%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU337+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 02:56:57 PM UTC 2026
% Result : Theorem 11.06s 2.96s
% Output : CNFRefutation 11.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 16
% Syntax : Number of formulae : 210 ( 26 unt; 0 def)
% Number of atoms : 721 ( 40 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 886 ( 375 ~; 416 |; 52 &)
% ( 16 <=>; 26 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-3 aty)
% Number of variables : 316 ( 0 sgn 300 !; 16 ?; 126 :)
% 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(f30,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f31,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_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(f36,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_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)
=> ( in(X0,X1)
| empty(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] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f49,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f51,plain,
? [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(ennf_transformation,[],[f40]) ).
fof(f53,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f23]) ).
fof(f54,plain,
! [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) ) ) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f55,plain,
! [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) ) ) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f56,plain,
! [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) ) ) ) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [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) ) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f58,plain,
! [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) ) ) ) ),
inference(flattening,[],[f57]) ).
fof(f60,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f33]) ).
fof(f61,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f46]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f66,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f69,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f70,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( open_subset(X1,X0)
<=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f71,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f72,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f73,plain,
? [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) )
& ( ~ open_subsets(X1,X0)
| ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f74,plain,
? [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) )
& ( ~ open_subsets(X1,X0)
| ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
( top_str(sK0)
& element(sK1,powerset(powerset(the_carrier(sK0))))
& ( open_subsets(sK1,sK0)
| closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0) )
& ( ~ open_subsets(sK1,sK0)
| ~ closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X3] :
( ~ element(X3,powerset(X0))
| ( ( ~ in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(subset_complement(X0,X3),X1)
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f77,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X3] :
( ~ element(X3,powerset(X0))
| ( ( ~ in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(subset_complement(X0,X3),X1)
| in(X3,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X4] :
( ~ element(X4,powerset(X0))
| ( ( ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) )
& ( ~ in(subset_complement(X0,X4),X1)
| in(X4,X2) ) ) ) )
& ( ? [X3] :
( element(X3,powerset(X0))
& ( in(X3,X2)
| in(subset_complement(X0,X3),X1) )
& ( ~ in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ! [X2] :
( ~ element(X2,powerset(powerset(X0)))
| ( ( complements_of_subsets(X0,X1) != X2
| ! [X4] :
( ~ element(X4,powerset(X0))
| ( ( ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) )
& ( ~ in(subset_complement(X0,X4),X1)
| in(X4,X2) ) ) ) )
& ( ( element(sK2(X0,X1,X2),powerset(X0))
& ( in(sK2(X0,X1,X2),X2)
| in(subset_complement(X0,sK2(X0,X1,X2)),X1) )
& ( ~ in(sK2(X0,X1,X2),X2)
| ~ in(subset_complement(X0,sK2(X0,X1,X2)),X1) ) )
| X2 = complements_of_subsets(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f78]) ).
fof(f80,plain,
! [X0] : element(sK3(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f30]) ).
fof(f82,plain,
! [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) ) )
& ( ? [X2] :
( element(X2,powerset(the_carrier(X0)))
& in(X2,X1)
& ~ open_subset(X2,X0) )
| open_subsets(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f83,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( ( ~ open_subsets(X1,X0)
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,X1)
| open_subset(X3,X0) ) )
& ( ? [X2] :
( element(X2,powerset(the_carrier(X0)))
& in(X2,X1)
& ~ open_subset(X2,X0) )
| open_subsets(X1,X0) ) ) ) ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( ( ~ open_subsets(X1,X0)
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,X1)
| open_subset(X3,X0) ) )
& ( ( element(sK5(X0,X1),powerset(the_carrier(X0)))
& in(sK5(X0,X1),X1)
& ~ open_subset(sK5(X0,X1),X0) )
| open_subsets(X1,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f83]) ).
fof(f85,plain,
! [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) ) )
& ( ? [X2] :
( element(X2,powerset(the_carrier(X0)))
& in(X2,X1)
& ~ closed_subset(X2,X0) )
| closed_subsets(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f86,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( ( ~ closed_subsets(X1,X0)
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,X1)
| closed_subset(X3,X0) ) )
& ( ? [X2] :
( element(X2,powerset(the_carrier(X0)))
& in(X2,X1)
& ~ closed_subset(X2,X0) )
| closed_subsets(X1,X0) ) ) ) ),
inference(rectify,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( ( ~ closed_subsets(X1,X0)
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,X1)
| closed_subset(X3,X0) ) )
& ( ( element(sK6(X0,X1),powerset(the_carrier(X0)))
& in(sK6(X0,X1),X1)
& ~ closed_subset(sK6(X0,X1),X0) )
| closed_subsets(X1,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f86]) ).
