%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU315+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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:18 PM UTC 2026
% Result : Theorem 3.24s 1.32s
% Output : Refutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 10
% Syntax : Number of formulae : 111 ( 11 unt; 4 def)
% Number of atoms : 531 ( 33 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 711 ( 291 ~; 296 |; 100 &)
% ( 13 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 182 ( 0 sgn 145 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f29,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f30,axiom,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
fof(f31,axiom,
! [X0,X1] :
( ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) )
& ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f35,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f39,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f58,plain,
? [X0,X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( in(X3,X2)
<~> ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) )
& element(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f59,plain,
? [X0,X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( in(X3,X2)
<~> ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) )
& element(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f58]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f30]) ).
fof(f75,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) )
& ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f77,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f79,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f81,plain,
? [X0,X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) )
| ~ in(X3,X2) )
& ( ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) )
| in(X3,X2) )
& element(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(nnf_transformation,[],[f59]) ).
fof(f82,plain,
? [X0,X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) )
| ~ in(X3,X2) )
& ( ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) )
| in(X3,X2) )
& element(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
? [X0,X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) )
| ~ in(X3,X2) )
& ( ? [X5] :
( element(X5,powerset(the_carrier(X0)))
& X3 = X5
& closed_subset(X5,X0)
& subset(X1,X3) )
| in(X3,X2) )
& element(X3,powerset(the_carrier(X0))) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK0))))
| ( ( ! [X4] :
( ~ element(X4,powerset(the_carrier(sK0)))
| sK2(X2) != X4
| ~ closed_subset(X4,sK0)
| ~ subset(sK1,sK2(X2)) )
| ~ in(sK2(X2),X2) )
& ( ( element(sK3(X2),powerset(the_carrier(sK0)))
& sK2(X2) = sK3(X2)
& closed_subset(sK3(X2),sK0)
& subset(sK1,sK2(X2)) )
| in(sK2(X2),X2) )
& element(sK2(X2),powerset(the_carrier(sK0))) ) )
& topological_space(sK0)
& top_str(sK0)
& element(sK1,powerset(the_carrier(sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2(X2)),skolemize(X5,sK3(X2))],[f83]) ).
fof(f89,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) ) )
& ( ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) )
| ~ in(X3,X2) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(nnf_transformation,[],[f75]) ).
fof(f90,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) ) )
& ( ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) )
| ~ in(X3,X2) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) ) )
& ( ( in(X3,powerset(the_carrier(X0)))
& ? [X5] :
( element(X5,powerset(the_carrier(X0)))
& X3 = X5
& closed_subset(X5,X0)
& subset(X1,X3) ) )
| ~ in(X3,X2) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(rectify,[],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK8(X0,X1))
| ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) ) )
& ( ( in(X3,powerset(the_carrier(X0)))
& element(sK9(X0,X1,X3),powerset(the_carrier(X0)))
& sK9(X0,X1,X3) = X3
& closed_subset(sK9(X0,X1,X3),X0)
& subset(X1,X3) )
| ~ in(X3,sK8(X0,X1)) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X2,sK8(X0,X1)),skolemize(X5,sK9(X0,X1,X3))],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) )
& ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f95,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ( ~ in(sK11(X0,X1),X1)
& in(sK11(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f77]) ).
fof(f98,plain,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f84]) ).
fof(f99,plain,
top_str(sK0),
inference(cnf_transformation,[],[f84]) ).
fof(f100,plain,
topological_space(sK0),
inference(cnf_transformation,[],[f84]) ).
