%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU337+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 : Tue Sep 29 12:48:24 PM UTC 2026
% Result : Theorem 1.84s 1.75s
% Output : Refutation 5.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 13
% Syntax : Number of formulae : 117 ( 9 unt; 0 def)
% Number of atoms : 495 ( 15 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 647 ( 269 ~; 287 |; 49 &)
% ( 16 <=>; 25 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 219 ( 206 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( open_subsets(X1,X0)
<=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( in(X2,X1)
=> open_subset(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_2) ).
fof(f18,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( closed_subsets(X1,X0)
<=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( in(X2,X1)
=> closed_subset(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tops_2) ).
fof(f19,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ! [X2] :
( element(X2,powerset(powerset(X0)))
=> ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( element(X3,powerset(X0))
=> ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(f22,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f23,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f33,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f39,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( open_subsets(X1,X0)
<=> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_tops_2) ).
fof(f40,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( open_subsets(X1,X0)
<=> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f41,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f42,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tops_1) ).
fof(f43,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f44,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( open_subset(X1,X0)
<=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tops_1) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f49,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f51,plain,
? [X0] :
( ? [X1] :
( ( open_subsets(X1,X0)
<~> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& top_str(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f53,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f23]) ).
fof(f54,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) )
| ~ element(X3,powerset(X0)) ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f19]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( open_subsets(X1,X0)
<=> ! [X2] :
( open_subset(X2,X0)
| ~ in(X2,X1)
| ~ element(X2,powerset(the_carrier(X0))) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ( open_subsets(X1,X0)
<=> ! [X2] :
( open_subset(X2,X0)
| ~ in(X2,X1)
| ~ element(X2,powerset(the_carrier(X0))) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ top_str(X0) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( closed_subsets(X1,X0)
<=> ! [X2] :
( closed_subset(X2,X0)
| ~ in(X2,X1)
| ~ element(X2,powerset(the_carrier(X0))) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( closed_subsets(X1,X0)
<=> ! [X2] :
( closed_subset(X2,X0)
| ~ in(X2,X1)
| ~ element(X2,powerset(the_carrier(X0))) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ top_str(X0) ),
inference(flattening,[],[f57]) ).
fof(f60,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f61,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f63,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f46]) ).
fof(f64,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f66,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f69,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ( open_subset(X1,X0)
<=> closed_subset(subset_complement(the_carrier(X0),X1),X0) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f73,plain,
? [X0] :
( ? [X1] :
( ( ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ open_subsets(X1,X0) )
& ( closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| open_subsets(X1,X0) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& top_str(X0) ),
inference(nnf_transformation,[],[f51]) ).
fof(f74,plain,
? [X0] :
( ? [X1] :
( ( ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ open_subsets(X1,X0) )
& ( closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| open_subsets(X1,X0) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& top_str(X0) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
( ( ~ closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| ~ open_subsets(sK1,sK0) )
& ( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| open_subsets(sK1,sK0) )
& element(sK1,powerset(powerset(the_carrier(sK0))))
& top_str(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(nnf_transformation,[],[f54]) ).
