%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM071-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 01:38:37 PM UTC 2026
% Result : Unsatisfiable 133.00s 17.26s
% Output : CNFRefutation 133.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 61 ( 16 unt; 0 def)
% Number of atoms : 137 ( 31 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 147 ( 71 ~; 76 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 95 ( 95 !; 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(f8,axiom,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
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(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f125,axiom,
! [Xr,Y,U,V] :
( member(least(Xr,U),U)
| ~ member(V,U)
| ~ subclass(U,Y)
| ~ well_ordering(Xr,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f127,axiom,
! [Xr,Y,U,V] :
( ~ member(ordered_pair(V,least(Xr,U)),Xr)
| ~ member(V,U)
| ~ subclass(U,Y)
| ~ well_ordering(Xr,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f159,negated_conjecture,
well_ordering(xr,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f160,negated_conjecture,
member(ordered_pair(u,u),xr),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f161,negated_conjecture,
member(u,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f162,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f163,plain,
! [X0,X1,X2] :
( ~ member(X2,X0)
| member(X2,X1)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f164,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f165,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f166,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f170,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f171,plain,
! [X0,X1,X2] :
( X0 = X1
| X2 = X0
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f174,plain,
! [Y] :
( ! [X] : member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f175,plain,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f177,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f306,plain,
! [Xr,U] :
( member(least(Xr,U),U)
| ! [V] : ~ member(V,U)
| ! [Y] :
( ~ subclass(U,Y)
| ~ well_ordering(Xr,Y) ) ),
inference(miniscoping,[status(thm)],[f125]) ).
fof(f307,plain,
! [X0,X1,X2,X3] :
( ~ subclass(X2,X1)
| ~ member(X3,X2)
| member(least(X0,X2),X2)
| ~ well_ordering(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f306]) ).
fof(f310,plain,
! [Xr,U,V] :
( ~ member(ordered_pair(V,least(Xr,U)),Xr)
| ~ member(V,U)
| ! [Y] :
( ~ subclass(U,Y)
| ~ well_ordering(Xr,Y) ) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f311,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X2,least(X3,X0)),X3)
| ~ well_ordering(X3,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f310]) ).
fof(f349,plain,
well_ordering(xr,y),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f350,plain,
member(ordered_pair(u,u),xr),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f351,plain,
member(u,y),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f385,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f177,f175]) ).
fof(f395,plain,
! [X0,X1] :
( X0 = X1
| X1 = X0
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f177,f171]) ).
fof(f396,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f395]) ).
fof(f405,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| not_subclass_element(singleton(X0),X1) = X0 ),
inference(resolution,[status(thm)],[f164,f396]) ).
fof(f460,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f163,f166]) ).
fof(f509,plain,
! [X0,X1] :
( member(least(xr,X1),X1)
| ~ subclass(X1,y)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f307,f349]) ).
fof(f570,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| member(least(xr,singleton(X0)),singleton(X0))
| not_subclass_element(singleton(X0),y) = X0 ),
inference(resolution,[status(thm)],[f405,f509]) ).
fof(f573,plain,
! [X0,X1] :
( X1 = least(xr,singleton(X1))
| X1 = not_subclass_element(singleton(X1),y)
| ~ member(X0,singleton(X1)) ),
inference(resolution,[status(thm)],[f570,f396]) ).
fof(f591,plain,
! [X0] :
( ~ member(X0,universal_class)
| X0 = not_subclass_element(singleton(X0),y)
| least(xr,singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[f573,f385]) ).
fof(f619,plain,
! [X0,X1] :
( X0 = not_subclass_element(singleton(X0),y)
| ~ member(X0,X1)
| X0 = least(xr,singleton(X0)) ),
inference(resolution,[status(thm)],[f591,f460]) ).
fof(f653,plain,
( least(xr,singleton(u)) = u
| not_subclass_element(singleton(u),y) = u ),
inference(resolution,[status(thm)],[f619,f351]) ).
fof(f6552,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ subclass(X1,y)
| ~ member(ordered_pair(X0,least(xr,X1)),xr) ),
inference(resolution,[status(thm)],[f311,f349]) ).