fof(f101,plain,
! [X2] :
( element(sK2(X2),powerset(the_carrier(sK0)))
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f102,plain,
! [X2] :
( subset(sK1,sK2(X2))
| ~ element(X2,powerset(powerset(the_carrier(sK0))))
| in(sK2(X2),X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f103,plain,
! [X2] :
( closed_subset(sK3(X2),sK0)
| ~ element(X2,powerset(powerset(the_carrier(sK0))))
| in(sK2(X2),X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f104,plain,
! [X2] :
( in(sK2(X2),X2)
| sK2(X2) = sK3(X2)
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f106,plain,
! [X2,X4] :
( ~ element(X2,powerset(powerset(the_carrier(sK0))))
| ~ element(X4,powerset(the_carrier(sK0)))
| sK2(X2) != X4
| ~ closed_subset(X4,sK0)
| ~ subset(sK1,sK2(X2))
| ~ in(sK2(X2),X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f145,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f146,plain,
! [X3,X0,X1] :
( subset(X1,X3)
| ~ in(X3,sK8(X0,X1))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f147,plain,
! [X3,X0,X1] :
( closed_subset(sK9(X0,X1,X3),X0)
| ~ in(X3,sK8(X0,X1))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f148,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| ~ in(X3,sK8(X0,X1))
| ~ topological_space(X0)
| sK9(X0,X1,X3) = X3
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f150,plain,
! [X3,X0,X1] :
( ~ top_str(X0)
| ~ in(X3,sK8(X0,X1))
| ~ topological_space(X0)
| in(X3,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f151,plain,
! [X3,X0,X1,X4] :
( in(X3,sK8(X0,X1))
| ~ in(X3,powerset(the_carrier(X0)))
| ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f154,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f155,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f158,plain,
! [X0,X1] :
( in(sK11(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f159,plain,
! [X0,X1] :
( ~ in(sK11(X0,X1),X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f163,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f165,plain,
! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK0))))
| ~ element(sK2(X2),powerset(the_carrier(sK0)))
| ~ closed_subset(sK2(X2),sK0)
| ~ subset(sK1,sK2(X2))
| ~ in(sK2(X2),X2) ),
inference(equality_resolution,[],[f106]) ).
fof(f166,plain,
! [X0,X1,X4] :
( in(X4,sK8(X0,X1))
| ~ in(X4,powerset(the_carrier(X0)))
| ~ element(X4,powerset(the_carrier(X0)))
| ~ closed_subset(X4,X0)
| ~ subset(X1,X4)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(equality_resolution,[],[f151]) ).
fof(f167,plain,
! [X2] :
( ~ closed_subset(sK2(X2),sK0)
| ~ element(X2,powerset(powerset(the_carrier(sK0))))
| ~ subset(sK1,sK2(X2))
| ~ in(sK2(X2),X2) ),
inference(forward_subsumption_resolution,[],[f165,f101]) ).
fof(f244,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,X0) ),
inference(forward_subsumption_resolution,[],[f155,f163]) ).
fof(f264,plain,
! [X0,X1] :
( ~ in(X0,sK8(sK0,X1))
| ~ topological_space(sK0)
| in(X0,powerset(the_carrier(sK0)))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f150,f99]) ).
fof(f265,plain,
! [X0,X1] :
( ~ in(X0,sK8(sK0,X1))
| in(X0,powerset(the_carrier(sK0)))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f264,f100]) ).
fof(f268,plain,
! [X0,X1] :
( element(sK8(sK0,X0),powerset(X1))
| ~ element(X0,powerset(the_carrier(sK0)))
| in(sK11(sK8(sK0,X0),X1),powerset(the_carrier(sK0))) ),
inference(resolution,[],[f265,f158]) ).
fof(f272,plain,
! [X0,X1] :
( ~ in(X0,sK8(sK0,X1))
| ~ topological_space(sK0)
| sK9(sK0,X1,X0) = X0
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f148,f99]) ).
fof(f273,plain,
! [X0,X1] :
( sK9(sK0,X1,X0) = X0
| ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f272,f100]) ).
fof(f274,plain,
! [X0,X1] :
( closed_subset(X0,sK0)
| ~ in(X0,sK8(sK0,X1))
| ~ topological_space(sK0)
| ~ top_str(sK0)
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(superposition,[],[f147,f273]) ).
fof(f275,plain,
! [X0,X1] :
( closed_subset(X0,sK0)
| ~ in(X0,sK8(sK0,X1))
| ~ topological_space(sK0)
| ~ top_str(sK0)
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(duplicate_literal_removal,[],[f274]) ).
fof(f276,plain,
! [X0,X1] :
( closed_subset(X0,sK0)
| ~ in(X0,sK8(sK0,X1))
| ~ top_str(sK0)
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f275,f100]) ).
fof(f277,plain,
! [X0,X1] :
( closed_subset(X0,sK0)
| ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f276,f99]) ).