fof(f88,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( ~ 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) ) ) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f89,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( ~ 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) ) ) ) ),
inference(nnf_transformation,[],[f71]) ).
fof(f91,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK8(X0))
& element(sK8(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8(X0))],[f72]) ).
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,
( open_subsets(sK1,sK0)
| closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f95,plain,
( ~ open_subsets(sK1,sK0)
| ~ closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f97,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f53]) ).
fof(f98,plain,
! [X2,X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| complements_of_subsets(X0,X1) != X2
| ~ element(X4,powerset(X0))
| ~ in(X4,X2)
| in(subset_complement(X0,X4),X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f99,plain,
! [X2,X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| complements_of_subsets(X0,X1) != X2
| ~ element(X4,powerset(X0))
| ~ in(subset_complement(X0,X4),X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f103,plain,
! [X0] : element(sK3(X0),X0),
inference(cnf_transformation,[],[f80]) ).
fof(f105,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ open_subsets(X1,X0)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,X1)
| open_subset(X3,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f106,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| element(sK5(X0,X1),powerset(the_carrier(X0)))
| open_subsets(X1,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f107,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| in(sK5(X0,X1),X1)
| open_subsets(X1,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f108,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ open_subset(sK5(X0,X1),X0)
| open_subsets(X1,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f109,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ closed_subsets(X1,X0)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ in(X3,X1)
| closed_subset(X3,X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f110,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| element(sK6(X0,X1),powerset(the_carrier(X0)))
| closed_subsets(X1,X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f111,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| in(sK6(X0,X1),X1)
| closed_subsets(X1,X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f112,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ closed_subset(sK6(X0,X1),X0)
| closed_subsets(X1,X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f114,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f60]) ).
fof(f115,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,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] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f119,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f121,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f122,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(X1,X0)
| closed_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f123,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
| open_subset(X1,X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f125,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f128,plain,
! [X0] :
( empty(X0)
| ~ empty(sK8(X0)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f129,plain,
! [X0] :
( empty(X0)
| element(sK8(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f130,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f31]) ).
fof(f131,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X4,powerset(X0))
| ~ in(subset_complement(X0,X4),X1)
| in(X4,complements_of_subsets(X0,X1)) ),
inference(equality_resolution,[],[f99]) ).
fof(f132,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X4,powerset(X0))
| ~ in(X4,complements_of_subsets(X0,X1))
| in(subset_complement(X0,X4),X1) ),
inference(equality_resolution,[],[f98]) ).
tcf(c_49,negated_conjecture,
( ~ open_subsets(sK1,sK0)
| ~ closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_50,negated_conjecture,
( open_subsets(sK1,sK0)
| closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_51,negated_conjecture,
element(sK1,powerset(powerset(the_carrier(sK0)))),
inference(cnf_transformation,[],[f93]) ).
tcf(c_52,negated_conjecture,
top_str(sK0),
inference(cnf_transformation,[],[f92]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,complements_of_subsets(X0,X1))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(powerset(X0)))
| ~ in(subset_complement(X0,X2),X1)
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X0,X2),X1)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(powerset(X0)))
| ~ in(X2,complements_of_subsets(X0,X1))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_60,plain,
! [X0: $i] : element(sK3(X0),X0),
inference(cnf_transformation,[],[f103]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( open_subsets(X0,X1)
| ~ top_str(X1)
| ~ open_subset(sK5(X1,X0),X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( open_subsets(X0,X1)
| in(sK5(X1,X0),X0)
| ~ top_str(X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( open_subsets(X0,X1)
| element(sK5(X1,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( open_subset(X2,X1)
| ~ top_str(X1)
| ~ in(X2,X0)
| ~ open_subsets(X0,X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( closed_subsets(X0,X1)
| ~ top_str(X1)
| ~ closed_subset(sK6(X1,X0),X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( closed_subsets(X0,X1)
| in(sK6(X1,X0),X0)
| ~ top_str(X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( closed_subsets(X0,X1)
| element(sK6(X1,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(X2,X1)
| ~ top_str(X1)
| ~ in(X2,X0)
| ~ closed_subsets(X0,X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( open_subset(X1,X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( closed_subset(subset_complement(the_carrier(X1),X0),X1)
| ~ top_str(X1)
| ~ open_subset(X0,X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_85,plain,
! [X0: $i] :
( empty(X0)
| element(sK8(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_86,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK8(X0)) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_87,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f130]) ).