fof(f6558,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,least(xr,singleton(X0))),xr)
| ~ member(X1,singleton(X0))
| not_subclass_element(singleton(X0),y) = X0 ),
inference(resolution,[status(thm)],[f6552,f405]) ).
fof(f7137,plain,
! [X0] :
( X0 = not_subclass_element(singleton(X0),y)
| ~ member(ordered_pair(X0,least(xr,singleton(X0))),xr)
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[f6558,f385]) ).
fof(f7399,plain,
! [X0,X1] :
( ~ member(X0,X1)
| X0 = not_subclass_element(singleton(X0),y)
| ~ member(ordered_pair(X0,least(xr,singleton(X0))),xr) ),
inference(resolution,[status(thm)],[f7137,f460]) ).
fof(f7451,plain,
! [X0] :
( not_subclass_element(singleton(u),y) = u
| ~ member(u,X0)
| u = not_subclass_element(singleton(u),y)
| ~ member(ordered_pair(u,u),xr) ),
inference(paramodulation,[status(thm)],[f653,f7399]) ).
fof(f7469,plain,
! [X0] :
( ~ member(u,X0)
| u = not_subclass_element(singleton(u),y)
| ~ member(ordered_pair(u,u),xr) ),
inference(duplicate_literals_removal,[status(thm)],[f7451]) ).
fof(f7471,plain,
! [X0] :
( u = not_subclass_element(singleton(u),y)
| ~ member(u,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f7469,f350]) ).
fof(f7509,plain,
not_subclass_element(singleton(u),y) = u,
inference(resolution,[status(thm)],[f7471,f351]) ).
fof(f7556,plain,
( subclass(singleton(u),y)
| ~ member(u,y) ),
inference(paramodulation,[status(thm)],[f7509,f165]) ).
fof(f7557,plain,
subclass(singleton(u),y),
inference(forward_subsumption_resolution,[status(thm)],[f7556,f351]) ).
fof(f7558,plain,
! [X0] :
( ~ member(X0,singleton(u))
| ~ member(ordered_pair(X0,least(xr,singleton(u))),xr) ),
inference(resolution,[status(thm)],[f7557,f6552]) ).
fof(f7560,plain,
! [X0] :
( ~ member(X0,singleton(u))
| member(least(xr,singleton(u)),singleton(u)) ),
inference(resolution,[status(thm)],[f7557,f509]) ).
fof(f7667,plain,
( member(least(xr,singleton(u)),singleton(u))
| ~ member(u,universal_class) ),
inference(resolution,[status(thm)],[f7560,f385]) ).
fof(f7830,plain,
! [X0] :
( member(least(xr,singleton(u)),singleton(u))
| ~ member(u,X0) ),
inference(resolution,[status(thm)],[f7667,f460]) ).
fof(f7855,plain,
! [X0] :
( u = least(xr,singleton(u))
| ~ member(u,X0) ),
inference(resolution,[status(thm)],[f7830,f396]) ).
fof(f7875,plain,
u = least(xr,singleton(u)),
inference(resolution,[status(thm)],[f7855,f351]) ).
fof(f7902,plain,
! [X0] :
( ~ member(u,X0)
| member(u,singleton(u)) ),
inference(backward_demodulation,[status(thm)],[f7875,f7830]) ).
fof(f7934,plain,
! [X0] :
( ~ member(ordered_pair(X0,u),xr)
| ~ member(X0,singleton(u)) ),
inference(backward_demodulation,[status(thm)],[f7875,f7558]) ).
fof(f8142,plain,
~ member(u,singleton(u)),
inference(resolution,[status(thm)],[f7934,f350]) ).
fof(f8146,plain,
! [X0] : ~ member(u,X0),
inference(backward_subsumption_resolution,[status(thm)],[f7902,f8142]) ).
fof(f8160,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f351,f8146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM071-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 01:57:26 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 133.00/17.26 % Refutation found
% 133.00/17.26 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 133.00/17.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.52/17.56 % Elapsed time: 17.189387 seconds
% 8.52/17.56 % CPU time: 134.251808 seconds
% 8.52/17.56 % Total memory used: 611.150 MB
% 8.52/17.56 % Net memory used: 547.342 MB
%------------------------------------------------------------------------------