fof(f282,plain,
! [X0,X1] :
( ~ subset(sK1,sK2(X0))
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ element(X0,powerset(powerset(the_carrier(sK0))))
| ~ in(sK2(X0),sK8(sK0,X1))
| ~ in(sK2(X0),X0) ),
inference(resolution,[],[f277,f167]) ).
fof(f283,plain,
! [X0,X1,X4] :
( ~ top_str(X0)
| ~ in(X4,powerset(the_carrier(X0)))
| ~ closed_subset(X4,X0)
| ~ subset(X1,X4)
| ~ topological_space(X0)
| in(X4,sK8(X0,X1))
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(forward_subsumption_resolution,[],[f166,f244]) ).
fof(f284,plain,
! [X0,X1] :
( ~ in(X0,powerset(the_carrier(sK0)))
| ~ closed_subset(X0,sK0)
| ~ subset(X1,X0)
| ~ topological_space(sK0)
| in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f283,f99]) ).
fof(f285,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ closed_subset(X0,sK0)
| ~ in(X0,powerset(the_carrier(sK0)))
| in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f284,f100]) ).
fof(f288,plain,
! [X0] :
( ~ closed_subset(sK2(X0),sK0)
| ~ in(sK2(X0),powerset(the_carrier(sK0)))
| in(sK2(X0),sK8(sK0,sK1))
| ~ element(sK1,powerset(the_carrier(sK0)))
| ~ element(X0,powerset(powerset(the_carrier(sK0))))
| in(sK2(X0),X0) ),
inference(resolution,[],[f285,f102]) ).
fof(f292,plain,
! [X0] :
( ~ in(sK2(X0),powerset(the_carrier(sK0)))
| ~ closed_subset(sK2(X0),sK0)
| in(sK2(X0),sK8(sK0,sK1))
| ~ element(X0,powerset(powerset(the_carrier(sK0))))
| in(sK2(X0),X0) ),
inference(forward_subsumption_resolution,[],[f288,f98]) ).
fof(f350,plain,
! [X0] :
( ~ closed_subset(sK2(X0),sK0)
| in(sK2(X0),sK8(sK0,sK1))
| ~ element(X0,powerset(powerset(the_carrier(sK0))))
| in(sK2(X0),X0)
| ~ element(sK2(X0),powerset(the_carrier(sK0)))
| empty(powerset(the_carrier(sK0))) ),
inference(resolution,[],[f292,f154]) ).
fof(f352,plain,
! [X0] :
( ~ closed_subset(sK2(X0),sK0)
| in(sK2(X0),sK8(sK0,sK1))
| ~ element(X0,powerset(powerset(the_carrier(sK0))))
| in(sK2(X0),X0)
| ~ element(sK2(X0),powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f350,f145]) ).
fof(f353,plain,
! [X0] :
( ~ closed_subset(sK2(X0),sK0)
| in(sK2(X0),sK8(sK0,sK1))
| ~ element(X0,powerset(powerset(the_carrier(sK0))))
| in(sK2(X0),X0) ),
inference(forward_subsumption_resolution,[],[f352,f101]) ).
fof(f516,plain,
! [X2,X0,X1] :
( ~ top_str(X2)
| ~ element(X1,powerset(powerset(the_carrier(sK0))))
| ~ in(sK2(X1),sK8(sK0,X0))
| ~ in(sK2(X1),X1)
| ~ in(sK2(X1),sK8(X2,sK1))
| ~ topological_space(X2)
| ~ element(X0,powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(the_carrier(X2))) ),
inference(resolution,[],[f282,f146]) ).
fof(f911,definition,
( spl14_36
<=> element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0)))) ),
introduced(definition,[new_symbols(definition,[spl14_36])],[avatar_definition]) ).
fof(f912,plain,
( element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| ~ spl14_36 ),
inference(avatar_component_clause,[],[f911]) ).
fof(f913,plain,
( ~ element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| spl14_36 ),
inference(avatar_component_clause,[],[f911]) ).
fof(f915,definition,
( spl14_37
<=> sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl14_37])],[avatar_definition]) ).