fof(f77,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X0,X4),X1) )
& ( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ( ( ~ in(subset_complement(X0,sK2(X0,X1,X2)),X1)
| ~ in(sK2(X0,X1,X2),X2) )
& ( in(subset_complement(X0,sK2(X0,X1,X2)),X1)
| in(sK2(X0,X1,X2),X2) )
& element(sK2(X0,X1,X2),powerset(X0)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X0,X4),X1) )
& ( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f78]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ( ( open_subsets(X1,X0)
| ? [X2] :
( ~ open_subset(X2,X0)
& in(X2,X1)
& element(X2,powerset(the_carrier(X0))) ) )
& ( ! [X2] :
( open_subset(X2,X0)
| ~ in(X2,X1)
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ open_subsets(X1,X0) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f56]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( ( open_subsets(X1,X0)
| ? [X2] :
( ~ open_subset(X2,X0)
& in(X2,X1)
& element(X2,powerset(the_carrier(X0))) ) )
& ( ! [X3] :
( open_subset(X3,X0)
| ~ in(X3,X1)
| ~ element(X3,powerset(the_carrier(X0))) )
| ~ open_subsets(X1,X0) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ top_str(X0) ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ( ( open_subsets(X1,X0)
| ( ~ open_subset(sK5(X0,X1),X0)
& in(sK5(X0,X1),X1)
& element(sK5(X0,X1),powerset(the_carrier(X0))) ) )
& ( ! [X3] :
( open_subset(X3,X0)
| ~ in(X3,X1)
| ~ element(X3,powerset(the_carrier(X0))) )
| ~ open_subsets(X1,X0) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ top_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f83]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subsets(X1,X0)
| ? [X2] :
( ~ closed_subset(X2,X0)
& in(X2,X1)
& element(X2,powerset(the_carrier(X0))) ) )
& ( ! [X2] :
( closed_subset(X2,X0)
| ~ in(X2,X1)
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ closed_subsets(X1,X0) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f58]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subsets(X1,X0)
| ? [X2] :
( ~ closed_subset(X2,X0)
& in(X2,X1)
& element(X2,powerset(the_carrier(X0))) ) )
& ( ! [X3] :
( closed_subset(X3,X0)
| ~ in(X3,X1)
| ~ element(X3,powerset(the_carrier(X0))) )
| ~ closed_subsets(X1,X0) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ top_str(X0) ),
inference(rectify,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subsets(X1,X0)
| ( ~ closed_subset(sK6(X0,X1),X0)
& in(sK6(X0,X1),X1)
& element(sK6(X0,X1),powerset(the_carrier(X0))) ) )
& ( ! [X3] :
( closed_subset(X3,X0)
| ~ in(X3,X1)
| ~ element(X3,powerset(the_carrier(X0))) )
| ~ closed_subsets(X1,X0) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ top_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f86]) ).
fof(f88,plain,
! [X0] :
( ! [X1] :
( ( ( open_subset(X1,X0)
| ~ closed_subset(subset_complement(the_carrier(X0),X1),X0) )
& ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ open_subset(X1,X0) ) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f70]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subset(X1,X0)
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0) )
& ( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0) ) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f71]) ).
fof(f92,plain,
top_str(sK0),
inference(cnf_transformation,[],[f75]) ).
fof(f93,plain,
element(sK1,powerset(powerset(the_carrier(sK0)))),
inference(cnf_transformation,[],[f75]) ).
fof(f94,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| open_subsets(sK1,sK0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f95,plain,
( ~ closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| ~ open_subsets(sK1,sK0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f97,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f53]) ).
fof(f98,plain,
! [X2,X0,X1,X4] :
( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2)
| ~ element(X4,powerset(X0))
| complements_of_subsets(X0,X1) != X2
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f79]) ).
fof(f99,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(subset_complement(X0,X4),X1)
| ~ element(X4,powerset(X0))
| complements_of_subsets(X0,X1) != X2
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f79]) ).
fof(f105,plain,
! [X3,X0,X1] :
( open_subset(X3,X0)
| ~ in(X3,X1)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ open_subsets(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f107,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| in(sK5(X0,X1),X1)
| open_subsets(X1,X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f108,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ open_subset(sK5(X0,X1),X0)
| open_subsets(X1,X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f109,plain,
! [X3,X0,X1] :
( closed_subset(X3,X0)
| ~ in(X3,X1)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ closed_subsets(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f111,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| in(sK6(X0,X1),X1)
| closed_subsets(X1,X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f112,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ closed_subset(sK6(X0,X1),X0)
| closed_subsets(X1,X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f114,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f115,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f118,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f119,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f121,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f123,plain,
! [X0,X1] :
( ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
| open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f125,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,[],[f89]) ).
fof(f131,plain,
! [X0,X1,X4] :
( in(X4,complements_of_subsets(X0,X1))
| ~ in(subset_complement(X0,X4),X1)
| ~ element(X4,powerset(X0))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(equality_resolution,[],[f99]) ).
fof(f132,plain,
! [X0,X1,X4] :
( in(subset_complement(X0,X4),X1)
| ~ in(X4,complements_of_subsets(X0,X1))
| ~ element(X4,powerset(X0))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(equality_resolution,[],[f98]) ).
fof(f147,plain,
! [X0] :
( element(X0,powerset(the_carrier(sK0)))
| ~ in(X0,sK1) ),
inference(resolution,[],[f117,f93]) ).
fof(f163,plain,
! [X2,X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| ~ in(X2,complements_of_subsets(X1,X0))
| element(X2,powerset(X1)) ),
inference(resolution,[],[f97,f117]) ).
