%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU322+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:48:20 PM UTC 2026
% Result : Theorem 4.40s 1.54s
% Output : Refutation 5.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 108 ( 21 unt; 3 def)
% Number of atoms : 294 ( 10 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 312 ( 126 ~; 138 |; 18 &)
% ( 11 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 148 ( 0 sgn 144 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] :
( one_sorted_str(X0)
=> ( empty_carrier(X0)
<=> empty(the_carrier(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_struct_0) ).
fof(f18,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_1) ).
fof(f19,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f23,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f24,axiom,
! [X0,X1] :
( ( top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(f25,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f34,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f35,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_tops_1) ).
fof(f42,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f43,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(interior(X0,X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_tops_1) ).
fof(f44,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(interior(X0,X1),X1) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(X1,topstr_closure(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_pre_topc) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f47,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,subset_complement(X0,X2))
& in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f50,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f69,plain,
! [X0] :
( ( empty_carrier(X0)
<=> empty(the_carrier(X0)) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1)))
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f71,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f74,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f75,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f24]) ).
fof(f76,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f80,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f34]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f81]) ).
fof(f88,plain,
? [X0] :
( ? [X1] :
( ~ subset(interior(X0,X1),X1)
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( subset(X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f90,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f46]) ).
fof(f91,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ in(X1,subset_complement(X0,X2))
| ~ in(X1,X2)
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ in(X1,subset_complement(X0,X2))
| ~ in(X1,X2)
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f92]) ).
fof(f96,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f98,plain,
! [X0] :
( ( ( empty_carrier(X0)
| ~ empty(the_carrier(X0)) )
& ( empty(the_carrier(X0))
| ~ empty_carrier(X0) ) )
| ~ one_sorted_str(X0) ),
inference(nnf_transformation,[],[f69]) ).
fof(f99,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f71]) ).
fof(f100,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f100]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(X2,subset_complement(the_carrier(X0),X1))
| in(X2,X1) )
& ( ~ in(X2,X1)
| ~ in(X2,subset_complement(the_carrier(X0),X1)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(nnf_transformation,[],[f82]) ).
fof(f109,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f110,plain,
( ~ subset(interior(sK7,sK8),sK8)
& element(sK8,powerset(the_carrier(sK7)))
& top_str(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f88]) ).
fof(f151,plain,
! [X0] :
( ~ empty_carrier(X0)
| empty(the_carrier(X0))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f153,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ),
inference(cnf_transformation,[],[f70]) ).
fof(f154,plain,
! [X3,X0,X1] :
( ~ in(X3,X0)
| in(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f155,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f156,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f158,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f159,plain,
! [X0,X1] :
( ~ top_str(X0)
| element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f160,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f171,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f80]) ).
fof(f173,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| in(X2,X1)
| in(X2,subset_complement(the_carrier(X0),X1))
| ~ element(X1,powerset(the_carrier(X0)))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f187,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f189,plain,
top_str(sK7),
inference(cnf_transformation,[],[f110]) ).
fof(f190,plain,
element(sK8,powerset(the_carrier(sK7))),
inference(cnf_transformation,[],[f110]) ).
fof(f191,plain,
~ subset(interior(sK7,sK8),sK8),
inference(cnf_transformation,[],[f110]) ).
fof(f192,plain,
! [X0,X1] :
( subset(X1,topstr_closure(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f193,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| element(X0,X2)
| ~ element(X1,powerset(X2)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f194,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f197,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f202,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK7)))
| interior(sK7,X0) = subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),X0))) ),
inference(resolution,[],[f153,f189]) ).
fof(f205,plain,
interior(sK7,sK8) = subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))),
inference(resolution,[],[f202,f190]) ).
fof(f210,plain,
element(subset_complement(the_carrier(sK7),sK8),powerset(the_carrier(sK7))),
inference(resolution,[],[f158,f190]) ).