tcf(c_118,plain,
( ~ closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| ~ open_subsets(sK1,sK0) ),
inference(prop_impl_just,[status(thm)],[c_49]) ).
tcf(c_119,plain,
( ~ open_subsets(sK1,sK0)
| ~ closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0) ),
inference(renaming,[status(thm)],[c_118]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] :
( element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(prop_impl_just,[status(thm)],[c_54]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X1,X0),X2)
| ~ element(X0,powerset(X1))
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X0,complements_of_subsets(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_59,c_124]) ).
tcf(c_284,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,complements_of_subsets(X0,X2))
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(powerset(X0)))
| ~ in(subset_complement(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_58,c_124]) ).
tcf(c_319,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(X2,X1)
| ~ top_str(X1)
| ~ in(X2,X0)
| ~ closed_subsets(X0,X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_69,c_74]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i,X2: $i] :
( open_subset(X2,X1)
| ~ top_str(X1)
| ~ in(X2,X0)
| ~ open_subsets(X0,X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_65,c_74]) ).
tcf(c_760,plain,
! [X0: $i,X1: $i] :
( element(sK6(X1,X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ open_subsets(sK1,sK0)
| ~ element(X0,powerset(powerset(the_carrier(X1))))
| ( X1 != sK0 )
| ( complements_of_subsets(the_carrier(sK0),sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_119,c_68]) ).
tcf(c_761,plain,
( element(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),powerset(the_carrier(sK0)))
| ~ top_str(sK0)
| ~ open_subsets(sK1,sK0)
| ~ element(complements_of_subsets(the_carrier(sK0),sK1),powerset(powerset(the_carrier(sK0)))) ),
inference(unflattening,[status(thm)],[c_760]) ).
tcf(c_786,plain,
! [X0: $i,X1: $i] :
( ~ top_str(X1)
| ~ open_subsets(sK1,sK0)
| ~ closed_subset(sK6(X1,X0),X1)
| ~ element(X0,powerset(powerset(the_carrier(X1))))
| ( X1 != sK0 )
| ( complements_of_subsets(the_carrier(sK0),sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_119,c_66]) ).
tcf(c_787,plain,
( ~ top_str(sK0)
| ~ open_subsets(sK1,sK0)
| ~ closed_subset(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),sK0)
| ~ element(complements_of_subsets(the_carrier(sK0),sK1),powerset(powerset(the_carrier(sK0)))) ),
inference(unflattening,[status(thm)],[c_786]) ).
tcf(c_1352,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_81]) ).
tcf(c_1353,plain,
! [X0: $i] :
( closed_subset(X0,sK0)
| ~ element(X0,powerset(the_carrier(sK0)))
| ~ open_subset(subset_complement(the_carrier(sK0),X0),sK0) ),
inference(unflattening,[status(thm)],[c_1352]) ).
tcf(c_1364,plain,
! [X0: $i,X1: $i] :
( open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_79]) ).
tcf(c_1365,plain,
! [X0: $i] :
( open_subset(X0,sK0)
| ~ element(X0,powerset(the_carrier(sK0)))
| ~ closed_subset(subset_complement(the_carrier(sK0),X0),sK0) ),
inference(unflattening,[status(thm)],[c_1364]) ).
tcf(c_1376,plain,
! [X0: $i,X1: $i,X2: $i] :
( open_subset(X2,X0)
| ~ in(X2,X1)
| ~ open_subsets(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_320]) ).
tcf(c_1377,plain,
! [X0: $i,X1: $i] :
( open_subset(X1,sK0)
| ~ open_subsets(X0,sK0)
| ~ in(X1,X0)
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(unflattening,[status(thm)],[c_1376]) ).
