%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU336+2 : 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 : 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 : Tue Sep 29 12:48:24 PM UTC 2026
% Result : Theorem 6.88s 2.31s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 95 ( 10 unt; 2 def)
% Number of atoms : 388 ( 17 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 480 ( 187 ~; 204 |; 48 &)
% ( 18 <=>; 22 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 149 ( 0 sgn 136 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f66,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(f78,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(f118,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(f169,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(f260,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(f404,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( closed_subsets(X1,X0)
<=> open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_tops_2) ).
fof(f405,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( closed_subsets(X1,X0)
<=> open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f404]) ).
fof(f448,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(f455,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(f501,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f685,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,[],[f66]) ).
fof(f686,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,[],[f685]) ).
fof(f697,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,[],[f78]) ).
fof(f698,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,[],[f697]) ).
fof(f736,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,[],[f118]) ).
fof(f770,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f169]) ).
fof(f856,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f260]) ).
fof(f1026,plain,
? [X0] :
( ? [X1] :
( ( closed_subsets(X1,X0)
<~> open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& top_str(X0) ),
inference(ennf_transformation,[],[f405]) ).
fof(f1086,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,[],[f448]) ).
fof(f1092,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,[],[f455]) ).
fof(f1142,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f501]) ).
fof(f1143,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f1142]) ).
fof(f1370,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,[],[f686]) ).
fof(f1371,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,[],[f1370]) ).
fof(f1372,plain,
! [X0] :
( ! [X1] :
( ( ( open_subsets(X1,X0)
| ( ~ open_subset(sK92(X0,X1),X0)
& in(sK92(X0,X1),X1)
& element(sK92(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,[sK92]),skolemize(X2,sK92(X0,X1))],[f1371]) ).
fof(f1401,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,[],[f698]) ).
fof(f1402,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,[],[f1401]) ).
fof(f1403,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subsets(X1,X0)
| ( ~ closed_subset(sK104(X0,X1),X0)
& in(sK104(X0,X1),X1)
& element(sK104(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,[sK104]),skolemize(X2,sK104(X0,X1))],[f1402]) ).
fof(f1493,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,[],[f736]) ).
fof(f1494,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,[],[f1493]) ).
fof(f1495,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,[],[f1494]) ).
fof(f1496,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ( ( ~ in(subset_complement(X0,sK155(X0,X1,X2)),X1)
| ~ in(sK155(X0,X1,X2),X2) )
& ( in(subset_complement(X0,sK155(X0,X1,X2)),X1)
| in(sK155(X0,X1,X2),X2) )
& element(sK155(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,[sK155]),skolemize(X3,sK155(X0,X1,X2))],[f1495]) ).
fof(f1820,plain,
? [X0] :
( ? [X1] :
( ( ~ open_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ closed_subsets(X1,X0) )
& ( open_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| closed_subsets(X1,X0) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& top_str(X0) ),
inference(nnf_transformation,[],[f1026]) ).
fof(f1821,plain,
? [X0] :
( ? [X1] :
( ( ~ open_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ closed_subsets(X1,X0) )
& ( open_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| closed_subsets(X1,X0) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& top_str(X0) ),
inference(flattening,[],[f1820]) ).
fof(f1822,plain,
( ( ~ open_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| ~ closed_subsets(sK448,sK447) )
& ( open_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| closed_subsets(sK448,sK447) )
& element(sK448,powerset(powerset(the_carrier(sK447))))
& top_str(sK447) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK447,sK448]),skolemize(X0,sK447),skolemize(X1,sK448)],[f1821]) ).
fof(f1836,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,[],[f1086]) ).
fof(f1839,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,[],[f1092]) ).
fof(f2085,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,[],[f1372]) ).
fof(f2086,plain,
! [X0,X1] :
( element(sK92(X0,X1),powerset(the_carrier(X0)))
| open_subsets(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f2087,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| in(sK92(X0,X1),X1)
| open_subsets(X1,X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f2088,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ open_subset(sK92(X0,X1),X0)
| open_subsets(X1,X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f1372]) ).
fof(f2130,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,[],[f1403]) ).
