%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET503-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 02:10:01 PM UTC 2026
% Result : Unsatisfiable 0.20s 5.75s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 21
% Syntax : Number of formulae : 84 ( 25 unt; 0 def)
% Number of atoms : 170 ( 55 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 150 ( 64 ~; 86 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 134 ( 134 !; 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(f11,axiom,
! [X,Y] : member(unordered_pair(X,Y),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(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ 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(f28,axiom,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = 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(f54,axiom,
! [X] :
( member(sum_class(X),universal_class)
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [Xf,X] :
( member(image(Xf,X),universal_class)
| ~ member(X,universal_class)
| ~ function(Xf) ),
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(f68,axiom,
! [Xf,Y] : sum_class(image(Xf,singleton(Y))) = apply(Xf,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
function(choice),
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,
member(universal_class,x),
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(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(f121,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f122,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f123,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f125,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
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(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(f145,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
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(f152,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f176,plain,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f187,plain,
! [X0,X1] :
( member(image(X0,X1),universal_class)
| ~ member(X1,universal_class)
| ~ function(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
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(f190,plain,
! [X0,X1] : sum_class(image(X0,singleton(X1))) = apply(X0,X1),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f191,plain,
function(choice),
inference(cnf_transformation,[status(thm)],[f69]) ).
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,
member(universal_class,x),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f251,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f118,f115]) ).
fof(f254,plain,
! [X0] : member(singleton(X0),universal_class),
inference(paramodulation,[status(thm)],[f129,f128]) ).
fof(f261,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f129,f123]) ).
fof(f262,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f261]) ).
fof(f264,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f129,f125]) ).
fof(f271,plain,
! [X0] :
( regular(singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(resolution,[status(thm)],[f188,f262]) ).
fof(f295,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(f319,plain,
! [X0,X1] :
( X1 = null_class
| member(X0,null_class)
| ~ member(X0,regular(X1))
| ~ member(X0,X1) ),
inference(paramodulation,[status(thm)],[f189,f145]) ).
fof(f322,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f271,f188]) ).
fof(f324,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f322]) ).
fof(f379,plain,
! [X0,X1] :
( member(apply(X0,X1),universal_class)
| ~ member(image(X0,singleton(X1)),universal_class) ),
inference(paramodulation,[status(thm)],[f190,f176]) ).
fof(f580,plain,
! [X0] :
( apply(choice,singleton(X0)) = X0
| singleton(X0) = null_class
| ~ member(singleton(X0),universal_class) ),
inference(resolution,[status(thm)],[f192,f262]) ).
fof(f583,plain,
! [X0] :
( apply(choice,singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(forward_subsumption_resolution,[status(thm)],[f580,f254]) ).
fof(f1094,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f295,f117]) ).
fof(f1122,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f1094]) ).
fof(f1175,plain,
! [X0,X1,X2] : subclass(restrict(X0,X1,X2),X0),
inference(paramodulation,[status(thm)],[f150,f1122]) ).
fof(f1176,plain,
! [X0] :
( X0 = null_class
| subclass(null_class,X0) ),
inference(paramodulation,[status(thm)],[f189,f1122]) ).
fof(f1203,plain,
! [X0] :
( X0 = null_class
| ~ subclass(X0,null_class)
| X0 = null_class ),
inference(resolution,[status(thm)],[f1176,f121]) ).
fof(f1207,plain,
! [X0] :
( ~ subclass(X0,null_class)
| X0 = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f1203]) ).
fof(f1209,plain,
! [X0,X1] : restrict(null_class,X0,X1) = null_class,
inference(resolution,[status(thm)],[f1207,f1175]) ).
fof(f1342,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(resolution,[status(thm)],[f1209,f152]) ).
fof(f1359,plain,
domain_of(null_class) = null_class,
inference(resolution,[status(thm)],[f1342,f188]) ).
fof(f1368,plain,
! [X0] : ~ member(X0,null_class),
inference(backward_demodulation,[status(thm)],[f1359,f1342]) ).
fof(f1436,plain,
! [X0,X1] :
( X1 = null_class
| ~ member(X0,regular(X1))
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f319,f1368]) ).
fof(f1448,plain,
! [X0,X1] :
( singleton(X1) = null_class
| singleton(X1) = null_class
| ~ member(X0,X1)
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f271,f1436]) ).
fof(f1450,plain,
! [X0,X1] :
( singleton(X1) = null_class
| ~ member(X0,X1)
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f1448]) ).
fof(f2327,plain,
! [X0,X1] :
( ~ member(singleton(X1),universal_class)
| ~ function(X0)
| member(apply(X0,X1),universal_class) ),
inference(resolution,[status(thm)],[f379,f187]) ).
fof(f2331,plain,
! [X0,X1] :
( ~ function(X0)
| member(apply(X0,X1),universal_class) ),
inference(forward_subsumption_resolution,[status(thm)],[f2327,f254]) ).
fof(f2335,plain,
! [X0] :
( singleton(X0) = null_class
| ~ function(choice)
| member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f583,f2331]) ).
fof(f2336,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,universal_class) ),
inference(forward_subsumption_resolution,[status(thm)],[f2335,f191]) ).
fof(f2906,plain,
! [X0] :
( singleton(X0) = null_class
| singleton(X0) = null_class
| ~ member(X0,X0) ),
inference(resolution,[status(thm)],[f1450,f324]) ).
fof(f2912,plain,
! [X0] :
( singleton(X0) = null_class
| ~ member(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2906]) ).
fof(f2937,plain,
( singleton(universal_class) = null_class
| singleton(universal_class) = null_class ),
inference(resolution,[status(thm)],[f2912,f2336]) ).
fof(f2944,plain,
singleton(universal_class) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f2937]) ).
fof(f2978,plain,
( member(universal_class,null_class)
| ~ member(universal_class,universal_class) ),
inference(paramodulation,[status(thm)],[f2944,f264]) ).
fof(f3002,plain,
~ member(universal_class,universal_class),
inference(forward_subsumption_resolution,[status(thm)],[f2978,f1368]) ).
fof(f3005,plain,
! [X0] : ~ member(universal_class,X0),
inference(resolution,[status(thm)],[f3002,f251]) ).
fof(f3007,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f245,f3005]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET503-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.42 % Computer : n020.cluster.edu
% 0.15/5.42 % Model : x86_64 x86_64
% 0.15/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.42 % Memory : 8046.5625MB
% 0.15/5.42 % OS : Linux 6.8.0-71-generic
% 0.15/5.42 % CPULimit : 300
% 0.15/5.42 % WCLimit : 300
% 0.15/5.42 % DateTime : Mon Sep 21 05:23:08 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.45 % Drodi V4.1.1
% 0.20/5.75 % Refutation found
% 0.20/5.75 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/5.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/5.79 % Elapsed time: 0.347787 seconds
% 0.20/5.79 % CPU time: 2.288723 seconds
% 0.20/5.79 % Total memory used: 135.957 MB
% 0.20/5.79 % Net memory used: 132.934 MB
%------------------------------------------------------------------------------