%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU372+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 12:48:35 PM UTC 2026
% Result : Theorem 4.64s 1.58s
% Output : Refutation 5.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 28
% Syntax : Number of formulae : 238 ( 26 unt; 12 def)
% Number of atoms : 975 ( 15 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1314 ( 577 ~; 577 |; 102 &)
% ( 22 <=>; 34 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 8 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 360 ( 0 sgn 333 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( X2 = topstr_closure(X0,X1)
<=> ! [X3] :
( in(X3,the_carrier(X0))
=> ( in(X3,X2)
<=> ! [X4] :
( element(X4,powerset(the_carrier(X0)))
=> ~ ( open_subset(X4,X0)
& in(X3,X4)
& disjoint(X1,X4) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_pre_topc) ).
fof(f6,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(f7,axiom,
! [X0,X1] :
( ( top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> element(interior(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(f10,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(f11,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f13,axiom,
! [X0,X1] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0)
& element(X1,the_carrier(X0)) )
=> ! [X2] :
( point_neighbourhood(X2,X0,X1)
=> element(X2,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
fof(f21,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f37,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f39,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f40,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f41,axiom,
! [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(f42,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f43,axiom,
! [X0] :
( ( topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> open_subset(interior(X0,X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tops_1) ).
fof(f44,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( open_subset(X1,X0)
& in(X2,X1) )
=> point_neighbourhood(X1,X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& disjoint(X1,X2) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f48,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( point_neighbourhood(X3,X0,X2)
=> ~ disjoint(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_6) ).
fof(f49,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( point_neighbourhood(X3,X0,X2)
=> ~ disjoint(X3,X1) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = topstr_closure(X0,X1)
<=> ! [X3] :
( ( in(X3,X2)
<=> ! [X4] :
( ~ open_subset(X4,X0)
| ~ in(X3,X4)
| ~ disjoint(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) ) )
| ~ in(X3,the_carrier(X0)) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = topstr_closure(X0,X1)
<=> ! [X3] :
( ( in(X3,X2)
<=> ! [X4] :
( ~ open_subset(X4,X0)
| ~ in(X3,X4)
| ~ disjoint(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) ) )
| ~ in(X3,the_carrier(X0)) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f7]) ).
fof(f69,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f10]) ).
fof(f71,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f73,plain,
! [X0,X1] :
( ! [X2] :
( element(X2,powerset(the_carrier(X0)))
| ~ point_neighbourhood(X2,X0,X1) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f74,plain,
! [X0,X1] :
( ! [X2] :
( element(X2,powerset(the_carrier(X0)))
| ~ point_neighbourhood(X2,X0,X1) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(flattening,[],[f73]) ).
fof(f77,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f78,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f77]) ).
fof(f82,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f84,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f85,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( subset(interior(X0,X1),X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f87,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f88,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( open_subset(interior(X0,X1),X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( open_subset(interior(X0,X1),X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( point_neighbourhood(X1,X0,X2)
| ~ open_subset(X1,X0)
| ~ in(X2,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( point_neighbourhood(X1,X0,X2)
| ~ open_subset(X1,X0)
| ~ in(X2,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f91]) ).
fof(f94,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ subset(X0,X1)
| ~ disjoint(X1,X2) ),
inference(ennf_transformation,[],[f46]) ).
fof(f95,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ subset(X0,X1)
| ~ disjoint(X1,X2) ),
inference(flattening,[],[f94]) ).
fof(f97,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,topstr_closure(X0,X1))
<~> ! [X3] :
( ~ disjoint(X3,X1)
| ~ point_neighbourhood(X3,X0,X2) ) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,topstr_closure(X0,X1))
<~> ! [X3] :
( ~ disjoint(X3,X1)
| ~ point_neighbourhood(X3,X0,X2) ) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(flattening,[],[f97]) ).
fof(f101,definition,
! [X0,X1,X2] :
( sP0(X0,X1,X2)
<=> ! [X3] :
( ( in(X3,X2)
<=> ! [X4] :
( ~ open_subset(X4,X0)
| ~ in(X3,X4)
| ~ disjoint(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) ) )
| ~ in(X3,the_carrier(X0)) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f102,definition,
! [X2,X1,X0] :
( ( X2 = topstr_closure(X0,X1)
<=> sP0(X0,X1,X2) )
| ~ sP1(X2,X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sP1(X2,X1,X0)
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(definition_folding,[],[f65,f102,f101]) ).