fof(f221,plain,
one_sorted_str(sK7),
inference(resolution,[],[f160,f189]) ).
fof(f236,plain,
! [X2,X0,X1] :
( ~ in(sK0(X0,X1),subset_complement(X2,X0))
| ~ element(X0,powerset(X2))
| subset(X0,X1) ),
inference(resolution,[],[f194,f155]) ).
fof(f248,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK7)))
| element(topstr_closure(sK7,X0),powerset(the_carrier(sK7))) ),
inference(resolution,[],[f159,f189]) ).
fof(f251,plain,
element(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),powerset(the_carrier(sK7))),
inference(resolution,[],[f248,f210]) ).
fof(f293,plain,
! [X2,X0,X1] :
( ~ element(X0,powerset(X2))
| element(sK0(X0,X1),X2)
| subset(X0,X1) ),
inference(resolution,[],[f193,f155]) ).
fof(f304,definition,
( spl9_9
<=> empty(the_carrier(sK7)) ),
introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition]) ).
fof(f305,plain,
( empty(the_carrier(sK7))
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f312,definition,
( spl9_11
<=> empty_carrier(sK7) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
fof(f313,plain,
( empty_carrier(sK7)
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f318,plain,
! [X2,X0,X1] :
( in(sK0(X0,X1),X2)
| ~ subset(X0,X2)
| subset(X0,X1) ),
inference(resolution,[],[f154,f155]) ).
fof(f370,plain,
element(subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))),powerset(the_carrier(sK7))),
inference(resolution,[],[f251,f158]) ).
fof(f372,plain,
topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)) = subset_complement(the_carrier(sK7),subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))),
inference(resolution,[],[f251,f171]) ).
fof(f374,plain,
topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)) = subset_complement(the_carrier(sK7),interior(sK7,sK8)),
inference(forward_demodulation,[],[f372,f205]) ).
fof(f375,plain,
element(interior(sK7,sK8),powerset(the_carrier(sK7))),
inference(forward_demodulation,[],[f370,f205]) ).
fof(f381,plain,
! [X0] :
( element(sK0(interior(sK7,sK8),X0),the_carrier(sK7))
| subset(interior(sK7,sK8),X0) ),
inference(resolution,[],[f375,f293]) ).
fof(f383,plain,
subset(interior(sK7,sK8),the_carrier(sK7)),
inference(resolution,[],[f375,f187]) ).
fof(f395,plain,
! [X0,X1] :
( subset(interior(sK7,sK8),X0)
| in(sK0(interior(sK7,sK8),X0),X1)
| in(sK0(interior(sK7,sK8),X0),subset_complement(the_carrier(sK7),X1))
| ~ element(X1,powerset(the_carrier(sK7)))
| empty_carrier(sK7)
| ~ one_sorted_str(sK7) ),
inference(resolution,[],[f381,f173]) ).
fof(f399,plain,
( subset(subset_complement(the_carrier(sK7),sK8),subset_complement(the_carrier(sK7),interior(sK7,sK8)))
| ~ element(subset_complement(the_carrier(sK7),sK8),powerset(the_carrier(sK7)))
| ~ top_str(sK7) ),
inference(superposition,[],[f192,f374]) ).
fof(f400,plain,
( subset(subset_complement(the_carrier(sK7),sK8),subset_complement(the_carrier(sK7),interior(sK7,sK8)))
| ~ top_str(sK7) ),
inference(forward_subsumption_resolution,[],[f399,f210]) ).
fof(f401,plain,
subset(subset_complement(the_carrier(sK7),sK8),subset_complement(the_carrier(sK7),interior(sK7,sK8))),
inference(forward_subsumption_resolution,[],[f400,f189]) ).
fof(f418,plain,
( ! [X0] : ~ in(X0,the_carrier(sK7))
| ~ spl9_9 ),
inference(resolution,[],[f197,f305]) ).