fof(f2131,plain,
! [X0,X1] :
( element(sK104(X0,X1),powerset(the_carrier(X0)))
| closed_subsets(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f1403]) ).
fof(f2132,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| in(sK104(X0,X1),X1)
| closed_subsets(X1,X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f1403]) ).
fof(f2133,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ closed_subset(sK104(X0,X1),X0)
| closed_subsets(X1,X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f1403]) ).
fof(f2305,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,[],[f1496]) ).
fof(f2337,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f770]) ).
fof(f2505,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f856]) ).
fof(f3189,plain,
top_str(sK447),
inference(cnf_transformation,[],[f1822]) ).
fof(f3190,plain,
element(sK448,powerset(powerset(the_carrier(sK447)))),
inference(cnf_transformation,[],[f1822]) ).
fof(f3191,plain,
( open_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| closed_subsets(sK448,sK447) ),
inference(cnf_transformation,[],[f1822]) ).
fof(f3192,plain,
( ~ open_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| ~ closed_subsets(sK448,sK447) ),
inference(cnf_transformation,[],[f1822]) ).
fof(f3256,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,[],[f1836]) ).
fof(f3266,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,[],[f1839]) ).
fof(f3348,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f1143]) ).
fof(f3485,definition,
( spl476_5
<=> closed_subsets(sK448,sK447) ),
introduced(definition,[new_symbols(definition,[spl476_5])],[avatar_definition]) ).
fof(f3486,plain,
( ~ closed_subsets(sK448,sK447)
| spl476_5 ),
inference(avatar_component_clause,[],[f3485]) ).
fof(f3487,plain,
( closed_subsets(sK448,sK447)
| ~ spl476_5 ),
inference(avatar_component_clause,[],[f3485]) ).
fof(f3489,definition,
( spl476_6
<=> open_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447) ),
introduced(definition,[new_symbols(definition,[spl476_6])],[avatar_definition]) ).
fof(f3490,plain,
( ~ open_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| spl476_6 ),
inference(avatar_component_clause,[],[f3489]) ).
fof(f3491,plain,
( open_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| ~ spl476_6 ),
inference(avatar_component_clause,[],[f3489]) ).
fof(f3492,plain,
( spl476_5
| spl476_6 ),
inference(avatar_split_clause,[],[f3191,f3489,f3485]) ).
fof(f3493,plain,
( ~ spl476_5
| ~ spl476_6 ),
inference(avatar_split_clause,[],[f3192,f3489,f3485]) ).
fof(f3735,plain,
element(complements_of_subsets(the_carrier(sK447),sK448),powerset(powerset(the_carrier(sK447)))),
inference(unit_resulting_resolution,[],[f2337,f3190]) ).
fof(f3737,plain,
element(complements_of_subsets(the_carrier(sK447),complements_of_subsets(the_carrier(sK447),sK448)),powerset(powerset(the_carrier(sK447)))),
inference(unit_resulting_resolution,[],[f2337,f3735]) ).
fof(f3739,plain,
sK448 = complements_of_subsets(the_carrier(sK447),complements_of_subsets(the_carrier(sK447),sK448)),
inference(unit_resulting_resolution,[],[f2505,f3190]) ).
fof(f3741,plain,
complements_of_subsets(the_carrier(sK447),sK448) = complements_of_subsets(the_carrier(sK447),complements_of_subsets(the_carrier(sK447),complements_of_subsets(the_carrier(sK447),sK448))),
inference(unit_resulting_resolution,[],[f2505,f3735]) ).
fof(f3759,plain,
( in(sK92(sK447,complements_of_subsets(the_carrier(sK447),sK448)),complements_of_subsets(the_carrier(sK447),sK448))
| spl476_6 ),
inference(unit_resulting_resolution,[],[f2087,f3189,f3490,f3735]) ).
fof(f3762,plain,
( ~ open_subset(sK92(sK447,complements_of_subsets(the_carrier(sK447),sK448)),sK447)
| spl476_6 ),
inference(unit_resulting_resolution,[],[f2088,f3189,f3490,f3735]) ).