fof(f917,plain,
( sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1))
| ~ spl14_37 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f949,plain,
( ~ element(sK1,powerset(the_carrier(sK0)))
| in(sK11(sK8(sK0,sK1),powerset(the_carrier(sK0))),powerset(the_carrier(sK0)))
| spl14_36 ),
inference(resolution,[],[f913,f268]) ).
fof(f955,plain,
( in(sK11(sK8(sK0,sK1),powerset(the_carrier(sK0))),powerset(the_carrier(sK0)))
| spl14_36 ),
inference(forward_subsumption_resolution,[],[f949,f98]) ).
fof(f957,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(the_carrier(sK0))))
| ~ in(sK2(X0),sK8(sK0,X1))
| ~ in(sK2(X0),X0)
| ~ in(sK2(X0),sK8(sK0,sK1))
| ~ topological_space(sK0)
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(the_carrier(sK0))) ),
inference(resolution,[],[f516,f99]) ).
fof(f958,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(the_carrier(sK0))))
| ~ in(sK2(X0),sK8(sK0,X1))
| ~ in(sK2(X0),X0)
| ~ in(sK2(X0),sK8(sK0,sK1))
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ element(sK1,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f957,f100]) ).
fof(f959,plain,
! [X0,X1] :
( ~ in(sK2(X0),X0)
| ~ in(sK2(X0),sK8(sK0,X1))
| ~ element(X0,powerset(powerset(the_carrier(sK0))))
| ~ in(sK2(X0),sK8(sK0,sK1))
| ~ element(X1,powerset(the_carrier(sK0))) ),
inference(forward_subsumption_resolution,[],[f958,f98]) ).
fof(f1123,plain,
( element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| spl14_36 ),
inference(resolution,[],[f955,f159]) ).
fof(f1136,plain,
( $false
| spl14_36 ),
inference(forward_subsumption_resolution,[],[f1123,f913]) ).
fof(f1137,plain,
spl14_36,
inference(avatar_contradiction_clause,[],[f1136]) ).
fof(f1707,definition,
( spl14_74
<=> ! [X0] :
( ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,X0))
| ~ element(X0,powerset(the_carrier(sK0))) ) ),
introduced(definition,[new_symbols(definition,[spl14_74])],[avatar_definition]) ).
fof(f1708,plain,
( ! [X0] :
( ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,X0))
| ~ element(X0,powerset(the_carrier(sK0))) )
| ~ spl14_74 ),
inference(avatar_component_clause,[],[f1707]) ).
fof(f1710,definition,
( spl14_75
<=> in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl14_75])],[avatar_definition]) ).
fof(f1711,plain,
( in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ spl14_75 ),
inference(avatar_component_clause,[],[f1710]) ).
fof(f1712,plain,
( ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| spl14_75 ),
inference(avatar_component_clause,[],[f1710]) ).
fof(f1714,plain,
( sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1))
| ~ element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| spl14_75 ),
inference(resolution,[],[f1712,f104]) ).
fof(f1717,plain,
( sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1))
| ~ spl14_36
| spl14_75 ),
inference(forward_subsumption_resolution,[],[f1714,f912]) ).
fof(f1718,plain,
( spl14_37
| ~ spl14_36
| spl14_75 ),
inference(avatar_split_clause,[],[f1717,f1710,f911,f915]) ).
fof(f1726,plain,
( closed_subset(sK2(sK8(sK0,sK1)),sK0)
| ~ element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ spl14_37 ),
inference(superposition,[],[f103,f917]) ).
fof(f1727,plain,
( closed_subset(sK2(sK8(sK0,sK1)),sK0)
| in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ spl14_36
| ~ spl14_37 ),
inference(forward_subsumption_resolution,[],[f1726,f912]) ).
fof(f1728,plain,
( closed_subset(sK2(sK8(sK0,sK1)),sK0)
| ~ spl14_36
| ~ spl14_37
| spl14_75 ),
inference(forward_subsumption_resolution,[],[f1727,f1712]) ).
fof(f1729,plain,
( in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ spl14_36
| ~ spl14_37
| spl14_75 ),
inference(resolution,[],[f1728,f353]) ).