tcf(c_1390,plain,
! [X0: $i,X1: $i,X2: $i] :
( closed_subset(X2,X0)
| ~ in(X2,X1)
| ~ closed_subsets(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_319]) ).
tcf(c_1391,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,sK0)
| ~ closed_subsets(X0,sK0)
| ~ in(X1,X0)
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(unflattening,[status(thm)],[c_1390]) ).
tcf(c_1416,plain,
! [X0: $i,X1: $i] :
( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_80]) ).
tcf(c_1417,plain,
! [X0: $i] :
( closed_subset(subset_complement(the_carrier(sK0),X0),sK0)
| ~ open_subset(X0,sK0)
| ~ element(X0,powerset(the_carrier(sK0))) ),
inference(unflattening,[status(thm)],[c_1416]) ).
tcf(c_1440,plain,
! [X0: $i,X1: $i] :
( closed_subsets(X1,X0)
| in(sK6(X0,X1),X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_67]) ).
tcf(c_1441,plain,
! [X0: $i] :
( closed_subsets(X0,sK0)
| in(sK6(sK0,X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(unflattening,[status(thm)],[c_1440]) ).
tcf(c_1464,plain,
! [X0: $i,X1: $i] :
( open_subsets(X1,X0)
| element(sK5(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_64]) ).
tcf(c_1465,plain,
! [X0: $i] :
( open_subsets(X0,sK0)
| element(sK5(sK0,X0),powerset(the_carrier(sK0)))
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(unflattening,[status(thm)],[c_1464]) ).
tcf(c_1476,plain,
! [X0: $i,X1: $i] :
( open_subsets(X1,X0)
| in(sK5(X0,X1),X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_63]) ).
tcf(c_1477,plain,
! [X0: $i] :
( open_subsets(X0,sK0)
| in(sK5(sK0,X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(unflattening,[status(thm)],[c_1476]) ).
tcf(c_1488,plain,
! [X0: $i,X1: $i] :
( open_subsets(X1,X0)
| ~ open_subset(sK5(X0,X1),X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_62]) ).
tcf(c_1489,plain,
! [X0: $i] :
( open_subsets(X0,sK0)
| ~ open_subset(sK5(sK0,X0),sK0)
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(unflattening,[status(thm)],[c_1488]) ).
tcf(c_5236,plain,
( open_subsets(sK1,sK0)
| in(sK5(sK0,sK1),sK1) ),
inference(superposition,[status(thm)],[c_51,c_1477]) ).
tcf(c_5275,plain,
( open_subsets(sK1,sK0)
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_5236,c_72]) ).
tcf(c_5334,plain,
( open_subsets(sK1,sK0)
| ~ open_subset(sK5(sK0,sK1),sK0) ),
inference(superposition,[status(thm)],[c_51,c_1489]) ).
tcf(c_5406,plain,
! [X0: $i] :
( empty(X0)
| in(sK3(X0),X0) ),
inference(superposition,[status(thm)],[c_60,c_75]) ).
tcf(c_5462,plain,
! [X0: $i] :
( open_subset(X0,sK0)
| ~ open_subsets(sK1,sK0)
| ~ in(X0,sK1) ),
inference(superposition,[status(thm)],[c_51,c_1377]) ).
tcf(c_5670,plain,
! [X0: $i] :
( element(X0,powerset(the_carrier(sK0)))
| ~ in(X0,sK1) ),
inference(superposition,[status(thm)],[c_51,c_74]) ).
tcf(c_5674,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(X0,X1)
| ~ in(X0,sK8(X1)) ),
inference(superposition,[status(thm)],[c_85,c_74]) ).
tcf(c_5717,plain,
( open_subsets(sK1,sK0)
| element(sK5(sK0,sK1),powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(instantiation,[status(thm)],[c_1465]) ).
tcf(c_5873,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(X1))
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X0,complements_of_subsets(X1,X2)) ),
inference(superposition,[status(thm)],[c_54,c_74]) ).
tcf(c_5876,plain,
! [X0: $i,X1: $i] :
( closed_subset(X0,sK0)
| ~ element(X1,powerset(powerset(the_carrier(sK0))))
| ~ closed_subsets(complements_of_subsets(the_carrier(sK0),X1),sK0)
| ~ in(X0,complements_of_subsets(the_carrier(sK0),X1)) ),
inference(superposition,[status(thm)],[c_54,c_1391]) ).