fof(f490,plain,
( $false
| ~ spl9_9 ),
inference(unit_resulting_resolution,[],[f318,f191,f383,f418]) ).
fof(f494,plain,
~ spl9_9,
inference(avatar_contradiction_clause,[],[f490]) ).
fof(f603,plain,
( empty(the_carrier(sK7))
| ~ one_sorted_str(sK7)
| ~ spl9_11 ),
inference(resolution,[],[f151,f313]) ).
fof(f604,plain,
( empty(the_carrier(sK7))
| ~ spl9_11 ),
inference(forward_subsumption_resolution,[],[f603,f221]) ).
fof(f605,plain,
( spl9_9
| ~ spl9_11 ),
inference(avatar_split_clause,[],[f604,f312,f304]) ).
fof(f607,plain,
! [X0,X1] :
( subset(interior(sK7,sK8),X0)
| in(sK0(interior(sK7,sK8),X0),X1)
| in(sK0(interior(sK7,sK8),X0),subset_complement(the_carrier(sK7),X1))
| ~ element(X1,powerset(the_carrier(sK7)))
| empty_carrier(sK7) ),
inference(forward_subsumption_resolution,[],[f395,f221]) ).
fof(f613,definition,
( spl9_34
<=> ! [X0,X1] :
( subset(interior(sK7,sK8),X0)
| ~ element(X1,powerset(the_carrier(sK7)))
| in(sK0(interior(sK7,sK8),X0),subset_complement(the_carrier(sK7),X1))
| in(sK0(interior(sK7,sK8),X0),X1) ) ),
introduced(definition,[new_symbols(definition,[spl9_34])],[avatar_definition]) ).
fof(f614,plain,
( ! [X0,X1] :
( ~ element(X1,powerset(the_carrier(sK7)))
| subset(interior(sK7,sK8),X0)
| in(sK0(interior(sK7,sK8),X0),subset_complement(the_carrier(sK7),X1))
| in(sK0(interior(sK7,sK8),X0),X1) )
| ~ spl9_34 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f615,plain,
( spl9_11
| spl9_34 ),
inference(avatar_split_clause,[],[f607,f613,f312]) ).
fof(f666,plain,
( ! [X0] :
( in(sK0(interior(sK7,sK8),X0),subset_complement(the_carrier(sK7),sK8))
| subset(interior(sK7,sK8),X0)
| in(sK0(interior(sK7,sK8),X0),sK8) )
| ~ spl9_34 ),
inference(resolution,[],[f614,f190]) ).
fof(f675,plain,
( ! [X0,X1] :
( ~ subset(subset_complement(the_carrier(sK7),sK8),X1)
| in(sK0(interior(sK7,sK8),X0),sK8)
| in(sK0(interior(sK7,sK8),X0),X1)
| subset(interior(sK7,sK8),X0) )
| ~ spl9_34 ),
inference(resolution,[],[f666,f154]) ).
fof(f703,plain,
( ! [X0] :
( in(sK0(interior(sK7,sK8),X0),subset_complement(the_carrier(sK7),interior(sK7,sK8)))
| in(sK0(interior(sK7,sK8),X0),sK8)
| subset(interior(sK7,sK8),X0) )
| ~ spl9_34 ),
inference(resolution,[],[f675,f401]) ).
fof(f706,plain,
( ! [X0] :
( in(sK0(interior(sK7,sK8),X0),sK8)
| subset(interior(sK7,sK8),X0)
| ~ element(interior(sK7,sK8),powerset(the_carrier(sK7)))
| subset(interior(sK7,sK8),X0) )
| ~ spl9_34 ),
inference(resolution,[],[f703,f236]) ).
fof(f713,plain,
( ! [X0] :
( in(sK0(interior(sK7,sK8),X0),sK8)
| subset(interior(sK7,sK8),X0)
| ~ element(interior(sK7,sK8),powerset(the_carrier(sK7))) )
| ~ spl9_34 ),
inference(duplicate_literal_removal,[],[f706]) ).