fof(f104,plain,
! [X2,X1,X0] :
( ( ( X2 = topstr_closure(X0,X1)
| ~ sP0(X0,X1,X2) )
& ( sP0(X0,X1,X2)
| topstr_closure(X0,X1) != X2 ) )
| ~ sP1(X2,X1,X0) ),
inference(nnf_transformation,[],[f102]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ( ( topstr_closure(X2,X1) = X0
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| topstr_closure(X2,X1) != X0 ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ? [X4] :
( open_subset(X4,X0)
& in(X3,X4)
& disjoint(X1,X4)
& element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) )
& ( ! [X4] :
( ~ open_subset(X4,X0)
| ~ in(X3,X4)
| ~ disjoint(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| in(X3,X2) )
& in(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ? [X4] :
( open_subset(X4,X0)
& in(X3,X4)
& disjoint(X1,X4)
& element(X4,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ open_subset(X4,X0)
| ~ in(X3,X4)
| ~ disjoint(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| ~ in(X3,the_carrier(X0)) )
| ~ sP0(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ? [X4] :
( open_subset(X4,X0)
& in(X3,X4)
& disjoint(X1,X4)
& element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) )
& ( ! [X4] :
( ~ open_subset(X4,X0)
| ~ in(X3,X4)
| ~ disjoint(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| in(X3,X2) )
& in(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ? [X4] :
( open_subset(X4,X0)
& in(X3,X4)
& disjoint(X1,X4)
& element(X4,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ open_subset(X4,X0)
| ~ in(X3,X4)
| ~ disjoint(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| ~ in(X3,the_carrier(X0)) )
| ~ sP0(X0,X1,X2) ) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ? [X4] :
( open_subset(X4,X0)
& in(X3,X4)
& disjoint(X1,X4)
& element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) )
& ( ! [X5] :
( ~ open_subset(X5,X0)
| ~ in(X3,X5)
| ~ disjoint(X1,X5)
| ~ element(X5,powerset(the_carrier(X0))) )
| in(X3,X2) )
& in(X3,the_carrier(X0)) ) )
& ( ! [X6] :
( ( ( in(X6,X2)
| ? [X7] :
( open_subset(X7,X0)
& in(X6,X7)
& disjoint(X1,X7)
& element(X7,powerset(the_carrier(X0))) ) )
& ( ! [X8] :
( ~ open_subset(X8,X0)
| ~ in(X6,X8)
| ~ disjoint(X1,X8)
| ~ element(X8,powerset(the_carrier(X0))) )
| ~ in(X6,X2) ) )
| ~ in(X6,the_carrier(X0)) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f107]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ( open_subset(sK3(X0,X1,X2),X0)
& in(sK2(X0,X1,X2),sK3(X0,X1,X2))
& disjoint(X1,sK3(X0,X1,X2))
& element(sK3(X0,X1,X2),powerset(the_carrier(X0))) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( ! [X5] :
( ~ open_subset(X5,X0)
| ~ in(sK2(X0,X1,X2),X5)
| ~ disjoint(X1,X5)
| ~ element(X5,powerset(the_carrier(X0))) )
| in(sK2(X0,X1,X2),X2) )
& in(sK2(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X6] :
( ( ( in(X6,X2)
| ( open_subset(sK4(X0,X1,X6),X0)
& in(X6,sK4(X0,X1,X6))
& disjoint(X1,sK4(X0,X1,X6))
& element(sK4(X0,X1,X6),powerset(the_carrier(X0))) ) )
& ( ! [X8] :
( ~ open_subset(X8,X0)
| ~ in(X6,X8)
| ~ disjoint(X1,X8)
| ~ element(X8,powerset(the_carrier(X0))) )
| ~ in(X6,X2) ) )
| ~ in(X6,the_carrier(X0)) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X4,sK3(X0,X1,X2)),skolemize(X7,sK4(X0,X1,X6))],[f108]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( point_neighbourhood(X2,X0,X1)
| ~ in(X1,interior(X0,X2)) )
& ( in(X1,interior(X0,X2))
| ~ point_neighbourhood(X2,X0,X1) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f67]) ).
fof(f127,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f128,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ? [X3] :
( disjoint(X3,X1)
& point_neighbourhood(X3,X0,X2) )
| ~ in(X2,topstr_closure(X0,X1)) )
& ( ! [X3] :
( ~ disjoint(X3,X1)
| ~ point_neighbourhood(X3,X0,X2) )
| in(X2,topstr_closure(X0,X1)) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(nnf_transformation,[],[f98]) ).
fof(f129,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ? [X3] :
( disjoint(X3,X1)
& point_neighbourhood(X3,X0,X2) )
| ~ in(X2,topstr_closure(X0,X1)) )
& ( ! [X3] :
( ~ disjoint(X3,X1)
| ~ point_neighbourhood(X3,X0,X2) )
| in(X2,topstr_closure(X0,X1)) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(flattening,[],[f128]) ).
fof(f130,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ? [X3] :
( disjoint(X3,X1)
& point_neighbourhood(X3,X0,X2) )
| ~ in(X2,topstr_closure(X0,X1)) )
& ( ! [X4] :
( ~ disjoint(X4,X1)
| ~ point_neighbourhood(X4,X0,X2) )
| in(X2,topstr_closure(X0,X1)) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(rectify,[],[f129]) ).
fof(f131,plain,
( ( ( disjoint(sK24,sK22)
& point_neighbourhood(sK24,sK21,sK23) )
| ~ in(sK23,topstr_closure(sK21,sK22)) )
& ( ! [X4] :
( ~ disjoint(X4,sK22)
| ~ point_neighbourhood(X4,sK21,sK23) )
| in(sK23,topstr_closure(sK21,sK22)) )
& element(sK23,the_carrier(sK21))
& element(sK22,powerset(the_carrier(sK21)))
& ~ empty_carrier(sK21)
& topological_space(sK21)
& top_str(sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22,sK23,sK24]),skolemize(X0,sK21),skolemize(X1,sK22),skolemize(X2,sK23),skolemize(X3,sK24)],[f130]) ).
fof(f137,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| topstr_closure(X2,X1) != X0
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f105]) ).
fof(f139,plain,
! [X2,X0,X1,X8,X6] :
( ~ element(X8,powerset(the_carrier(X0)))
| ~ in(X6,X8)
| ~ disjoint(X1,X8)
| ~ open_subset(X8,X0)
| ~ in(X6,X2)
| ~ in(X6,the_carrier(X0))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f140,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| element(sK4(X0,X1,X6),powerset(the_carrier(X0)))
| ~ in(X6,the_carrier(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f141,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| disjoint(X1,sK4(X0,X1,X6))
| ~ in(X6,the_carrier(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f142,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| in(X6,sK4(X0,X1,X6))
| ~ in(X6,the_carrier(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f143,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| open_subset(sK4(X0,X1,X6),X0)
| ~ in(X6,the_carrier(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(the_carrier(X0)))
| sP1(X2,X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f151,plain,
! [X2,X0,X1] :
( in(X1,interior(X0,X2))
| ~ point_neighbourhood(X2,X0,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f153,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f69]) ).