tcf(c_5881,plain,
! [X0: $i] :
( closed_subsets(complements_of_subsets(the_carrier(sK0),X0),sK0)
| in(sK6(sK0,complements_of_subsets(the_carrier(sK0),X0)),complements_of_subsets(the_carrier(sK0),X0))
| ~ element(X0,powerset(powerset(the_carrier(sK0)))) ),
inference(superposition,[status(thm)],[c_54,c_1441]) ).
tcf(c_5925,plain,
! [X0: $i] :
( ( subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),X0)) = X0 )
| ~ in(X0,sK1) ),
inference(superposition,[status(thm)],[c_5670,c_71]) ).
tcf(c_5991,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X1,X0),X2)
| ~ in(X0,complements_of_subsets(X1,X2))
| ~ element(X2,powerset(powerset(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_283,c_283,c_5873]) ).
tcf(c_5992,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(subset_complement(X1,X0),X2)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X0,complements_of_subsets(X1,X2)) ),
inference(renaming,[status(thm)],[c_5991]) ).
tcf(c_6000,plain,
! [X0: $i] :
( in(subset_complement(the_carrier(sK0),X0),sK1)
| ~ in(X0,complements_of_subsets(the_carrier(sK0),sK1)) ),
inference(superposition,[status(thm)],[c_51,c_5992]) ).
tcf(c_6105,plain,
( element(complements_of_subsets(the_carrier(sK0),sK1),powerset(powerset(the_carrier(sK0))))
| ~ element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_6213,plain,
! [X0: $i] :
( in(X0,complements_of_subsets(the_carrier(sK0),sK1))
| ~ element(X0,powerset(the_carrier(sK0)))
| ~ in(subset_complement(the_carrier(sK0),X0),sK1) ),
inference(superposition,[status(thm)],[c_51,c_284]) ).
tcf(c_6879,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| in(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),complements_of_subsets(the_carrier(sK0),sK1))
| ~ element(complements_of_subsets(the_carrier(sK0),sK1),powerset(powerset(the_carrier(sK0)))) ),
inference(instantiation,[status(thm)],[c_1441]) ).
tcf(c_7004,plain,
( open_subsets(sK1,sK0)
| ( subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK5(sK0,sK1))) = sK5(sK0,sK1) ) ),
inference(superposition,[status(thm)],[c_5236,c_5925]) ).
tcf(c_7262,plain,
! [X0: $i] :
( empty(X0)
| empty(sK8(X0))
| element(sK3(sK8(X0)),X0) ),
inference(superposition,[status(thm)],[c_5406,c_5674]) ).
tcf(c_7608,plain,
! [X0: $i] :
( open_subset(X0,sK0)
| ( subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK5(sK0,sK1))) = sK5(sK0,sK1) )
| ~ in(X0,sK1) ),
inference(superposition,[status(thm)],[c_7004,c_5462]) ).
tcf(c_9688,plain,
! [X0: $i] :
( closed_subset(X0,sK0)
| ~ closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| ~ in(X0,complements_of_subsets(the_carrier(sK0),sK1)) ),
inference(superposition,[status(thm)],[c_51,c_5876]) ).
tcf(c_9783,plain,
! [X0: $i] :
( open_subsets(sK1,sK0)
| closed_subset(X0,sK0)
| ~ in(X0,complements_of_subsets(the_carrier(sK0),sK1)) ),
inference(superposition,[status(thm)],[c_50,c_9688]) ).
tcf(c_10281,plain,
! [X0: $i] :
( empty(X0)
| element(sK3(sK8(X0)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_7262,c_86,c_7262]) ).
tcf(c_10294,plain,
! [X0: $i] :
( empty(X0)
| in(sK3(sK8(X0)),X0) ),
inference(superposition,[status(thm)],[c_10281,c_75]) ).
tcf(c_10453,plain,
( empty(complements_of_subsets(the_carrier(sK0),sK1))
| in(subset_complement(the_carrier(sK0),sK3(sK8(complements_of_subsets(the_carrier(sK0),sK1)))),sK1) ),
inference(superposition,[status(thm)],[c_10294,c_6000]) ).