fof(f721,plain,
( ! [X0] :
( in(sK0(interior(sK7,sK8),X0),sK8)
| subset(interior(sK7,sK8),X0) )
| ~ spl9_34 ),
inference(forward_subsumption_resolution,[],[f713,f375]) ).
fof(f722,plain,
( subset(interior(sK7,sK8),sK8)
| subset(interior(sK7,sK8),sK8)
| ~ spl9_34 ),
inference(resolution,[],[f721,f156]) ).
fof(f727,plain,
( subset(interior(sK7,sK8),sK8)
| ~ spl9_34 ),
inference(duplicate_literal_removal,[],[f722]) ).
fof(f728,plain,
( $false
| ~ spl9_34 ),
inference(forward_subsumption_resolution,[],[f727,f191]) ).
fof(f729,plain,
~ spl9_34,
inference(avatar_contradiction_clause,[],[f728]) ).
cnf(s16,plain,
~ spl9_9,
inference(sat_conversion,[],[f494]) ).
cnf(s25,plain,
( spl9_9
| ~ spl9_11 ),
inference(sat_conversion,[],[f605]) ).
cnf(s27,plain,
( spl9_11
| spl9_34 ),
inference(sat_conversion,[],[f615]) ).
cnf(s31,plain,
~ spl9_34,
inference(sat_conversion,[],[f729]) ).
cnf(s32,plain,
spl9_11,
inference(rat,[],[s27,s31]) ).
cnf(s33,plain,
spl9_9,
inference(rat,[],[s25,s32]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s16,s33]) ).
fof(f730,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU322+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 04:40:37 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.40/1.54 % (807100)Detected formulas, will run a generic FOF schedule.
% 4.40/1.54 % (807106)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=831843511:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.40/1.54 % (807109)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3716224745:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.40/1.54 % (807105)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=4263545789:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.40/1.54 % (807108)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2889210481:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.40/1.54 % (807107)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=129664408:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.40/1.54 % (807111)dis-21_1_sil=8000:lcm=predicate:random_seed=3347320735: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)
% 4.40/1.54 % (807110)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=318444114:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.40/1.54 % (807108)Refutation not found, incomplete strategy
% 4.40/1.54 % (807108)------------------------------
% 4.40/1.54 % (807108)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.54 % (807108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.54 % (807108)CaDiCaL version: 2.1.3
% 4.40/1.54 % (807108)Termination reason: Refutation not found, incomplete strategy
% 4.40/1.54 % (807108)Time elapsed: 0.002 s
% 4.40/1.54 % (807108)Peak memory usage: 88 MB
% 4.40/1.54 % (807108)Instructions burned: 1 (million)
% 4.40/1.54 % (807111)Instruction limit reached!
% 4.40/1.54 % (807111)------------------------------
% 4.40/1.54 % (807111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.54 % (807111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.54 % (807111)CaDiCaL version: 2.1.3
% 4.40/1.54 % (807111)Termination reason: Instruction limit
% 4.40/1.54 % (807111)Termination phase: Saturation
% 4.40/1.54 % (807111)Time elapsed: 0.050 s
% 4.40/1.54 % (807111)Peak memory usage: 88 MB
% 4.40/1.54 % (807111)Instructions burned: 130 (million)
% 4.40/1.54 % (807109)Instruction limit reached!
% 4.40/1.54 % (807109)------------------------------
% 4.40/1.54 % (807109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.54 % (807109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.54 % (807109)CaDiCaL version: 2.1.3
% 4.40/1.54 % (807109)Termination reason: Instruction limit
% 4.40/1.54 % (807109)Termination phase: Saturation
% 4.40/1.54 % (807109)Time elapsed: 0.077 s
% 4.40/1.54 % (807109)Peak memory usage: 88 MB
% 4.40/1.54 % (807109)Instructions burned: 120 (million)
% 4.40/1.54 % (807110)Instruction limit reached!