fof(f154,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f71]) ).
fof(f155,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ point_neighbourhood(X2,X0,X1)
| element(X2,powerset(the_carrier(X0)))
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f163,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f192,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f194,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f195,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f196,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f197,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset(interior(X0,X1),X1)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f199,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| open_subset(interior(X0,X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(X1,X0)
| ~ in(X2,X1)
| ~ element(X2,the_carrier(X0))
| point_neighbourhood(X1,X0,X2)
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f202,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| disjoint(X0,X2)
| ~ disjoint(X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f204,plain,
top_str(sK21),
inference(cnf_transformation,[],[f131]) ).
fof(f205,plain,
topological_space(sK21),
inference(cnf_transformation,[],[f131]) ).
fof(f206,plain,
~ empty_carrier(sK21),
inference(cnf_transformation,[],[f131]) ).
fof(f207,plain,
element(sK22,powerset(the_carrier(sK21))),
inference(cnf_transformation,[],[f131]) ).
fof(f208,plain,
element(sK23,the_carrier(sK21)),
inference(cnf_transformation,[],[f131]) ).
fof(f209,plain,
! [X4] :
( ~ disjoint(X4,sK22)
| ~ point_neighbourhood(X4,sK21,sK23)
| in(sK23,topstr_closure(sK21,sK22)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f210,plain,
( point_neighbourhood(sK24,sK21,sK23)
| ~ in(sK23,topstr_closure(sK21,sK22)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f211,plain,
( disjoint(sK24,sK22)
| ~ in(sK23,topstr_closure(sK21,sK22)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f214,plain,
! [X2,X1] :
( ~ sP1(topstr_closure(X2,X1),X1,X2)
| sP0(X2,X1,topstr_closure(X2,X1)) ),
inference(equality_resolution,[],[f137]) ).
fof(f215,definition,
sF25 = topstr_closure(sK21,sK22),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f216,plain,
topstr_closure(sK21,sK22) = sF25,
inference(reorient_equations,[],[f215]) ).
fof(f217,plain,
( disjoint(sK24,sK22)
| ~ in(sK23,sF25) ),
inference(definition_folding,[],[f211,f216]) ).
fof(f218,plain,
( point_neighbourhood(sK24,sK21,sK23)
| ~ in(sK23,sF25) ),
inference(definition_folding,[],[f210,f216]) ).
fof(f219,plain,
! [X4] :
( ~ disjoint(X4,sK22)
| ~ point_neighbourhood(X4,sK21,sK23)
| in(sK23,sF25) ),
inference(definition_folding,[],[f209,f216]) ).
fof(f220,definition,
sF26 = the_carrier(sK21),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f221,plain,
the_carrier(sK21) = sF26,
inference(reorient_equations,[],[f220]) ).
fof(f222,plain,
element(sK23,sF26),
inference(definition_folding,[],[f208,f221]) ).
fof(f223,definition,
sF27 = powerset(sF26),
introduced(definition,[new_symbols(definition,[sF27])],[function_definition]) ).
fof(f224,plain,
powerset(sF26) = sF27,
inference(reorient_equations,[],[f223]) ).
fof(f225,plain,
element(sK22,sF27),
inference(definition_folding,[],[f207,f224,f221]) ).
fof(f227,definition,
( spl28_1
<=> in(sK23,sF25) ),
introduced(definition,[new_symbols(definition,[spl28_1])],[avatar_definition]) ).
fof(f228,plain,
( ~ in(sK23,sF25)
| spl28_1 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f229,plain,
( in(sK23,sF25)
| ~ spl28_1 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f231,definition,
( spl28_2
<=> ! [X4] :
( ~ disjoint(X4,sK22)
| ~ point_neighbourhood(X4,sK21,sK23) ) ),
introduced(definition,[new_symbols(definition,[spl28_2])],[avatar_definition]) ).
fof(f232,plain,
( ! [X4] :
( ~ point_neighbourhood(X4,sK21,sK23)
| ~ disjoint(X4,sK22) )
| ~ spl28_2 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f233,plain,
( spl28_1
| spl28_2 ),
inference(avatar_split_clause,[],[f219,f231,f227]) ).
fof(f235,definition,
( spl28_3
<=> point_neighbourhood(sK24,sK21,sK23) ),
introduced(definition,[new_symbols(definition,[spl28_3])],[avatar_definition]) ).
fof(f237,plain,
( point_neighbourhood(sK24,sK21,sK23)
| ~ spl28_3 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f238,plain,
( ~ spl28_1
| spl28_3 ),
inference(avatar_split_clause,[],[f218,f235,f227]) ).
fof(f240,definition,
( spl28_4
<=> disjoint(sK24,sK22) ),
introduced(definition,[new_symbols(definition,[spl28_4])],[avatar_definition]) ).
fof(f242,plain,
( disjoint(sK24,sK22)
| ~ spl28_4 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f243,plain,
( ~ spl28_1
| spl28_4 ),
inference(avatar_split_clause,[],[f217,f240,f227]) ).
fof(f244,plain,
! [X2,X0,X1] :
( in(X1,interior(X0,X2))
| ~ point_neighbourhood(X2,X0,X1)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(forward_subsumption_resolution,[],[f151,f156]) ).
fof(f245,plain,
( element(sF25,powerset(the_carrier(sK21)))
| ~ top_str(sK21)
| ~ element(sK22,powerset(the_carrier(sK21))) ),
inference(superposition,[],[f154,f216]) ).
fof(f246,plain,
! [X0] :
( element(topstr_closure(sK21,X0),powerset(sF26))
| ~ top_str(sK21)
| ~ element(X0,powerset(sF26)) ),
inference(superposition,[],[f154,f221]) ).