fof(f3766,plain,
( element(sK92(sK447,complements_of_subsets(the_carrier(sK447),sK448)),powerset(the_carrier(sK447)))
| spl476_6 ),
inference(unit_resulting_resolution,[],[f2086,f3189,f3490,f3735]) ).
fof(f3827,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,[],[f2085,f3348]) ).
fof(f3829,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,[],[f2130,f3348]) ).
fof(f3832,plain,
! [X2,X0,X1,X4] :
( complements_of_subsets(X0,X1) != X2
| ~ in(X4,X2)
| in(subset_complement(X0,X4),X1)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[],[f2305,f3348]) ).
fof(f3833,plain,
( in(subset_complement(the_carrier(sK447),sK92(sK447,complements_of_subsets(the_carrier(sK447),sK448))),complements_of_subsets(the_carrier(sK447),complements_of_subsets(the_carrier(sK447),sK448)))
| spl476_6 ),
inference(unit_resulting_resolution,[],[f3832,f3759,f3737,f3741,f3735]) ).
fof(f3868,plain,
( in(subset_complement(the_carrier(sK447),sK92(sK447,complements_of_subsets(the_carrier(sK447),sK448))),sK448)
| spl476_6 ),
inference(superposition,[],[f3833,f3739]) ).
fof(f3873,plain,
( closed_subset(subset_complement(the_carrier(sK447),sK92(sK447,complements_of_subsets(the_carrier(sK447),sK448))),sK447)
| ~ spl476_5
| spl476_6 ),
inference(unit_resulting_resolution,[],[f3829,f3189,f3487,f3190,f3868]) ).
fof(f4619,plain,
( ~ top_str(sK447)
| ~ spl476_5
| spl476_6 ),
inference(unit_resulting_resolution,[],[f3266,f3762,f3766,f3873]) ).
fof(f4628,plain,
( $false
| ~ spl476_5
| spl476_6 ),
inference(forward_subsumption_resolution,[],[f4619,f3189]) ).
fof(f4629,plain,
( ~ spl476_5
| spl476_6 ),
inference(avatar_contradiction_clause,[],[f4628]) ).
fof(f4630,plain,
( element(sK104(sK447,sK448),powerset(the_carrier(sK447)))
| spl476_5 ),
inference(unit_resulting_resolution,[],[f2131,f3189,f3190,f3486]) ).
fof(f4631,plain,
( ~ closed_subset(sK104(sK447,sK448),sK447)
| spl476_5 ),
inference(unit_resulting_resolution,[],[f2133,f3189,f3190,f3486]) ).
fof(f4632,plain,
( in(sK104(sK447,sK448),sK448)
| spl476_5 ),
inference(unit_resulting_resolution,[],[f2132,f3189,f3190,f3486]) ).
fof(f4691,plain,
( in(subset_complement(the_carrier(sK447),sK104(sK447,sK448)),complements_of_subsets(the_carrier(sK447),sK448))
| spl476_5 ),
inference(unit_resulting_resolution,[],[f3832,f3735,f3739,f3190,f4632]) ).
fof(f4692,plain,
( ~ open_subset(subset_complement(the_carrier(sK447),sK104(sK447,sK448)),sK447)
| spl476_5 ),
inference(unit_resulting_resolution,[],[f3256,f3189,f4631,f4630]) ).
fof(f5147,plain,
( ~ top_str(sK447)
| spl476_5
| ~ spl476_6 ),
inference(unit_resulting_resolution,[],[f3827,f3491,f4692,f3735,f4691]) ).
fof(f5159,plain,
( $false
| spl476_5
| ~ spl476_6 ),
inference(forward_subsumption_resolution,[],[f5147,f3189]) ).
fof(f5160,plain,
( spl476_5
| ~ spl476_6 ),
inference(avatar_contradiction_clause,[],[f5159]) ).
cnf(s3,plain,
( spl476_5
| spl476_6 ),
inference(sat_conversion,[],[f3492]) ).
cnf(s4,plain,
( ~ spl476_5
| ~ spl476_6 ),
inference(sat_conversion,[],[f3493]) ).
cnf(s63,plain,
( ~ spl476_5
| spl476_6 ),
inference(sat_conversion,[],[f4629]) ).