tcf(c_10656,plain,
( empty(complements_of_subsets(the_carrier(sK0),sK1))
| element(subset_complement(the_carrier(sK0),sK3(sK8(complements_of_subsets(the_carrier(sK0),sK1)))),sK1) ),
inference(superposition,[status(thm)],[c_10453,c_76]) ).
tcf(c_10662,plain,
( empty(complements_of_subsets(the_carrier(sK0),sK1))
| in(sK3(sK8(complements_of_subsets(the_carrier(sK0),sK1))),complements_of_subsets(the_carrier(sK0),sK1))
| ~ element(sK3(sK8(complements_of_subsets(the_carrier(sK0),sK1))),powerset(the_carrier(sK0))) ),
inference(superposition,[status(thm)],[c_10453,c_6213]) ).
tcf(c_12456,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| in(subset_complement(the_carrier(sK0),sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1))),sK1)
| ~ element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(superposition,[status(thm)],[c_5881,c_6000]) ).
tcf(c_12460,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| in(subset_complement(the_carrier(sK0),sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1))),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12456,c_51]) ).
tcf(c_12531,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_12460,c_72]) ).
tcf(c_12532,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| open_subset(subset_complement(the_carrier(sK0),sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1))),sK0)
| ( subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK5(sK0,sK1))) = sK5(sK0,sK1) ) ),
inference(superposition,[status(thm)],[c_12460,c_7608]) ).
tcf(c_12536,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| in(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),complements_of_subsets(the_carrier(sK0),sK1))
| ~ element(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),powerset(the_carrier(sK0))) ),
inference(superposition,[status(thm)],[c_12460,c_6213]) ).
tcf(c_12569,plain,
~ empty(sK1),
inference(global_subsumption_just,[status(thm)],[c_12531,c_49,c_5275,c_12531]) ).
tcf(c_13421,plain,
( element(subset_complement(the_carrier(sK0),sK5(sK0,sK1)),powerset(the_carrier(sK0)))
| ~ element(sK5(sK0,sK1),powerset(the_carrier(sK0))) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_13426,plain,
( open_subset(sK5(sK0,sK1),sK0)
| ~ element(sK5(sK0,sK1),powerset(the_carrier(sK0)))
| ~ closed_subset(subset_complement(the_carrier(sK0),sK5(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_1365]) ).
tcf(c_13854,plain,
! [X0: $i] :
( element(X0,powerset(the_carrier(sK0)))
| ~ in(X0,complements_of_subsets(the_carrier(sK0),sK1)) ),
inference(superposition,[status(thm)],[c_51,c_5873]) ).
tcf(c_14011,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| element(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(powerset(the_carrier(sK0)))) ),
inference(superposition,[status(thm)],[c_5881,c_13854]) ).
tcf(c_14018,plain,
( empty(complements_of_subsets(the_carrier(sK0),sK1))
| element(sK3(sK8(complements_of_subsets(the_carrier(sK0),sK1))),powerset(the_carrier(sK0))) ),
inference(superposition,[status(thm)],[c_10294,c_13854]) ).
tcf(c_14025,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| element(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14011,c_51]) ).
tcf(c_14051,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| ( subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)))) = sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)) ) ),
inference(superposition,[status(thm)],[c_14025,c_71]) ).
tcf(c_14054,plain,
( empty(powerset(the_carrier(sK0)))
| closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| in(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),powerset(the_carrier(sK0))) ),
inference(superposition,[status(thm)],[c_14025,c_75]) ).
tcf(c_14061,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| in(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14054,c_87]) ).
tcf(c_14840,plain,
( ( subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)))) = sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)) )
| ~ open_subsets(sK1,sK0) ),
inference(superposition,[status(thm)],[c_14051,c_49]) ).
tcf(c_15234,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| in(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),complements_of_subsets(the_carrier(sK0),sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_12536,c_51,c_6105,c_6879]) ).
tcf(c_15244,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0)
| ~ empty(complements_of_subsets(the_carrier(sK0),sK1)) ),
inference(superposition,[status(thm)],[c_15234,c_72]) ).
tcf(c_15316,plain,
( ~ open_subsets(sK1,sK0)
| ~ empty(complements_of_subsets(the_carrier(sK0),sK1)) ),
inference(superposition,[status(thm)],[c_15244,c_49]) ).
