%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU320+1 : TPTP v9.3.1. Released v3.3.0.
% 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 02:20:09 PM UTC 2026
% Result : Theorem 0.14s 0.58s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 87 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 35 ~; 33 |; 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 : 30 ( 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [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(f13,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(f14,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)],[f13]) ).
fof(f16,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0,X1] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f26,plain,
! [A,B] :
( subset_complement(A,subset_complement(A,B)) = B
| ~ element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
! [X0,X1] :
( subset_complement(X1,subset_complement(X1,X0)) = X0
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f30,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)],[f12]) ).
fof(f31,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)],[f30]) ).
fof(f32,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)],[f31]) ).
fof(f33,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)],[f31]) ).
fof(f34,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)],[f14]) ).
fof(f35,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)],[f34]) ).
fof(f36,plain,
( ( ~ closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)
| ~ open_subset(sK4_skl,sK3_skl) )
& ( closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)
| open_subset(sK4_skl,sK3_skl) )
& element(sK4_skl,powerset(the_carrier(sK3_skl)))
& top_str(sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f35]) ).
fof(f37,plain,
top_str(sK3_skl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
element(sK4_skl,powerset(the_carrier(sK3_skl))),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
( closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)
| open_subset(sK4_skl,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f40,plain,
( ~ closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)
| ~ open_subset(sK4_skl,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f46,plain,
subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)) = sK4_skl,
inference(resolution,[status(thm)],[f27,f38]) ).
fof(f47,plain,
element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl))),
inference(resolution,[status(thm)],[f17,f38]) ).
fof(f51,plain,
( open_subset(subset_complement(the_carrier(sK3_skl),subset_complement(the_carrier(sK3_skl),sK4_skl)),sK3_skl)
| ~ closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)
| ~ top_str(sK3_skl) ),
inference(resolution,[status(thm)],[f32,f47]) ).
fof(f53,plain,
( open_subset(sK4_skl,sK3_skl)
| ~ closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)
| ~ top_str(sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f46,f51]) ).
fof(f54,plain,
( open_subset(sK4_skl,sK3_skl)
| ~ closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f37]) ).
fof(f56,plain,
~ closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl),
inference(backward_subsumption_resolution,[status(thm)],[f40,f57]) ).
fof(f57,plain,
open_subset(sK4_skl,sK3_skl),
inference(forward_subsumption_resolution,[status(thm)],[f54,f39]) ).
fof(f58,plain,
( ~ open_subset(sK4_skl,sK3_skl)
| closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)
| ~ element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl)))
| ~ top_str(sK3_skl) ),
inference(paramodulation,[status(thm)],[f46,f33]) ).
fof(f59,plain,
( ~ open_subset(sK4_skl,sK3_skl)
| closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl)
| ~ element(subset_complement(the_carrier(sK3_skl),sK4_skl),powerset(the_carrier(sK3_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f37]) ).
fof(f60,plain,
( ~ open_subset(sK4_skl,sK3_skl)
| closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f59,f47]) ).
fof(f61,plain,
closed_subset(subset_complement(the_carrier(sK3_skl),sK4_skl),sK3_skl),
inference(resolution,[status(thm)],[f60,f57]) ).
fof(f62,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f61,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU320+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.55 % Computer : n007.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.09/0.55 % CPULimit : 300
% 0.09/0.55 % WCLimit : 300
% 0.09/0.55 % DateTime : Mon Sep 21 06:09:22 UTC 2026
% 0.09/0.55 % CPUTime :
% 0.09/0.56 % Drodi V4.1.1
% 0.14/0.58 % Refutation found
% 0.14/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.60 % Elapsed time: 0.046771 seconds
% 0.14/0.60 % CPU time: 0.141873 seconds
% 0.14/0.60 % Total memory used: 80.362 MB
% 0.14/0.60 % Net memory used: 79.949 MB
%------------------------------------------------------------------------------