cnf(s70,plain,
( spl476_5
| ~ spl476_6 ),
inference(sat_conversion,[],[f5160]) ).
cnf(s71,plain,
spl476_5,
inference(rat,[],[s3,s70]) ).
cnf(s72,plain,
spl476_6,
inference(rat,[],[s63,s71]) ).
cnf(s73,plain,
$false,
inference(rat,[],[s4,s72,s71]) ).
fof(f5161,plain,
$false,
inference(avatar_sat_refutation,[],[s73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU336+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 % Computer : n017.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Mon Sep 28 04:43:29 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.46 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
% 6.88/2.31 % (3210069)Detected formulas, will run a generic FOF schedule.
% 6.88/2.31 % (3210077)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4242237169:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.88/2.31 % (3210078)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2342936804:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.88/2.31 % (3210077)Instruction limit reached!
% 6.88/2.31 % (3210077)------------------------------
% 6.88/2.31 % (3210077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.31 % (3210077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.31 % (3210077)CaDiCaL version: 2.1.3
% 6.88/2.31 % (3210077)Termination reason: Instruction limit
% 6.88/2.31 % (3210077)Termination phase: Saturation
% 6.88/2.31 % (3210077)Time elapsed: 0.056 s
% 6.88/2.31 % (3210077)Peak memory usage: 91 MB
% 6.88/2.31 % (3210077)Instructions burned: 110 (million)
% 6.88/2.31 % (3210075)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=3249318500:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.88/2.31 % (3210074)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=3715334757:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.88/2.31 % (3210076)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=3982746655:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.88/2.31 % (3210078)Instruction limit reached!
% 6.88/2.31 % (3210078)------------------------------
% 6.88/2.31 % (3210078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.31 % (3210078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.31 % (3210078)CaDiCaL version: 2.1.3
% 6.88/2.31 % (3210078)Termination reason: Instruction limit
% 6.88/2.31 % (3210078)Termination phase: Saturation
% 6.88/2.31 % (3210078)Time elapsed: 0.097 s
% 6.88/2.31 % (3210078)Peak memory usage: 91 MB
% 6.88/2.31 % (3210078)Instructions burned: 119 (million)
% 6.88/2.31 % (3210079)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3330096222:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.88/2.31 % (3210080)dis-21_1_sil=8000:lcm=predicate:random_seed=2494319363: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)
% 6.88/2.31 % (3210080)Instruction limit reached!
% 6.88/2.31 % (3210080)------------------------------
% 6.88/2.31 % (3210080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.31 % (3210080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.31 % (3210080)CaDiCaL version: 2.1.3
% 6.88/2.31 % (3210080)Termination reason: Instruction limit
% 6.88/2.31 % (3210080)Termination phase: Saturation
% 6.88/2.31 % (3210080)Time elapsed: 0.113 s
% 6.88/2.31 % (3210080)Peak memory usage: 91 MB
% 6.88/2.31 % (3210080)Instructions burned: 129 (million)
% 6.88/2.31 % (3210079)Instruction limit reached!
% 6.88/2.31 % (3210079)------------------------------
% 6.88/2.31 % (3210079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.31 % (3210079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.31 % (3210079)CaDiCaL version: 2.1.3
% 6.88/2.31 % (3210079)Termination reason: Instruction limit
% 6.88/2.31 % (3210079)Termination phase: Saturation
% 6.88/2.31 % (3210079)Time elapsed: 0.141 s
% 6.88/2.31 % (3210079)Peak memory usage: 91 MB
% 6.88/2.31 % (3210079)Instructions burned: 139 (million)
% 6.88/2.31 % (3210083)lrs+10_1_sil=8000:sp=occurrence:random_seed=1509499733:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.88/2.31 % (3210089)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3289439858:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.88/2.31 % (3210083)Instruction limit reached!
% 6.88/2.31 % (3210083)------------------------------
% 6.88/2.31 % (3210083)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.31 % (3210083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.31 % (3210083)CaDiCaL version: 2.1.3
% 6.88/2.31 % (3210083)Termination reason: Instruction limit
% 6.88/2.31 % (3210083)Termination phase: Saturation
% 6.88/2.31 % (3210083)Time elapsed: 0.165 s
% 6.88/2.31 % (3210083)Peak memory usage: 95 MB
% 6.88/2.31 % (3210083)Instructions burned: 286 (million)
% 6.88/2.31 % (3210089)Instruction limit reached!
