%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM142-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 01:38:41 PM UTC 2026
% Result : Unsatisfiable 44.72s 6.28s
% Output : CNFRefutation 22.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 16 unt; 0 def)
% Number of atoms : 83 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 67 ( 29 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 79 ( 79 !; 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(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ 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(f25,axiom,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [X] : union(X,singleton(X)) = successor(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f159,negated_conjecture,
~ subclass(x,successor(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f160,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f161,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f162,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f163,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f164,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f167,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f187,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f188,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f192,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f193,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f194,plain,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f211,plain,
! [X0] : union(X0,singleton(X0)) = successor(X0),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f347,plain,
~ subclass(x,successor(x)),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f354,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f161,f164]) ).
fof(f360,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1) ),
inference(resolution,[status(thm)],[f162,f354]) ).
fof(f481,plain,
! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[f192,f162]) ).
fof(f607,plain,
! [X0,X1] :
( subclass(X0,complement(X1))
| member(not_subclass_element(X0,complement(X1)),X1)
| ~ member(not_subclass_element(X0,complement(X1)),universal_class) ),
inference(resolution,[status(thm)],[f193,f163]) ).
fof(f611,plain,
! [X0,X1] :
( subclass(X0,complement(X1))
| member(not_subclass_element(X0,complement(X1)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f607,f360]) ).
fof(f627,plain,
! [X0,X1,X2] :
( member(not_subclass_element(X0,complement(intersection(X1,X2))),X1)
| subclass(X0,complement(intersection(X1,X2))) ),
inference(resolution,[status(thm)],[f611,f188]) ).
fof(f629,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,complement(complement(X1))),X1)
| subclass(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[f611,f192]) ).
fof(f3723,plain,
! [X0,X1] :
( member(not_subclass_element(complement(complement(X0)),X1),X0)
| ~ member(not_subclass_element(complement(complement(X0)),X1),universal_class)
| subclass(complement(complement(X0)),X1) ),
inference(resolution,[status(thm)],[f481,f193]) ).
fof(f3759,plain,
! [X0,X1] :
( member(not_subclass_element(complement(complement(X0)),X1),X0)
| subclass(complement(complement(X0)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3723,f360]) ).
fof(f4832,plain,
! [X0,X1] :
( subclass(complement(X0),complement(intersection(X0,X1)))
| subclass(complement(X0),complement(intersection(X0,X1))) ),
inference(resolution,[status(thm)],[f627,f481]) ).
fof(f4895,plain,
! [X0,X1] : subclass(complement(X0),complement(intersection(X0,X1))),
inference(duplicate_literals_removal,[status(thm)],[f4832]) ).
fof(f4942,plain,
! [X0,X1] : subclass(complement(complement(X0)),union(X0,X1)),
inference(paramodulation,[status(thm)],[f194,f4895]) ).
fof(f4992,plain,
! [X0] : subclass(complement(complement(X0)),successor(X0)),
inference(paramodulation,[status(thm)],[f211,f4942]) ).
fof(f5271,plain,
! [X0] :
( subclass(X0,complement(complement(X0)))
| subclass(X0,complement(complement(X0))) ),
inference(resolution,[status(thm)],[f629,f162]) ).
fof(f5318,plain,
! [X0] : subclass(X0,complement(complement(X0))),
inference(duplicate_literals_removal,[status(thm)],[f5271]) ).
fof(f5339,plain,
! [X0] :
( complement(complement(X0)) = X0
| ~ subclass(complement(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f5318,f167]) ).
fof(f33686,plain,
! [X0] :
( subclass(complement(complement(X0)),X0)
| subclass(complement(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f3759,f163]) ).
fof(f33855,plain,
! [X0] : subclass(complement(complement(X0)),X0),
inference(duplicate_literals_removal,[status(thm)],[f33686]) ).
fof(f33938,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_subsumption_resolution,[status(thm)],[f5339,f33855]) ).
fof(f34091,plain,
! [X0] : subclass(X0,successor(X0)),
inference(backward_demodulation,[status(thm)],[f33938,f4992]) ).
fof(f34214,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f347,f34091]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM142-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.52 % Computer : n007.cluster.edu
% 0.09/0.52 % Model : x86_64 x86_64
% 0.09/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.52 % Memory : 8046.5625MB
% 0.09/0.52 % OS : Linux 6.8.0-71-generic
% 0.09/0.52 % CPULimit : 300
% 0.09/0.52 % WCLimit : 300
% 0.09/0.52 % DateTime : Mon Sep 21 02:05:35 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.53 % Drodi V4.1.1
% 44.72/6.28 % Refutation found
% 44.72/6.28 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 44.72/6.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 22.95/6.34 % Elapsed time: 5.795873 seconds
% 22.95/6.34 % CPU time: 45.726502 seconds
% 22.95/6.34 % Total memory used: 439.384 MB
% 22.95/6.34 % Net memory used: 388.516 MB
%------------------------------------------------------------------------------