tcf(c_16586,plain,
( ( subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK5(sK0,sK1))) = sK5(sK0,sK1) )
| open_subset(subset_complement(the_carrier(sK0),sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1))),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_12532,c_49,c_7004,c_12532]) ).
tcf(c_16587,plain,
( open_subset(subset_complement(the_carrier(sK0),sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1))),sK0)
| ( subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK5(sK0,sK1))) = sK5(sK0,sK1) ) ),
inference(renaming,[status(thm)],[c_16586]) ).
tcf(c_16592,plain,
( closed_subset(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),sK0)
| ( subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK5(sK0,sK1))) = sK5(sK0,sK1) )
| ~ element(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),powerset(the_carrier(sK0))) ),
inference(superposition,[status(thm)],[c_16587,c_1353]) ).
tcf(c_17379,plain,
subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK5(sK0,sK1))) = sK5(sK0,sK1),
inference(global_subsumption_just,[status(thm)],[c_16592,c_52,c_51,c_761,c_787,c_6105,c_7004,c_16592]) ).
tcf(c_17385,plain,
( in(subset_complement(the_carrier(sK0),sK5(sK0,sK1)),complements_of_subsets(the_carrier(sK0),sK1))
| ~ in(sK5(sK0,sK1),sK1)
| ~ element(subset_complement(the_carrier(sK0),sK5(sK0,sK1)),powerset(the_carrier(sK0))) ),
inference(superposition,[status(thm)],[c_17379,c_6213]) ).
tcf(c_17803,plain,
( open_subsets(sK1,sK0)
| closed_subset(subset_complement(the_carrier(sK0),sK5(sK0,sK1)),sK0)
| ~ in(sK5(sK0,sK1),sK1)
| ~ element(subset_complement(the_carrier(sK0),sK5(sK0,sK1)),powerset(the_carrier(sK0))) ),
inference(superposition,[status(thm)],[c_17385,c_9783]) ).
tcf(c_17885,plain,
element(subset_complement(the_carrier(sK0),sK3(sK8(complements_of_subsets(the_carrier(sK0),sK1)))),sK1),
inference(global_subsumption_just,[status(thm)],[c_10656,c_51,c_5236,c_5334,c_5717,c_10656,c_13421,c_13426,c_15316,c_17803]) ).
tcf(c_17887,plain,
( empty(sK1)
| in(subset_complement(the_carrier(sK0),sK3(sK8(complements_of_subsets(the_carrier(sK0),sK1)))),sK1) ),
inference(superposition,[status(thm)],[c_17885,c_75]) ).
tcf(c_17888,plain,
in(subset_complement(the_carrier(sK0),sK3(sK8(complements_of_subsets(the_carrier(sK0),sK1)))),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_17887,c_12569]) ).
tcf(c_17897,plain,
( in(sK3(sK8(complements_of_subsets(the_carrier(sK0),sK1))),complements_of_subsets(the_carrier(sK0),sK1))
| ~ element(sK3(sK8(complements_of_subsets(the_carrier(sK0),sK1))),powerset(the_carrier(sK0))) ),
inference(superposition,[status(thm)],[c_17888,c_6213]) ).
tcf(c_17908,plain,
in(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),powerset(the_carrier(sK0))),
inference(global_subsumption_just,[status(thm)],[c_14061,c_51,c_49,c_5236,c_5334,c_5717,c_13421,c_13426,c_14061,c_17803]) ).
tcf(c_17913,plain,
element(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),powerset(the_carrier(sK0))),
inference(superposition,[status(thm)],[c_17908,c_76]) ).
tcf(c_18046,plain,
in(sK3(sK8(complements_of_subsets(the_carrier(sK0),sK1))),complements_of_subsets(the_carrier(sK0),sK1)),
inference(global_subsumption_just,[status(thm)],[c_17897,c_51,c_5236,c_5334,c_5717,c_10662,c_13421,c_13426,c_14018,c_15316,c_17803]) ).
tcf(c_18056,plain,
( open_subsets(sK1,sK0)
| closed_subset(sK3(sK8(complements_of_subsets(the_carrier(sK0),sK1))),sK0) ),
inference(superposition,[status(thm)],[c_18046,c_9783]) ).
tcf(c_18140,plain,
open_subsets(sK1,sK0),
inference(global_subsumption_just,[status(thm)],[c_18056,c_51,c_5236,c_5334,c_5717,c_13421,c_13426,c_17803]) ).