% 6.88/2.31 % (3210089)------------------------------
% 6.88/2.31 % (3210089)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.31 % (3210089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.31 % (3210089)CaDiCaL version: 2.1.3
% 6.88/2.31 % (3210089)Termination reason: Instruction limit
% 6.88/2.31 % (3210089)Termination phase: Saturation
% 6.88/2.31 % (3210089)Time elapsed: 0.125 s
% 6.88/2.31 % (3210089)Peak memory usage: 89 MB
% 6.88/2.31 % (3210089)Instructions burned: 158 (million)
% 6.88/2.31 % (3210090)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1731708623:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 6.88/2.31 % (3210091)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=378575246:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.88/2.31 % (3210094)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3845504369:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 6.88/2.31 % (3210091)First to succeed.
% 6.88/2.31 % (3210091)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3210069"
% 6.88/2.31 % (3210095)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=276975121:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 6.88/2.31 % (3210094)Instruction limit reached!
% 6.88/2.31 % (3210094)------------------------------
% 6.88/2.31 % (3210094)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.31 % (3210094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.31 % (3210094)CaDiCaL version: 2.1.3
% 6.88/2.31 % (3210094)Termination reason: Instruction limit
% 6.88/2.31 % (3210094)Termination phase: Saturation
% 6.88/2.31 % (3210094)Time elapsed: 0.179 s
% 6.88/2.31 % (3210094)Peak memory usage: 93 MB
% 6.88/2.31 % (3210094)Instructions burned: 296 (million)
% 6.88/2.31 % (3210090)Instruction limit reached!
% 6.88/2.31 % (3210090)------------------------------
% 6.88/2.31 % (3210090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.31 % (3210090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.31 % (3210090)CaDiCaL version: 2.1.3
% 6.88/2.31 % (3210090)Termination reason: Instruction limit
% 6.88/2.31 % (3210090)Termination phase: Saturation
% 6.88/2.31 % (3210090)Time elapsed: 0.361 s
% 6.88/2.31 % (3210090)Peak memory usage: 94 MB
% 6.88/2.31 % (3210090)Instructions burned: 325 (million)
% 6.88/2.31 % (3210102)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4268087889:cts=off:i=113:fsr=off:ss=included:sgt=4_2990 on theBenchmark for (2990ds/113Mi)
% 6.88/2.31 % (3210102)Instruction limit reached!
% 6.88/2.31 % (3210102)------------------------------
% 6.88/2.31 % (3210102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.88/2.31 % (3210102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/2.31 % (3210102)CaDiCaL version: 2.1.3
% 6.88/2.31 % (3210102)Termination reason: Instruction limit
% 6.88/2.31 % (3210102)Termination phase: Saturation
% 6.88/2.31 % (3210102)Time elapsed: 0.061 s
% 6.88/2.31 % (3210102)Peak memory usage: 91 MB
% 6.88/2.31 % (3210102)Instructions burned: 114 (million)
% 6.88/2.31 % (3210091)Refutation found. Thanks to Tanya!
% 6.88/2.31 % SZS status Theorem for theBenchmark
% 6.88/2.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/2.51 % (3210091)------------------------------
% 0.24/2.51 % (3210091)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.24/2.51 % (3210091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/2.51 % (3210091)CaDiCaL version: 2.1.3
% 0.24/2.51 % (3210091)Termination reason: Refutation
% 0.24/2.51 % (3210091)Time elapsed: 0.141 s
% 0.24/2.51 % (3210091)Peak memory usage: 93 MB
% 0.24/2.51 % (3210091)Instructions burned: 137 (million)
% 0.24/2.51 % (3210091)------------------------------
% 0.24/2.51 % (3210091)------------------------------
% 0.24/2.51 % (3210069)Success in time 1.257 s
% 0.24/2.51 % Vampire exiting
%------------------------------------------------------------------------------