,negated_conjecture,
member(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
member(y,x),
file('/export/starexec/sandbox/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] :
( ~ subclass(X1,X2)
| member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f118,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f119,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f122,plain,
! [X0,X1] :
( ~ subclass(X1,X0)
| X1 = X0
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f123,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f124,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ member(X1,unordered_pair(X0,X2))
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f126,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [Y] :
( ! [X] : member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f128,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f142,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f143,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f144,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f145,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f146,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,intersection(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f147,plain,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f178,plain,
! [X0] : power_class(X0) = complement(image(element_relation,complement(X0))),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f189,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f190,plain,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f246,plain,
member(x,y),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f247,plain,
member(y,x),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f251,plain,
! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X1
| regular(unordered_pair(X0,X1)) = X0 ),
inference(resolution,[status(thm)],[f189,f124]) ).
fof(f307,plain,
! [X0,X1] :
( ~ member(X0,power_class(X1))
| ~ member(X0,image(element_relation,complement(X1))) ),
inference(paramodulation,[status(thm)],[f178,f147]) ).
fof(f316,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f145,f117]) ).
fof(f340,plain,
! [X0,X1] :
( member(X1,X0)
| ~ member(X1,null_class)
| X0 = null_class ),
inference(paramodulation,[status(thm)],[f190,f143]) ).
fof(f356,plain,
! [X0,X1] :
( X1 = null_class
| subclass(null_class,X0)
| member(not_subclass_element(null_class,X0),X1) ),
inference(resolution,[status(thm)],[f340,f117]) ).
fof(f471,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[f118,f316]) ).
fof(f475,plain,
! [X0] :
( X0 = null_class
| subclass(null_class,X0)
| subclass(null_class,X0) ),
inference(resolution,[status(thm)],[f118,f356]) ).
fof(f490,plain,
! [X0,X1] : subclass(intersection(X0,X1),X1),
inference(duplicate_literals_removal,[status(thm)],[f471]) ).
fof(f492,plain,
! [X0] :
( subclass(null_class,X0)
| null_class = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f475]) ).
fof(f541,plain,
! [X0] :
( null_class = X0
| ~ subclass(X0,null_class)
| null_class = X0 ),
inference(resolution,[status(thm)],[f492,f122]) ).
fof(f542,plain,
! [X0] :
( X0 = null_class
| ~ subclass(X0,null_class) ),
inference(duplicate_literals_removal,[status(thm)],[f541]) ).
fof(f577,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[status(thm)],[f116,f119]) ).
fof(f701,plain,
! [X0,X1] :
( member(X0,null_class)
| ~ member(X0,regular(X1))
| X1 = null_class
| ~ member(X0,X1) ),
inference(paramodulation,[status(thm)],[f190,f146]) ).
fof(f743,plain,
! [X0,X1,X2] :
( unordered_pair(X1,X2) = null_class
| regular(unordered_pair(X1,X2)) = X2
| member(X0,null_class)
| ~ member(X0,X1)
| unordered_pair(X1,X2) = null_class
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(paramodulation,[status(thm)],[f251,f701]) ).
fof(f745,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| ~ member(X0,unordered_pair(X1,X2))
| unordered_pair(X1,X2) = null_class
| regular(unordered_pair(X1,X2)) = X2
| member(X0,null_class) ),
inference(duplicate_literals_removal,[status(thm)],[f743]) ).
fof(f3486,plain,
! [X0] : null_class = intersection(X0,null_class),
inference(resolution,[status(thm)],[f542,f490]) ).
fof(f3834,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f3486,f143]) ).
fof(f4461,plain,
! [X0,X1] :
( ~ member(X0,power_class(X1))
| ~ member(X0,null_class) ),
inference(resolution,[status(thm)],[f3834,f307]) ).
fof(f4471,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f4461,f3834]) ).
fof(f4790,plain,
! [X0,X1,X2] :
( ~ member(X2,unordered_pair(X0,X1))
| ~ member(X2,X0)
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ),
inference(backward_subsumption_resolution,[status(thm)],[f745,f4471]) ).
fof(f4791,plain,
! [X0,X1] :
( null_class = X1
| ~ member(X0,regular(X1))
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f701,f4471]) ).
fof(f5047,plain,
! [X0,X1] :
( ~ member(X1,universal_class)
| ~ member(X1,X0)
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ),
inference(resolution,[status(thm)],[f4790,f128]) ).
fof(f5061,plain,
! [X0,X1] :
( ~ member(X0,X1)
| unordered_pair(X1,X0) = null_class
| X0 = regular(unordered_pair(X1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f5047,f577]) ).
fof(f20648,plain,
( null_class = unordered_pair(x,y)
| regular(unordered_pair(x,y)) = y ),
inference(resolution,[status(thm)],[f5061,f247]) ).
fof(f20837,plain,
! [X0] :
( null_class = unordered_pair(x,y)
| null_class = unordered_pair(x,y)
| ~ member(X0,y)
| ~ member(X0,unordered_pair(x,y)) ),
inference(paramodulation,[status(thm)],[f20648,f4791]) ).
fof(f20878,plain,
! [X0] :
( ~ member(X0,unordered_pair(x,y))
| null_class = unordered_pair(x,y)
| ~ member(X0,y) ),
inference(duplicate_literals_removal,[status(thm)],[f20837]) ).
fof(f20916,plain,
( ~ member(x,unordered_pair(x,y))
| unordered_pair(x,y) = null_class ),
inference(resolution,[status(thm)],[f20878,f246]) ).
fof(f21343,plain,
( null_class = unordered_pair(x,y)
| ~ member(x,universal_class) ),
inference(resolution,[status(thm)],[f20916,f126]) ).
fof(f21363,plain,
! [X0] :
( ~ member(x,X0)
| unordered_pair(x,y) = null_class ),
inference(resolution,[status(thm)],[f21343,f577]) ).
fof(f21380,plain,
unordered_pair(x,y) = null_class,
inference(resolution,[status(thm)],[f21363,f246]) ).
fof(f22043,plain,
( ~ member(x,universal_class)
| member(x,null_class) ),
inference(paramodulation,[status(thm)],[f21380,f126]) ).
fof(f22113,plain,
~ member(x,universal_class),
inference(forward_subsumption_resolution,[status(thm)],[f22043,f4471]) ).
fof(f22333,plain,
! [X0] : ~ member(x,X0),
inference(resolution,[status(thm)],[f22113,f577]) ).
fof(f22358,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f246,f22333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET518-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:23:10 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.37 % Drodi V4.1.1
% 161.76/20.98 % Refutation found
% 161.76/20.98 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 161.76/20.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.90/21.25 % Elapsed time: 20.875877 seconds
% 9.90/21.25 % CPU time: 163.888005 seconds
% 9.90/21.25 % Total memory used: 759.236 MB
% 9.90/21.25 % Net memory used: 677.685 MB
%------------------------------------------------------------------------------