tcf(c_18145,plain,
subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)))) = sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),
inference(backward_subsumption_resolution,[status(thm)],[c_14840,c_18140]) ).
tcf(c_18146,plain,
! [X0: $i] :
( open_subset(X0,sK0)
| ~ in(X0,sK1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5462,c_18140]) ).
tcf(c_18147,plain,
~ closed_subsets(complements_of_subsets(the_carrier(sK0),sK1),sK0),
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_18140]) ).
tcf(c_18160,plain,
in(subset_complement(the_carrier(sK0),sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1))),sK1),
inference(backward_subsumption_resolution,[status(thm)],[c_12460,c_18147]) ).
tcf(c_18368,plain,
open_subset(subset_complement(the_carrier(sK0),sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1))),sK0),
inference(superposition,[status(thm)],[c_18160,c_18146]) ).
tcf(c_18599,plain,
( closed_subset(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),sK0)
| ~ open_subset(subset_complement(the_carrier(sK0),sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1))),sK0)
| ~ element(subset_complement(the_carrier(sK0),sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1))),powerset(the_carrier(sK0))) ),
inference(superposition,[status(thm)],[c_18145,c_1417]) ).
tcf(c_21491,plain,
~ element(subset_complement(the_carrier(sK0),sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1))),powerset(the_carrier(sK0))),
inference(global_subsumption_just,[status(thm)],[c_18599,c_52,c_51,c_787,c_6105,c_18140,c_18368,c_18599]) ).
tcf(c_21493,plain,
~ element(sK6(sK0,complements_of_subsets(the_carrier(sK0),sK1)),powerset(the_carrier(sK0))),
inference(superposition,[status(thm)],[c_78,c_21491]) ).
tcf(c_21495,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_21493,c_17913]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU337+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.44 % Computer : n017.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Thu Sep 24 13:40:16 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.50 Running first-order theorem proving
% 0.16/0.50 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.25/0.52
% 0.25/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.52
% 0.25/0.52 % Detected problem language: tptp
% 0.25/0.53 % Proving...
% 11.06/2.96 % SZS status Started for theBenchmark.p
% 11.06/2.96 % SZS status Theorem for theBenchmark.p
% 11.06/2.96
% 11.06/2.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 11.06/2.96
% 11.06/2.96 % ------ iProver source info
% 11.06/2.96
% 11.06/2.96 % git: date: 2026-07-19 20:42:38 +0200
% 11.06/2.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 11.06/2.96 % git: non_committed_changes: false
% 11.06/2.96
% 11.06/2.96 % ------ Parsing...
% 11.06/2.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 11.06/2.96
% 11.06/2.96 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 11.06/2.96
% 11.06/2.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 11.06/2.96
% 11.06/2.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 11.06/2.96 % ------ Proving...
% 11.06/2.96 % ------ Problem Properties
% 11.06/2.96
% 11.06/2.96 %
% 11.06/2.96 % clauses 49
% 11.06/2.96 % conjectures 3
% 11.06/2.96 % EPR 5
% 11.06/2.96 % Horn 36
% 11.06/2.96 % unary 5
% 11.06/2.96 % binary 11
% 11.06/2.96 % lits 137
% 11.06/2.96 % lits eq 6
% 11.06/2.96 % fd_pure 0
% 11.06/2.96 % fd_pseudo 0
% 11.06/2.96 % fd_cond 0
% 11.06/2.96 % fd_pseudo_cond 4
% 11.06/2.96 % AC symbols 0
% 11.06/2.96
% 11.06/2.96 % ------ Schedule dynamic 5 is on
% 11.06/2.96
% 11.06/2.96 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 11.06/2.96
% 11.06/2.96
% 11.06/2.96 % ------
% 11.06/2.96 % Current options:
% 11.06/2.96 % ------
% 11.06/2.96
% 11.06/2.96
% 11.06/2.96 %
% 11.06/2.96
% 11.06/2.96 % ------ Proving...
% 11.06/2.96 %
% 11.06/2.96
% 11.06/2.96 % SZS status Theorem for theBenchmark.p
% 11.06/2.96
% 11.06/2.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 11.06/2.96
% 11.06/2.96
%------------------------------------------------------------------------------