fof(f173,plain,
( in(sK5(sK0,sK1),sK1)
| open_subsets(sK1,sK0)
| ~ top_str(sK0) ),
inference(resolution,[],[f107,f93]) ).
fof(f178,plain,
( in(sK5(sK0,sK1),sK1)
| open_subsets(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f173,f92]) ).
fof(f180,plain,
( open_subsets(sK1,sK0)
| ~ empty(sK1) ),
inference(resolution,[],[f178,f115]) ).
fof(f184,plain,
( ~ open_subset(sK5(sK0,sK1),sK0)
| open_subsets(sK1,sK0)
| ~ top_str(sK0) ),
inference(resolution,[],[f108,f93]) ).
fof(f189,plain,
( ~ open_subset(sK5(sK0,sK1),sK0)
| open_subsets(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f184,f92]) ).
fof(f191,plain,
! [X0,X1] :
( in(sK6(X0,complements_of_subsets(the_carrier(X0),X1)),complements_of_subsets(the_carrier(X0),X1))
| closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(resolution,[],[f111,f97]) ).
fof(f202,plain,
! [X0,X1] :
( ~ closed_subset(sK6(X0,complements_of_subsets(the_carrier(X0),X1)),X0)
| closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(resolution,[],[f112,f97]) ).
fof(f268,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ in(X3,X1)
| ~ open_subsets(X1,X0)
| open_subset(X3,X0)
| ~ top_str(X0) ),
inference(forward_subsumption_resolution,[],[f105,f117]) ).
fof(f276,plain,
! [X0] :
( ~ in(X0,sK1)
| ~ open_subsets(sK1,sK0)
| open_subset(X0,sK0)
| ~ top_str(sK0) ),
inference(resolution,[],[f268,f93]) ).
fof(f282,plain,
! [X0] :
( open_subset(X0,sK0)
| ~ open_subsets(sK1,sK0)
| ~ in(X0,sK1) ),
inference(forward_subsumption_resolution,[],[f276,f92]) ).
fof(f284,plain,
! [X0] :
( ~ open_subsets(sK1,sK0)
| ~ in(subset_complement(the_carrier(sK0),X0),sK1)
| closed_subset(X0,sK0)
| ~ element(X0,powerset(the_carrier(sK0)))
| ~ top_str(sK0) ),
inference(resolution,[],[f282,f125]) ).
fof(f285,plain,
! [X0] :
( ~ in(subset_complement(the_carrier(sK0),X0),sK1)
| ~ open_subsets(sK1,sK0)
| closed_subset(X0,sK0)
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f284,f92]) ).
fof(f289,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ in(X3,X1)
| ~ closed_subsets(X1,X0)
| closed_subset(X3,X0)
| ~ top_str(X0) ),
inference(forward_subsumption_resolution,[],[f109,f117]) ).
fof(f294,plain,
! [X2,X0,X1] :
( ~ closed_subsets(complements_of_subsets(the_carrier(X1),X2),X1)
| ~ in(X0,complements_of_subsets(the_carrier(X1),X2))
| closed_subset(X0,X1)
| ~ top_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(resolution,[],[f289,f97]) ).
fof(f309,plain,
! [X0,X1,X4] :
( in(X4,complements_of_subsets(X0,X1))
| ~ in(subset_complement(X0,X4),X1)
| ~ element(X4,powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[],[f131,f97]) ).
fof(f338,plain,
! [X0,X1,X4] :
( in(subset_complement(X0,X4),X1)
| ~ in(X4,complements_of_subsets(X0,X1))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[],[f132,f117]) ).
fof(f339,plain,
! [X0,X1,X4] :
( in(subset_complement(X0,X4),X1)
| ~ in(X4,complements_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[],[f338,f97]) ).
fof(f771,plain,
! [X0] :
( ~ in(X0,complements_of_subsets(the_carrier(sK0),sK1))
| closed_subset(X0,sK0)
| ~ top_str(sK0)
| ~ element(sK1,powerset(powerset(the_carrier(sK0))))
| open_subsets(sK1,sK0) ),
inference(resolution,[],[f294,f94]) ).
fof(f773,plain,
! [X0] :
( ~ in(X0,complements_of_subsets(the_carrier(sK0),sK1))
| closed_subset(X0,sK0)
| ~ element(sK1,powerset(powerset(the_carrier(sK0))))
| open_subsets(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f771,f92]) ).