fof(f247,plain,
! [X0] :
( element(topstr_closure(sK21,X0),powerset(sF26))
| ~ element(X0,powerset(sF26)) ),
inference(forward_subsumption_resolution,[],[f246,f204]) ).
fof(f248,plain,
( element(sF25,powerset(the_carrier(sK21)))
| ~ element(sK22,powerset(the_carrier(sK21))) ),
inference(forward_subsumption_resolution,[],[f245,f204]) ).
fof(f249,plain,
! [X0] :
( element(topstr_closure(sK21,X0),sF27)
| ~ element(X0,powerset(sF26)) ),
inference(forward_demodulation,[],[f247,f224]) ).
fof(f250,plain,
( element(sF25,powerset(sF26))
| ~ element(sK22,powerset(the_carrier(sK21))) ),
inference(forward_demodulation,[],[f248,f221]) ).
fof(f251,plain,
! [X0] :
( element(topstr_closure(sK21,X0),sF27)
| ~ element(X0,sF27) ),
inference(forward_demodulation,[],[f249,f224]) ).
fof(f252,plain,
( element(sF25,sF27)
| ~ element(sK22,powerset(the_carrier(sK21))) ),
inference(forward_demodulation,[],[f250,f224]) ).
fof(f253,plain,
( ~ element(sK22,powerset(sF26))
| element(sF25,sF27) ),
inference(forward_demodulation,[],[f252,f221]) ).
fof(f254,plain,
( ~ element(sK22,sF27)
| element(sF25,sF27) ),
inference(forward_demodulation,[],[f253,f224]) ).
fof(f255,plain,
element(sF25,sF27),
inference(forward_subsumption_resolution,[],[f254,f225]) ).
fof(f257,plain,
! [X0] :
( ~ element(X0,powerset(sF26))
| open_subset(interior(sK21,X0),sK21)
| ~ topological_space(sK21)
| ~ top_str(sK21) ),
inference(superposition,[],[f199,f221]) ).
fof(f259,plain,
! [X0] :
( ~ element(X0,powerset(sF26))
| open_subset(interior(sK21,X0),sK21)
| ~ top_str(sK21) ),
inference(forward_subsumption_resolution,[],[f257,f205]) ).
fof(f260,plain,
! [X0] :
( ~ element(X0,powerset(sF26))
| open_subset(interior(sK21,X0),sK21) ),
inference(forward_subsumption_resolution,[],[f259,f204]) ).
fof(f261,plain,
! [X0] :
( open_subset(interior(sK21,X0),sK21)
| ~ element(X0,sF27) ),
inference(forward_demodulation,[],[f260,f224]) ).
fof(f264,definition,
( spl28_5
<=> sP0(sK21,sK22,sF25) ),
introduced(definition,[new_symbols(definition,[spl28_5])],[avatar_definition]) ).
fof(f266,plain,
( sP0(sK21,sK22,sF25)
| ~ spl28_5 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f273,plain,
! [X0,X1] :
( ~ element(X0,powerset(sF26))
| ~ open_subset(X0,sK21)
| ~ in(X1,X0)
| ~ element(X1,sF26)
| point_neighbourhood(X0,sK21,X1)
| empty_carrier(sK21)
| ~ topological_space(sK21)
| ~ top_str(sK21) ),
inference(superposition,[],[f200,f221]) ).
fof(f275,plain,
! [X0,X1] :
( ~ element(X0,powerset(sF26))
| ~ open_subset(X0,sK21)
| ~ in(X1,X0)
| point_neighbourhood(X0,sK21,X1)
| empty_carrier(sK21)
| ~ topological_space(sK21)
| ~ top_str(sK21) ),
inference(forward_subsumption_resolution,[],[f273,f198]) ).
fof(f276,plain,
! [X0,X1] :
( ~ element(X0,powerset(sF26))
| ~ open_subset(X0,sK21)
| ~ in(X1,X0)
| point_neighbourhood(X0,sK21,X1)
| ~ topological_space(sK21)
| ~ top_str(sK21) ),
inference(forward_subsumption_resolution,[],[f275,f206]) ).
fof(f277,plain,
! [X0,X1] :
( ~ element(X0,powerset(sF26))
| ~ open_subset(X0,sK21)
| ~ in(X1,X0)
| point_neighbourhood(X0,sK21,X1)
| ~ top_str(sK21) ),
inference(forward_subsumption_resolution,[],[f276,f205]) ).
fof(f278,plain,
! [X0,X1] :
( ~ element(X0,powerset(sF26))
| ~ open_subset(X0,sK21)
| ~ in(X1,X0)
| point_neighbourhood(X0,sK21,X1) ),
inference(forward_subsumption_resolution,[],[f277,f204]) ).
fof(f279,plain,
! [X0,X1] :
( point_neighbourhood(X0,sK21,X1)
| ~ open_subset(X0,sK21)
| ~ in(X1,X0)
| ~ element(X0,sF27) ),
inference(forward_demodulation,[],[f278,f224]) ).
fof(f280,plain,
( ! [X0] :
( ~ disjoint(X0,sK22)
| ~ in(sK23,X0)
| ~ element(X0,sF27)
| ~ open_subset(X0,sK21) )
| ~ spl28_2 ),
inference(resolution,[],[f279,f232]) ).
fof(f291,plain,
! [X0,X1] :
( ~ element(X0,powerset(sF26))
| sP1(X0,X1,sK21)
| ~ element(X1,powerset(sF26))
| ~ top_str(sK21) ),
inference(superposition,[],[f150,f221]) ).
fof(f293,plain,
! [X0,X1] :
( ~ element(X0,powerset(sF26))
| sP1(X0,X1,sK21)
| ~ element(X1,powerset(sF26)) ),
inference(forward_subsumption_resolution,[],[f291,f204]) ).