% 4.40/1.54 % (807110)------------------------------
% 4.40/1.54 % (807110)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.54 % (807110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.54 % (807110)CaDiCaL version: 2.1.3
% 4.40/1.54 % (807110)Termination reason: Instruction limit
% 4.40/1.54 % (807110)Termination phase: Saturation
% 4.40/1.54 % (807110)Time elapsed: 0.105 s
% 4.40/1.54 % (807110)Peak memory usage: 90 MB
% 4.40/1.54 % (807110)Instructions burned: 140 (million)
% 4.40/1.54 % (807119)lrs+10_1_sil=8000:sp=occurrence:random_seed=1870523766:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.40/1.54 % (807120)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2536281941:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.40/1.54 % (807121)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2118741139:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.40/1.54 % (807108)------------------------------
% 4.40/1.54 % (807108)------------------------------
% 4.40/1.54 % (807120)Instruction limit reached!
% 4.40/1.54 % (807120)------------------------------
% 4.40/1.54 % (807120)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.54 % (807120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.54 % (807120)CaDiCaL version: 2.1.3
% 4.40/1.54 % (807120)Termination reason: Instruction limit
% 4.40/1.54 % (807120)Termination phase: Saturation
% 4.40/1.54 % (807120)Time elapsed: 0.090 s
% 4.40/1.54 % (807120)Peak memory usage: 90 MB
% 4.40/1.54 % (807120)Instructions burned: 158 (million)
% 4.40/1.54 % (807119)Instruction limit reached!
% 4.40/1.54 % (807119)------------------------------
% 4.40/1.54 % (807119)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.54 % (807119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.54 % (807119)CaDiCaL version: 2.1.3
% 4.40/1.54 % (807119)Termination reason: Instruction limit
% 4.40/1.54 % (807119)Termination phase: Saturation
% 4.40/1.54 % (807119)Time elapsed: 0.185 s
% 4.40/1.54 % (807119)Peak memory usage: 92 MB
% 4.40/1.54 % (807119)Instructions burned: 286 (million)
% 4.40/1.54 % (807106)First to succeed.
% 4.40/1.54 % (807106)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-807100"
% 4.40/1.54 % (807125)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=985481817:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 4.40/1.54 % (807126)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3581232416:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.40/1.54 % (807121)Instruction limit reached!
% 4.40/1.54 % (807121)------------------------------
% 4.40/1.54 % (807121)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.40/1.54 % (807121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.40/1.54 % (807121)CaDiCaL version: 2.1.3
% 4.40/1.54 % (807121)Termination reason: Instruction limit
% 4.40/1.54 % (807121)Termination phase: Saturation
% 4.40/1.54 % (807121)Time elapsed: 0.202 s
% 4.40/1.54 % (807121)Peak memory usage: 92 MB
% 4.40/1.54 % (807121)Instructions burned: 325 (million)
% 4.40/1.54 % (807125)Also succeeded, but the first one will report.
% 4.40/1.54 % (807127)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3685710703:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.40/1.54 % (807106)Refutation found. Thanks to Tanya!
% 4.40/1.54 % SZS status Theorem for theBenchmark
% 4.40/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 5.55/1.73 % (807106)------------------------------
% 5.55/1.73 % (807106)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.73 % (807106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.73 % (807106)CaDiCaL version: 2.1.3
% 5.55/1.73 % (807106)Termination reason: Refutation
% 5.55/1.73 % (807106)Time elapsed: 0.415 s
% 5.55/1.73 % (807106)Peak memory usage: 130 MB
% 5.55/1.73 % (807106)Instructions burned: 1035 (million)
% 5.55/1.73 % (807106)------------------------------
% 5.55/1.73 % (807106)------------------------------
% 5.55/1.73 % (807100)Success in time 0.703 s
% 5.55/1.73 % Vampire exiting
%------------------------------------------------------------------------------