fof(f1731,plain,
( in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| ~ spl14_36
| ~ spl14_37
| spl14_75 ),
inference(duplicate_literal_removal,[],[f1729]) ).
fof(f1732,plain,
( ~ element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| ~ spl14_36
| ~ spl14_37
| spl14_75 ),
inference(forward_subsumption_resolution,[],[f1731,f1712]) ).
fof(f1733,plain,
( $false
| ~ spl14_36
| ~ spl14_37
| spl14_75 ),
inference(forward_subsumption_resolution,[],[f1732,f912]) ).
fof(f1734,plain,
( ~ spl14_36
| ~ spl14_37
| spl14_75 ),
inference(avatar_contradiction_clause,[],[f1733]) ).
fof(f1741,plain,
( ! [X0] :
( ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,X0))
| ~ element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0))))
| ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ element(X0,powerset(the_carrier(sK0))) )
| ~ spl14_75 ),
inference(resolution,[],[f1711,f959]) ).
fof(f1754,plain,
( ! [X0] :
( ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,X0))
| ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ element(X0,powerset(the_carrier(sK0))) )
| ~ spl14_36
| ~ spl14_75 ),
inference(forward_subsumption_resolution,[],[f1741,f912]) ).
fof(f1755,plain,
( ! [X0] :
( ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,X0))
| ~ element(X0,powerset(the_carrier(sK0))) )
| ~ spl14_36
| ~ spl14_75 ),
inference(forward_subsumption_resolution,[],[f1754,f1711]) ).
fof(f1756,plain,
( spl14_74
| ~ spl14_36
| ~ spl14_75 ),
inference(avatar_split_clause,[],[f1755,f1710,f911,f1707]) ).
fof(f1826,plain,
( ~ element(sK1,powerset(the_carrier(sK0)))
| ~ spl14_74
| ~ spl14_75 ),
inference(resolution,[],[f1708,f1711]) ).
fof(f1831,plain,
( $false
| ~ spl14_74
| ~ spl14_75 ),
inference(forward_subsumption_resolution,[],[f1826,f98]) ).
fof(f1832,plain,
( ~ spl14_74
| ~ spl14_75 ),
inference(avatar_contradiction_clause,[],[f1831]) ).
cnf(s39,plain,
spl14_36,
inference(sat_conversion,[],[f1137]) ).
cnf(s69,plain,
( ~ spl14_36
| spl14_37
| spl14_75 ),
inference(sat_conversion,[],[f1718]) ).
cnf(s70,plain,
( ~ spl14_36
| ~ spl14_37
| spl14_75 ),
inference(sat_conversion,[],[f1734]) ).
cnf(s72,plain,
( ~ spl14_36
| spl14_74
| ~ spl14_75 ),
inference(sat_conversion,[],[f1756]) ).
cnf(s80,plain,
( ~ spl14_74
| ~ spl14_75 ),
inference(sat_conversion,[],[f1832]) ).
cnf(s93,plain,
~ spl14_75,
inference(rat,[],[s72,s80,s39]) ).
cnf(s94,plain,
~ spl14_37,
inference(rat,[],[s70,s39,s93]) ).
cnf(s95,plain,
$false,
inference(rat,[],[s69,s39,s93,s94]) ).
fof(f1833,plain,
$false,
inference(avatar_sat_refutation,[],[s95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU315+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 04:39:45 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.24/1.32 % (2663503)Detected formulas, will run a generic FOF schedule.
% 3.24/1.32 % (2663514)dis-21_1_sil=8000:lcm=predicate:random_seed=1999739125: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)
% 3.24/1.32 % (2663508)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=648659723:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.24/1.32 % (2663514)Instruction limit reached!