fof(f294,plain,
! [X0,X1] :
( ~ element(X0,sF27)
| sP1(X0,X1,sK21)
| ~ element(X1,powerset(sF26)) ),
inference(forward_demodulation,[],[f293,f224]) ).
fof(f295,plain,
! [X0,X1] :
( sP1(X0,X1,sK21)
| ~ element(X0,sF27)
| ~ element(X1,sF27) ),
inference(forward_demodulation,[],[f294,f224]) ).
fof(f296,plain,
! [X0] :
( ~ element(topstr_closure(sK21,X0),sF27)
| ~ element(X0,sF27)
| sP0(sK21,X0,topstr_closure(sK21,X0)) ),
inference(resolution,[],[f295,f214]) ).
fof(f297,plain,
! [X0] :
( sP0(sK21,X0,topstr_closure(sK21,X0))
| ~ element(X0,sF27) ),
inference(forward_subsumption_resolution,[],[f296,f251]) ).
fof(f298,plain,
( sP0(sK21,sK22,sF25)
| ~ element(sK22,sF27) ),
inference(superposition,[],[f297,f216]) ).
fof(f299,plain,
sP0(sK21,sK22,sF25),
inference(forward_subsumption_resolution,[],[f298,f225]) ).
fof(f300,plain,
spl28_5,
inference(avatar_split_clause,[],[f299,f264]) ).
fof(f310,plain,
! [X0,X1] :
( in(X0,sK4(sK21,X1,X0))
| ~ in(X0,the_carrier(sK21))
| in(X0,topstr_closure(sK21,X1))
| ~ element(X1,sF27) ),
inference(resolution,[],[f142,f297]) ).
fof(f313,plain,
! [X0,X1] :
( in(X0,sK4(sK21,X1,X0))
| ~ in(X0,sF26)
| in(X0,topstr_closure(sK21,X1))
| ~ element(X1,sF27) ),
inference(forward_demodulation,[],[f310,f221]) ).
fof(f315,plain,
! [X0] :
( ~ element(X0,powerset(sF26))
| subset(interior(sK21,X0),X0)
| ~ top_str(sK21) ),
inference(superposition,[],[f197,f221]) ).
fof(f317,plain,
! [X0] :
( ~ element(X0,powerset(sF26))
| subset(interior(sK21,X0),X0) ),
inference(forward_subsumption_resolution,[],[f315,f204]) ).
fof(f318,plain,
! [X0] :
( subset(interior(sK21,X0),X0)
| ~ element(X0,sF27) ),
inference(forward_demodulation,[],[f317,f224]) ).
fof(f319,plain,
! [X0,X1] :
( disjoint(X0,sK4(sK21,X0,X1))
| ~ in(X1,the_carrier(sK21))
| in(X1,topstr_closure(sK21,X0))
| ~ element(X0,sF27) ),
inference(resolution,[],[f141,f297]) ).
fof(f322,plain,
! [X0,X1] :
( disjoint(X0,sK4(sK21,X0,X1))
| ~ in(X1,sF26)
| in(X1,topstr_closure(sK21,X0))
| ~ element(X0,sF27) ),
inference(forward_demodulation,[],[f319,f221]) ).
fof(f332,plain,
! [X0] :
( element(interior(sK21,X0),powerset(sF26))
| ~ top_str(sK21)
| ~ element(X0,powerset(sF26)) ),
inference(superposition,[],[f153,f221]) ).
fof(f338,plain,
! [X0] :
( element(interior(sK21,X0),powerset(sF26))
| ~ element(X0,powerset(sF26)) ),
inference(forward_subsumption_resolution,[],[f332,f204]) ).
fof(f340,plain,
! [X0] :
( element(interior(sK21,X0),sF27)
| ~ element(X0,powerset(sF26)) ),
inference(forward_demodulation,[],[f338,f224]) ).
fof(f341,plain,
! [X0] :
( element(interior(sK21,X0),sF27)
| ~ element(X0,sF27) ),
inference(forward_demodulation,[],[f340,f224]) ).
fof(f343,plain,
! [X0,X1] :
( disjoint(sK4(sK21,X0,X1),X0)
| ~ in(X1,sF26)
| in(X1,topstr_closure(sK21,X0))
| ~ element(X0,sF27) ),
inference(resolution,[],[f192,f322]) ).
fof(f348,plain,
! [X0] :
( ~ element(X0,sF27)
| subset(X0,sF26) ),
inference(superposition,[],[f195,f224]) ).
fof(f349,plain,
! [X0,X1] :
( open_subset(sK4(sK21,X0,X1),sK21)
| ~ in(X1,the_carrier(sK21))
| in(X1,topstr_closure(sK21,X0))
| ~ element(X0,sF27) ),
inference(resolution,[],[f143,f297]) ).
fof(f352,plain,
! [X0,X1] :
( open_subset(sK4(sK21,X0,X1),sK21)
| ~ in(X1,sF26)
| in(X1,topstr_closure(sK21,X0))
| ~ element(X0,sF27) ),
inference(forward_demodulation,[],[f349,f221]) ).
fof(f358,plain,
( in(sK23,sF26)
| empty(sF26) ),
inference(resolution,[],[f194,f222]) ).
fof(f370,definition,
( spl28_9
<=> empty(sF26) ),
introduced(definition,[new_symbols(definition,[spl28_9])],[avatar_definition]) ).
fof(f372,plain,
( empty(sF26)
| ~ spl28_9 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f374,definition,
( spl28_10
<=> in(sK23,sF26) ),
introduced(definition,[new_symbols(definition,[spl28_10])],[avatar_definition]) ).
fof(f376,plain,
( in(sK23,sF26)
| ~ spl28_10 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f377,plain,
( spl28_9
| spl28_10 ),
inference(avatar_split_clause,[],[f358,f374,f370]) ).