fof(f774,plain,
! [X0] :
( ~ in(X0,complements_of_subsets(the_carrier(sK0),sK1))
| closed_subset(X0,sK0)
| open_subsets(sK1,sK0) ),
inference(forward_subsumption_resolution,[],[f773,f93]) ).
fof(f775,plain,
! [X0] :
( closed_subset(X0,sK0)
| open_subsets(sK1,sK0)
| ~ in(subset_complement(the_carrier(sK0),X0),sK1)
| ~ element(X0,powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(resolution,[],[f774,f309]) ).
fof(f779,plain,
! [X0] :
( closed_subset(X0,sK0)
| ~ in(subset_complement(the_carrier(sK0),X0),sK1)
| ~ element(X0,powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(forward_subsumption_resolution,[],[f775,f285]) ).
fof(f780,plain,
! [X0] :
( ~ in(subset_complement(the_carrier(sK0),X0),sK1)
| closed_subset(X0,sK0)
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f779,f93]) ).
fof(f781,plain,
! [X0] :
( closed_subset(X0,sK0)
| ~ element(X0,powerset(the_carrier(sK0)))
| ~ in(X0,complements_of_subsets(the_carrier(sK0),sK1))
| ~ element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(resolution,[],[f780,f339]) ).
fof(f783,plain,
! [X0] :
( ~ element(subset_complement(the_carrier(sK0),X0),sK1)
| ~ element(X0,powerset(the_carrier(sK0)))
| empty(sK1)
| closed_subset(X0,sK0) ),
inference(resolution,[],[f780,f118]) ).
fof(f787,plain,
! [X0] :
( closed_subset(X0,sK0)
| ~ in(X0,complements_of_subsets(the_carrier(sK0),sK1))
| ~ element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(forward_subsumption_resolution,[],[f781,f163]) ).
fof(f789,plain,
! [X0] :
( ~ in(X0,complements_of_subsets(the_carrier(sK0),sK1))
| closed_subset(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f787,f93]) ).
fof(f839,plain,
! [X0] :
( ~ element(X0,sK1)
| ~ element(subset_complement(the_carrier(sK0),X0),powerset(the_carrier(sK0)))
| empty(sK1)
| closed_subset(subset_complement(the_carrier(sK0),X0),sK0)
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(superposition,[],[f783,f114]) ).
fof(f840,plain,
! [X0] :
( closed_subset(subset_complement(the_carrier(sK0),X0),sK0)
| empty(sK1)
| ~ element(X0,sK1)
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f839,f121]) ).
fof(f845,plain,
! [X0] :
( empty(sK1)
| ~ element(X0,sK1)
| ~ element(X0,powerset(the_carrier(sK0)))
| open_subset(X0,sK0)
| ~ element(X0,powerset(the_carrier(sK0)))
| ~ top_str(sK0) ),
inference(resolution,[],[f840,f123]) ).
fof(f847,plain,
! [X0] :
( empty(sK1)
| ~ element(X0,sK1)
| ~ element(X0,powerset(the_carrier(sK0)))
| open_subset(X0,sK0)
| ~ top_str(sK0) ),
inference(duplicate_literal_removal,[],[f845]) ).
fof(f848,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK0)))
| ~ element(X0,sK1)
| empty(sK1)
| open_subset(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f847,f92]) ).
fof(f849,plain,
! [X0] :
( ~ element(X0,sK1)
| empty(sK1)
| open_subset(X0,sK0)
| ~ in(X0,sK1) ),
inference(resolution,[],[f848,f147]) ).
fof(f862,plain,
! [X0] :
( ~ element(X0,sK1)
| empty(sK1)
| open_subset(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f849,f118]) ).
fof(f889,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| ~ top_str(sK0)
| ~ element(sK1,powerset(powerset(the_carrier(sK0))))
| closed_subset(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),sK0) ),
inference(resolution,[],[f191,f789]) ).
fof(f904,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| ~ top_str(sK0)
| ~ element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(forward_subsumption_resolution,[],[f889,f202]) ).
fof(f909,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| ~ element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(forward_subsumption_resolution,[],[f904,f92]) ).
fof(f911,plain,
closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0),
inference(forward_subsumption_resolution,[],[f909,f93]) ).
