%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU320+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 : Fri Sep 25 02:51:43 PM UTC 2026
% Result : Theorem 0.16s 15.82s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 7 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 79 ( 31 ~; 28 |; 10 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,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/sandbox2/benchmark/theBenchmark.p',t29_tops_1) ).
fof(f11_nnf,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)],[f11]) ).
fof(f11_sk,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(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c12,plain,
( ~ 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(esa)],[f11_sk]) ).
fof(f12,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/sandbox2/benchmark/theBenchmark.p',t30_tops_1) ).
fof(f12_neg,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)],[f12]) ).
fof(f12_nnf,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)],[f12_neg]) ).
fof(f12_sk,plain,
( ( ( closed_subset(subset_complement(the_carrier(sk3),sk4),sk3)
& ~ open_subset(sk4,sk3) )
| ( ~ closed_subset(subset_complement(the_carrier(sk3),sk4),sk3)
& open_subset(sk4,sk3) ) )
& element(sk4,powerset(the_carrier(sk3)))
& top_str(sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f12_nnf]) ).
cnf(c13,plain,
top_str(sk3),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p53,plain,
( ~ open_subset(subset_complement(the_carrier(sk3),X0),sk3)
| closed_subset(X0,sk3)
| ~ element(X0,powerset(the_carrier(sk3))) ),
inference(resolution,[status(thm)],[c12,c13]) ).
fof(f1,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f1_nnf,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,A] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(c14,plain,
element(sk4,powerset(the_carrier(sk3))),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p21,plain,
element(subset_complement(the_carrier(sk3),sk4),powerset(the_carrier(sk3))),
inference(resolution,[status(thm)],[c1,c14]) ).
cnf(p59,plain,
( ~ open_subset(sk4,sk3)
| closed_subset(subset_complement(the_carrier(sk3),sk4),sk3) ),
inference(resolution,[status(thm)],[p53,p21]) ).
cnf(c11,plain,
( 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(esa)],[f11_sk]) ).
cnf(p48,plain,
( open_subset(subset_complement(the_carrier(sk3),X0),sk3)
| ~ closed_subset(X0,sk3)
| ~ element(X0,powerset(the_carrier(sk3))) ),
inference(resolution,[status(thm)],[c11,c13]) ).
cnf(p51,plain,
( open_subset(sk4,sk3)
| ~ closed_subset(subset_complement(the_carrier(sk3),sk4),sk3) ),
inference(resolution,[status(thm)],[p48,p21]) ).
cnf(c16,plain,
( closed_subset(subset_complement(the_carrier(sk3),sk4),sk3)
| open_subset(sk4,sk3) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p55,plain,
( open_subset(sk4,sk3)
| open_subset(sk4,sk3) ),
inference(resolution,[status(thm)],[p51,c16]) ).
cnf(p56,plain,
open_subset(sk4,sk3),
inference(factoring,[status(thm)],[p55]) ).
cnf(p61,plain,
closed_subset(subset_complement(the_carrier(sk3),sk4),sk3),
inference(resolution,[status(thm)],[p59,p56]) ).
cnf(c17,plain,
( ~ open_subset(sk4,sk3)
| ~ closed_subset(subset_complement(the_carrier(sk3),sk4),sk3) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p62,plain,
~ open_subset(sk4,sk3),
inference(resolution,[status(thm)],[p61,c17]) ).
cnf(p68,plain,
$false,
inference(resolution,[status(thm)],[p62,p56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU320+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/15.39 % Computer : n008.cluster.edu
% 0.10/15.39 % Model : x86_64 x86_64
% 0.10/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.39 % Memory : 8046.5625MB
% 0.10/15.39 % OS : Linux 6.8.0-71-generic
% 0.10/15.39 % CPULimit : 300
% 0.10/15.39 % WCLimit : 300
% 0.10/15.39 % DateTime : Thu Sep 24 13:42:12 UTC 2026
% 0.14/15.40 % CPUTime :
% 0.14/15.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/15.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/15.82 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------