fof(f393,plain,
one_sorted_str(sK21),
inference(resolution,[],[f155,f204]) ).
fof(f400,plain,
! [X0,X1] :
( disjoint(interior(sK21,X0),X1)
| ~ disjoint(X0,X1)
| ~ element(X0,sF27) ),
inference(resolution,[],[f202,f318]) ).
fof(f402,plain,
! [X0,X1] :
( disjoint(X1,interior(sK21,X0))
| ~ element(X0,sF27)
| ~ disjoint(X0,X1) ),
inference(resolution,[],[f400,f192]) ).
fof(f407,plain,
! [X0] :
( subset(interior(sK21,X0),sF26)
| ~ element(X0,sF27) ),
inference(resolution,[],[f348,f341]) ).
fof(f427,plain,
! [X0,X1] :
( element(sK4(sK21,X0,X1),powerset(the_carrier(sK21)))
| ~ in(X1,the_carrier(sK21))
| in(X1,topstr_closure(sK21,X0))
| ~ element(X0,sF27) ),
inference(resolution,[],[f140,f297]) ).
fof(f445,plain,
! [X0,X1] :
( ~ element(X0,sF27)
| ~ in(X1,X0)
| element(X1,sF26) ),
inference(superposition,[],[f198,f224]) ).
fof(f447,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP0(X1,X3,X4)
| ~ in(X2,X0)
| ~ disjoint(X3,X0)
| ~ open_subset(X0,X1)
| ~ in(X2,X4)
| ~ in(X2,the_carrier(X1))
| ~ subset(X0,the_carrier(X1)) ),
inference(resolution,[],[f196,f139]) ).
fof(f498,plain,
( ~ empty(sF26)
| empty_carrier(sK21)
| ~ one_sorted_str(sK21) ),
inference(superposition,[],[f163,f221]) ).
fof(f499,plain,
( empty_carrier(sK21)
| ~ one_sorted_str(sK21)
| ~ spl28_9 ),
inference(forward_subsumption_resolution,[],[f498,f372]) ).
fof(f500,plain,
( ~ one_sorted_str(sK21)
| ~ spl28_9 ),
inference(forward_subsumption_resolution,[],[f499,f206]) ).
fof(f501,plain,
( $false
| ~ spl28_9 ),
inference(forward_subsumption_resolution,[],[f500,f393]) ).
fof(f502,plain,
~ spl28_9,
inference(avatar_contradiction_clause,[],[f501]) ).
fof(f512,plain,
! [X0,X1] :
( element(sK4(sK21,X0,X1),powerset(sF26))
| ~ in(X1,the_carrier(sK21))
| in(X1,topstr_closure(sK21,X0))
| ~ element(X0,sF27) ),
inference(forward_demodulation,[],[f427,f221]) ).
fof(f514,plain,
! [X0,X1] :
( element(sK4(sK21,X0,X1),sF27)
| ~ in(X1,the_carrier(sK21))
| in(X1,topstr_closure(sK21,X0))
| ~ element(X0,sF27) ),
inference(forward_demodulation,[],[f512,f224]) ).
fof(f516,plain,
! [X0,X1] :
( element(sK4(sK21,X0,X1),sF27)
| ~ in(X1,sF26)
| in(X1,topstr_closure(sK21,X0))
| ~ element(X0,sF27) ),
inference(forward_demodulation,[],[f514,f221]) ).
fof(f526,plain,
! [X0] :
( ~ in(X0,sF25)
| element(X0,sF26) ),
inference(resolution,[],[f445,f255]) ).
fof(f593,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(sK22,X1)
| ~ open_subset(X1,sK21)
| ~ in(X0,sF25)
| ~ in(X0,the_carrier(sK21))
| ~ subset(X1,the_carrier(sK21)) )
| ~ spl28_5 ),
inference(resolution,[],[f447,f266]) ).
fof(f594,plain,
( ! [X0,X1] :
( ~ in(X0,sF26)
| ~ in(X0,X1)
| ~ disjoint(sK22,X1)
| ~ open_subset(X1,sK21)
| ~ in(X0,sF25)
| ~ subset(X1,the_carrier(sK21)) )
| ~ spl28_5 ),
inference(forward_demodulation,[],[f593,f221]) ).
fof(f596,plain,
( ! [X0,X1] :
( ~ subset(X1,sF26)
| ~ in(X0,sF26)
| ~ in(X0,X1)
| ~ disjoint(sK22,X1)
| ~ open_subset(X1,sK21)
| ~ in(X0,sF25) )
| ~ spl28_5 ),
inference(forward_demodulation,[],[f594,f221]) ).
fof(f598,plain,
( ! [X0,X1] :
( ~ in(X0,sF26)
| ~ in(X0,interior(sK21,X1))
| ~ disjoint(sK22,interior(sK21,X1))
| ~ open_subset(interior(sK21,X1),sK21)
| ~ in(X0,sF25)
| ~ element(X1,sF27) )
| ~ spl28_5 ),
inference(resolution,[],[f596,f407]) ).
fof(f629,plain,
( ! [X0,X1] :
( ~ disjoint(sK22,interior(sK21,X1))
| ~ in(X0,interior(sK21,X1))
| ~ in(X0,sF26)
| ~ in(X0,sF25)
| ~ element(X1,sF27) )
| ~ spl28_5 ),
inference(forward_subsumption_resolution,[],[f598,f261]) ).
fof(f698,plain,
( ! [X0] :
( ~ in(X0,sF26)
| in(X0,topstr_closure(sK21,sK22))
| ~ element(sK22,sF27)
| ~ in(sK23,sK4(sK21,sK22,X0))
| ~ element(sK4(sK21,sK22,X0),sF27)
| ~ open_subset(sK4(sK21,sK22,X0),sK21) )
| ~ spl28_2 ),
inference(resolution,[],[f343,f280]) ).