% 3.24/1.32 % (2663514)------------------------------
% 3.24/1.32 % (2663514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.24/1.32 % (2663514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.32 % (2663514)CaDiCaL version: 2.1.3
% 3.24/1.32 % (2663514)Termination reason: Instruction limit
% 3.24/1.32 % (2663514)Termination phase: Saturation
% 3.24/1.32 % (2663514)Time elapsed: 0.035 s
% 3.24/1.32 % (2663514)Peak memory usage: 88 MB
% 3.24/1.32 % (2663514)Instructions burned: 132 (million)
% 3.24/1.32 % (2663511)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=956645517:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.24/1.32 % (2663510)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=2300830858:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.24/1.32 % (2663509)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=2622676061:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.24/1.32 % (2663511)Refutation not found, incomplete strategy
% 3.24/1.32 % (2663511)------------------------------
% 3.24/1.32 % (2663511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.24/1.32 % (2663511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.32 % (2663512)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3379651907:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.24/1.32 % (2663511)CaDiCaL version: 2.1.3
% 3.24/1.32 % (2663511)Termination reason: Refutation not found, incomplete strategy
% 3.24/1.32 % (2663511)Time elapsed: 0.006 s
% 3.24/1.32 % (2663511)Peak memory usage: 88 MB
% 3.24/1.32 % (2663511)Instructions burned: 8 (million)
% 3.24/1.32 % (2663513)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3177882449:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.24/1.32 % (2663513)First to succeed.
% 3.24/1.32 % (2663513)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2663503"
% 3.24/1.32 % (2663512)Instruction limit reached!
% 3.24/1.32 % (2663512)------------------------------
% 3.24/1.32 % (2663512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.24/1.32 % (2663512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.32 % (2663512)CaDiCaL version: 2.1.3
% 3.24/1.32 % (2663512)Termination reason: Instruction limit
% 3.24/1.32 % (2663512)Termination phase: Saturation
% 3.24/1.32 % (2663512)Time elapsed: 0.076 s
% 3.24/1.32 % (2663512)Peak memory usage: 88 MB
% 3.24/1.32 % (2663512)Instructions burned: 119 (million)
% 3.24/1.32 % (2663520)lrs+10_1_sil=8000:sp=occurrence:random_seed=3878391740:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.24/1.32 % (2663520)Instruction limit reached!
% 3.24/1.32 % (2663520)------------------------------
% 3.24/1.32 % (2663520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.24/1.32 % (2663520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.32 % (2663520)CaDiCaL version: 2.1.3
% 3.24/1.32 % (2663520)Termination reason: Instruction limit
% 3.24/1.32 % (2663520)Termination phase: Saturation
% 3.24/1.32 % (2663520)Time elapsed: 0.094 s
% 3.24/1.32 % (2663520)Peak memory usage: 91 MB
% 3.24/1.32 % (2663520)Instructions burned: 287 (million)
% 3.24/1.32 % (2663524)lrs+10_1_sil=32000:urr=on:br=off:random_seed=473572145:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.24/1.32 % (2663511)------------------------------
% 3.24/1.32 % (2663511)------------------------------
% 3.24/1.32 % (2663525)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3076218287:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.24/1.32 % (2663524)Instruction limit reached!
% 3.24/1.32 % (2663524)------------------------------
% 3.24/1.32 % (2663524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.24/1.32 % (2663524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.32 % (2663524)CaDiCaL version: 2.1.3
% 3.24/1.32 % (2663524)Termination reason: Instruction limit
% 3.24/1.32 % (2663524)Termination phase: Saturation
% 3.24/1.32 % (2663524)Time elapsed: 0.092 s
% 3.24/1.32 % (2663524)Peak memory usage: 89 MB
% 3.24/1.32 % (2663524)Instructions burned: 158 (million)
% 3.24/1.32 % (2663525)Also succeeded, but the first one will report.
% 3.24/1.32 % (2663513)Refutation found. Thanks to Tanya!
% 3.24/1.32 % SZS status Theorem for theBenchmark
% 3.24/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.95/1.52 % (2663513)------------------------------
% 3.95/1.52 % (2663513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.52 % (2663513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.52 % (2663513)CaDiCaL version: 2.1.3
% 3.95/1.52 % (2663513)Termination reason: Refutation
% 3.95/1.52 % (2663513)Time elapsed: 0.057 s
% 3.95/1.52 % (2663513)Peak memory usage: 91 MB
% 3.95/1.52 % (2663513)Instructions burned: 71 (million)
% 3.95/1.52 % (2663513)------------------------------
% 3.95/1.52 % (2663513)------------------------------
% 3.95/1.52 % (2663503)Success in time 0.469 s
% 3.95/1.52 % Vampire exiting
%------------------------------------------------------------------------------