%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU320+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:20:09 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 86 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 92 ( 38 ~; 32 |; 9 &)
% ( 4 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f145,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f247,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f418,lemma,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f425,conjecture,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( open_subset(B,A)
<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f426,negated_conjecture,
~ ! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( open_subset(B,A)
<=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
inference(negated_conjecture,[status(cth)],[f425]) ).
fof(f1219,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f145]) ).
fof(f1220,plain,
! [X0,X1] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f1219]) ).
fof(f1499,plain,
! [A,B] :
( subset_complement(A,subset_complement(A,B)) = B
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f247]) ).
fof(f1500,plain,
! [X0,X1] :
( subset_complement(X1,subset_complement(X1,X0)) = X0
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f1499]) ).
fof(f2330,plain,
! [A] :
( ! [B] :
( ( closed_subset(B,A)
<=> open_subset(subset_complement(the_carrier(A),B),A) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f418]) ).
fof(f2331,plain,
! [A] :
( ! [B] :
( ( ( ~ open_subset(subset_complement(the_carrier(A),B),A)
| closed_subset(B,A) )
& ( open_subset(subset_complement(the_carrier(A),B),A)
| ~ closed_subset(B,A) ) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(NNF_transformation,[status(thm)],[f2330]) ).
fof(f2332,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[status(thm)],[f2331]) ).
fof(f2333,plain,
! [X0,X1] :
( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[status(thm)],[f2331]) ).
fof(f2348,plain,
? [A] :
( ? [B] :
( ( open_subset(B,A)
<~> closed_subset(subset_complement(the_carrier(A),B),A) )
& element(B,powerset(the_carrier(A))) )
& top_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f426]) ).
fof(f2349,plain,
? [A] :
( ? [B] :
( ( ~ closed_subset(subset_complement(the_carrier(A),B),A)
| ~ open_subset(B,A) )
& ( closed_subset(subset_complement(the_carrier(A),B),A)
| open_subset(B,A) )
& element(B,powerset(the_carrier(A))) )
& top_str(A) ),
inference(NNF_transformation,[status(thm)],[f2348]) ).
fof(f2350,plain,
( ( ~ closed_subset(subset_complement(the_carrier(sK286_skl),sK287_skl),sK286_skl)
| ~ open_subset(sK287_skl,sK286_skl) )
& ( closed_subset(subset_complement(the_carrier(sK286_skl),sK287_skl),sK286_skl)
| open_subset(sK287_skl,sK286_skl) )
& element(sK287_skl,powerset(the_carrier(sK286_skl)))
& top_str(sK286_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK286_skl,sK287_skl]),skolemize(A,sK286_skl),skolemize(B,sK287_skl)],[f2349]) ).
fof(f2351,plain,
top_str(sK286_skl),
inference(cnf_transformation,[status(thm)],[f2350]) ).
fof(f2352,plain,
element(sK287_skl,powerset(the_carrier(sK286_skl))),
inference(cnf_transformation,[status(thm)],[f2350]) ).
fof(f2353,plain,
( closed_subset(subset_complement(the_carrier(sK286_skl),sK287_skl),sK286_skl)
| open_subset(sK287_skl,sK286_skl) ),
inference(cnf_transformation,[status(thm)],[f2350]) ).
fof(f2354,plain,
( ~ closed_subset(subset_complement(the_carrier(sK286_skl),sK287_skl),sK286_skl)
| ~ open_subset(sK287_skl,sK286_skl) ),
inference(cnf_transformation,[status(thm)],[f2350]) ).
fof(f3264,plain,
subset_complement(the_carrier(sK286_skl),subset_complement(the_carrier(sK286_skl),sK287_skl)) = sK287_skl,
inference(resolution,[status(thm)],[f1500,f2352]) ).
fof(f3265,plain,
element(subset_complement(the_carrier(sK286_skl),sK287_skl),powerset(the_carrier(sK286_skl))),
inference(resolution,[status(thm)],[f1220,f2352]) ).
fof(f3271,plain,
! [X0] :
( open_subset(subset_complement(the_carrier(sK286_skl),X0),sK286_skl)
| ~ closed_subset(X0,sK286_skl)
| ~ element(X0,powerset(the_carrier(sK286_skl))) ),
inference(resolution,[status(thm)],[f2332,f2351]) ).
fof(f3274,plain,
( open_subset(sK287_skl,sK286_skl)
| ~ closed_subset(subset_complement(the_carrier(sK286_skl),sK287_skl),sK286_skl)
| ~ element(subset_complement(the_carrier(sK286_skl),sK287_skl),powerset(the_carrier(sK286_skl))) ),
inference(paramodulation,[status(thm)],[f3264,f3271]) ).
fof(f3276,plain,
( open_subset(sK287_skl,sK286_skl)
| ~ closed_subset(subset_complement(the_carrier(sK286_skl),sK287_skl),sK286_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f3274,f3265]) ).
fof(f3277,plain,
~ closed_subset(subset_complement(the_carrier(sK286_skl),sK287_skl),sK286_skl),
inference(backward_subsumption_resolution,[status(thm)],[f2354,f3278]) ).
fof(f3278,plain,
open_subset(sK287_skl,sK286_skl),
inference(forward_subsumption_resolution,[status(thm)],[f3276,f2353]) ).
fof(f3281,plain,
( ~ open_subset(subset_complement(the_carrier(sK286_skl),subset_complement(the_carrier(sK286_skl),sK287_skl)),sK286_skl)
| ~ element(subset_complement(the_carrier(sK286_skl),sK287_skl),powerset(the_carrier(sK286_skl)))
| ~ top_str(sK286_skl) ),
inference(resolution,[status(thm)],[f3277,f2333]) ).
fof(f3282,plain,
( ~ open_subset(sK287_skl,sK286_skl)
| ~ element(subset_complement(the_carrier(sK286_skl),sK287_skl),powerset(the_carrier(sK286_skl)))
| ~ top_str(sK286_skl) ),
inference(forward_demodulation,[status(thm)],[f3264,f3281]) ).
fof(f3283,plain,
( ~ open_subset(sK287_skl,sK286_skl)
| ~ element(subset_complement(the_carrier(sK286_skl),sK287_skl),powerset(the_carrier(sK286_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f3282,f2351]) ).
fof(f3293,plain,
~ open_subset(sK287_skl,sK286_skl),
inference(forward_subsumption_resolution,[status(thm)],[f3283,f3265]) ).
fof(f3294,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f3278,f3293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU320+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 06:11:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.39 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.48 % Elapsed time: 0.114350 seconds
% 0.13/0.48 % CPU time: 0.358372 seconds
% 0.13/0.48 % Total memory used: 176.041 MB
% 0.13/0.48 % Net memory used: 175.189 MB
%------------------------------------------------------------------------------