fof(f699,plain,
( ! [X0] :
( ~ in(X0,sF26)
| in(X0,topstr_closure(sK21,sK22))
| ~ element(sK22,sF27)
| ~ in(sK23,sK4(sK21,sK22,X0))
| ~ open_subset(sK4(sK21,sK22,X0),sK21) )
| ~ spl28_2 ),
inference(forward_subsumption_resolution,[],[f698,f516]) ).
fof(f700,plain,
( ! [X0] :
( ~ in(X0,sF26)
| in(X0,topstr_closure(sK21,sK22))
| ~ element(sK22,sF27)
| ~ in(sK23,sK4(sK21,sK22,X0)) )
| ~ spl28_2 ),
inference(forward_subsumption_resolution,[],[f699,f352]) ).
fof(f701,plain,
( ! [X0] :
( ~ in(X0,sF26)
| in(X0,topstr_closure(sK21,sK22))
| ~ in(sK23,sK4(sK21,sK22,X0)) )
| ~ spl28_2 ),
inference(forward_subsumption_resolution,[],[f700,f225]) ).
fof(f702,plain,
( ! [X0] :
( ~ in(sK23,sK4(sK21,sK22,X0))
| ~ in(X0,sF26)
| in(X0,sF25) )
| ~ spl28_2 ),
inference(forward_demodulation,[],[f701,f216]) ).
fof(f704,plain,
( ~ in(sK23,sF26)
| in(sK23,sF25)
| ~ in(sK23,sF26)
| in(sK23,topstr_closure(sK21,sK22))
| ~ element(sK22,sF27)
| ~ spl28_2 ),
inference(resolution,[],[f702,f313]) ).
fof(f705,plain,
( ~ in(sK23,sF26)
| in(sK23,sF25)
| in(sK23,topstr_closure(sK21,sK22))
| ~ element(sK22,sF27)
| ~ spl28_2 ),
inference(duplicate_literal_removal,[],[f704]) ).
fof(f707,plain,
( in(sK23,sF25)
| in(sK23,topstr_closure(sK21,sK22))
| ~ element(sK22,sF27)
| ~ spl28_2
| ~ spl28_10 ),
inference(forward_subsumption_resolution,[],[f705,f376]) ).
fof(f709,plain,
( in(sK23,topstr_closure(sK21,sK22))
| ~ element(sK22,sF27)
| spl28_1
| ~ spl28_2
| ~ spl28_10 ),
inference(forward_subsumption_resolution,[],[f707,f228]) ).
fof(f712,plain,
( in(sK23,topstr_closure(sK21,sK22))
| spl28_1
| ~ spl28_2
| ~ spl28_10 ),
inference(forward_subsumption_resolution,[],[f709,f225]) ).
fof(f713,plain,
( in(sK23,sF25)
| spl28_1
| ~ spl28_2
| ~ spl28_10 ),
inference(forward_demodulation,[],[f712,f216]) ).
fof(f714,plain,
( $false
| spl28_1
| ~ spl28_2
| ~ spl28_10 ),
inference(forward_subsumption_resolution,[],[f713,f228]) ).
fof(f715,plain,
( spl28_1
| ~ spl28_2
| ~ spl28_10 ),
inference(avatar_contradiction_clause,[],[f714]) ).
fof(f717,plain,
( element(sK24,powerset(the_carrier(sK21)))
| empty_carrier(sK21)
| ~ topological_space(sK21)
| ~ top_str(sK21)
| ~ element(sK23,the_carrier(sK21))
| ~ spl28_3 ),
inference(resolution,[],[f237,f156]) ).
fof(f718,plain,
( element(sK24,powerset(the_carrier(sK21)))
| ~ topological_space(sK21)
| ~ top_str(sK21)
| ~ element(sK23,the_carrier(sK21))
| ~ spl28_3 ),
inference(forward_subsumption_resolution,[],[f717,f206]) ).
fof(f721,plain,
( element(sK24,powerset(the_carrier(sK21)))
| ~ top_str(sK21)
| ~ element(sK23,the_carrier(sK21))
| ~ spl28_3 ),
inference(forward_subsumption_resolution,[],[f718,f205]) ).
fof(f722,plain,
( element(sK24,powerset(the_carrier(sK21)))
| ~ element(sK23,the_carrier(sK21))
| ~ spl28_3 ),
inference(forward_subsumption_resolution,[],[f721,f204]) ).
fof(f723,plain,
( element(sK24,powerset(sF26))
| ~ element(sK23,the_carrier(sK21))
| ~ spl28_3 ),
inference(forward_demodulation,[],[f722,f221]) ).
fof(f724,plain,
( element(sK24,sF27)
| ~ element(sK23,the_carrier(sK21))
| ~ spl28_3 ),
inference(forward_demodulation,[],[f723,f224]) ).
fof(f725,plain,
( ~ element(sK23,sF26)
| element(sK24,sF27)
| ~ spl28_3 ),
inference(forward_demodulation,[],[f724,f221]) ).
fof(f726,plain,
( element(sK24,sF27)
| ~ spl28_3 ),
inference(forward_subsumption_resolution,[],[f725,f222]) ).
fof(f794,plain,
( ! [X0,X1] :
( ~ element(X0,sF27)
| ~ disjoint(X0,sK22)
| ~ in(X1,interior(sK21,X0))
| ~ in(X1,sF26)
| ~ in(X1,sF25)
| ~ element(X0,sF27) )
| ~ spl28_5 ),
inference(resolution,[],[f402,f629]) ).