fof(f913,plain,
~ open_subsets(sK1,sK0),
inference(resolution,[],[f911,f95]) ).
fof(f915,plain,
~ empty(sK1),
inference(resolution,[],[f913,f180]) ).
fof(f918,plain,
! [X0] :
( open_subset(X0,sK0)
| ~ element(X0,sK1) ),
inference(forward_subsumption_resolution,[],[f862,f915]) ).
fof(f926,plain,
( ~ element(sK5(sK0,sK1),sK1)
| open_subsets(sK1,sK0) ),
inference(resolution,[],[f918,f189]) ).
fof(f939,plain,
~ element(sK5(sK0,sK1),sK1),
inference(forward_subsumption_resolution,[],[f926,f913]) ).
fof(f947,plain,
~ in(sK5(sK0,sK1),sK1),
inference(resolution,[],[f939,f119]) ).
fof(f948,plain,
open_subsets(sK1,sK0),
inference(resolution,[],[f947,f178]) ).
fof(f950,plain,
$false,
inference(forward_subsumption_resolution,[],[f948,f913]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU337+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n004.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 28 04:48:09 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.84/1.74 % (4156722)Detected formulas, will run a generic FOF schedule.
% 1.84/1.74 % (4156727)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2467749567:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.84/1.74 % (4156728)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2108194581:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.84/1.74 % (4156732)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4004818286:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.84/1.74 % (4156731)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1135340715:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.84/1.74 % (4156729)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3785401025:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.84/1.75 % (4156730)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=624724427:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.84/1.75 % (4156730)Refutation not found, incomplete strategy
% 1.84/1.75 % (4156730)------------------------------
% 1.84/1.75 % (4156730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.84/1.75 % (4156730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/1.75 % (4156730)CaDiCaL version: 2.1.3
% 1.84/1.75 % (4156730)Termination reason: Refutation not found, incomplete strategy
% 1.84/1.75 % (4156730)Time elapsed: 0.005 s
% 1.84/1.75 % (4156730)Peak memory usage: 89 MB
% 1.84/1.75 % (4156730)Instructions burned: 2 (million)
% 1.84/1.75 % (4156733)dis-21_1_sil=8000:lcm=predicate:random_seed=641990824:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.84/1.75 % (4156731)First to succeed.
% 1.84/1.75 % (4156731)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4156722"
% 1.84/1.75 % (4156732)Also succeeded, but the first one will report.
% 1.84/1.75 % (4156733)Instruction limit reached!
% 1.84/1.75 % (4156733)------------------------------
% 1.84/1.75 % (4156733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.84/1.75 % (4156733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.84/1.75 % (4156733)CaDiCaL version: 2.1.3
% 1.84/1.75 % (4156733)Termination reason: Instruction limit
% 1.84/1.75 % (4156733)Termination phase: Saturation
% 1.84/1.75 % (4156733)Time elapsed: 0.124 s
% 1.84/1.75 % (4156733)Peak memory usage: 89 MB
% 1.84/1.75 % (4156733)Instructions burned: 130 (million)
% 1.84/1.75 % (4156741)lrs+10_1_sil=8000:sp=occurrence:random_seed=1827635809:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 1.84/1.75 % (4156730)------------------------------
% 1.84/1.75 % (4156730)------------------------------
% 1.84/1.75 % (4156727)Also succeeded, but the first one will report.
% 1.84/1.75 % (4156731)Refutation found. Thanks to Tanya!
% 1.84/1.75 % SZS status Theorem for theBenchmark
% 1.84/1.75 % SZS output start Proof for theBenchmark
% See solution above
% 5.97/2.01 % (4156731)------------------------------
% 5.97/2.01 % (4156731)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.97/2.01 % (4156731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.97/2.01 % (4156731)CaDiCaL version: 2.1.3
% 5.97/2.01 % (4156731)Termination reason: Refutation
% 5.97/2.01 % (4156731)Time elapsed: 0.052 s
% 5.97/2.01 % (4156731)Peak memory usage: 89 MB
% 5.97/2.01 % (4156731)Instructions burned: 48 (million)
% 5.97/2.01 % (4156731)------------------------------
% 5.97/2.01 % (4156731)------------------------------
% 5.97/2.01 % (4156722)Success in time 0.734 s
% 5.97/2.01 % Vampire exiting
%------------------------------------------------------------------------------