fof(f799,plain,
( ! [X0,X1] :
( ~ in(X1,interior(sK21,X0))
| ~ disjoint(X0,sK22)
| ~ element(X0,sF27)
| ~ in(X1,sF26)
| ~ in(X1,sF25) )
| ~ spl28_5 ),
inference(duplicate_literal_removal,[],[f794]) ).
fof(f982,plain,
( ! [X0,X1] :
( ~ disjoint(X0,sK22)
| ~ element(X0,sF27)
| ~ in(X1,sF26)
| ~ in(X1,sF25)
| ~ point_neighbourhood(X0,sK21,X1)
| ~ element(X1,the_carrier(sK21))
| empty_carrier(sK21)
| ~ topological_space(sK21)
| ~ top_str(sK21) )
| ~ spl28_5 ),
inference(resolution,[],[f799,f244]) ).
fof(f983,plain,
( ! [X0,X1] :
( ~ disjoint(X0,sK22)
| ~ element(X0,sF27)
| ~ in(X1,sF26)
| ~ in(X1,sF25)
| ~ point_neighbourhood(X0,sK21,X1)
| ~ element(X1,the_carrier(sK21))
| ~ topological_space(sK21)
| ~ top_str(sK21) )
| ~ spl28_5 ),
inference(forward_subsumption_resolution,[],[f982,f206]) ).
fof(f984,plain,
( ! [X0,X1] :
( ~ disjoint(X0,sK22)
| ~ element(X0,sF27)
| ~ in(X1,sF26)
| ~ in(X1,sF25)
| ~ point_neighbourhood(X0,sK21,X1)
| ~ element(X1,the_carrier(sK21))
| ~ top_str(sK21) )
| ~ spl28_5 ),
inference(forward_subsumption_resolution,[],[f983,f205]) ).
fof(f985,plain,
( ! [X0,X1] :
( ~ disjoint(X0,sK22)
| ~ element(X0,sF27)
| ~ in(X1,sF26)
| ~ in(X1,sF25)
| ~ point_neighbourhood(X0,sK21,X1)
| ~ element(X1,the_carrier(sK21)) )
| ~ spl28_5 ),
inference(forward_subsumption_resolution,[],[f984,f204]) ).
fof(f986,plain,
( ! [X0,X1] :
( ~ element(X1,sF26)
| ~ disjoint(X0,sK22)
| ~ element(X0,sF27)
| ~ in(X1,sF26)
| ~ in(X1,sF25)
| ~ point_neighbourhood(X0,sK21,X1) )
| ~ spl28_5 ),
inference(forward_demodulation,[],[f985,f221]) ).
fof(f987,plain,
( ! [X0,X1] :
( ~ point_neighbourhood(X0,sK21,X1)
| ~ element(X0,sF27)
| ~ in(X1,sF26)
| ~ in(X1,sF25)
| ~ disjoint(X0,sK22) )
| ~ spl28_5 ),
inference(forward_subsumption_resolution,[],[f986,f526]) ).
fof(f992,plain,
( ~ element(sK24,sF27)
| ~ in(sK23,sF26)
| ~ in(sK23,sF25)
| ~ disjoint(sK24,sK22)
| ~ spl28_3
| ~ spl28_5 ),
inference(resolution,[],[f987,f237]) ).
fof(f994,plain,
( ~ in(sK23,sF26)
| ~ in(sK23,sF25)
| ~ disjoint(sK24,sK22)
| ~ spl28_3
| ~ spl28_5 ),
inference(forward_subsumption_resolution,[],[f992,f726]) ).
fof(f998,plain,
( ~ in(sK23,sF25)
| ~ disjoint(sK24,sK22)
| ~ spl28_3
| ~ spl28_5
| ~ spl28_10 ),
inference(forward_subsumption_resolution,[],[f994,f376]) ).
fof(f1001,plain,
( ~ disjoint(sK24,sK22)
| ~ spl28_1
| ~ spl28_3
| ~ spl28_5
| ~ spl28_10 ),
inference(forward_subsumption_resolution,[],[f998,f229]) ).
fof(f1004,plain,
( $false
| ~ spl28_1
| ~ spl28_3
| ~ spl28_4
| ~ spl28_5
| ~ spl28_10 ),
inference(forward_subsumption_resolution,[],[f1001,f242]) ).
fof(f1005,plain,
( ~ spl28_1
| ~ spl28_3
| ~ spl28_4
| ~ spl28_5
| ~ spl28_10 ),
inference(avatar_contradiction_clause,[],[f1004]) ).
cnf(s1,plain,
( spl28_1
| spl28_2 ),
inference(sat_conversion,[],[f233]) ).
cnf(s2,plain,
( ~ spl28_1
| spl28_3 ),
inference(sat_conversion,[],[f238]) ).
cnf(s3,plain,
( ~ spl28_1
| spl28_4 ),
inference(sat_conversion,[],[f243]) ).
cnf(s5,plain,
spl28_5,
inference(sat_conversion,[],[f300]) ).
cnf(s7,plain,
( spl28_9
| spl28_10 ),
inference(sat_conversion,[],[f377]) ).
cnf(s13,plain,
~ spl28_9,
inference(sat_conversion,[],[f502]) ).
cnf(s23,plain,
( spl28_1
| ~ spl28_2
| ~ spl28_10 ),
inference(sat_conversion,[],[f715]) ).
cnf(s31,plain,
( ~ spl28_1
| ~ spl28_3
| ~ spl28_4
| ~ spl28_5
| ~ spl28_10 ),
inference(sat_conversion,[],[f1005]) ).
cnf(s36,plain,
spl28_10,
inference(rat,[],[s7,s13]) ).
cnf(s38,plain,
spl28_1,
inference(rat,[],[s1,s23,s36]) ).
cnf(s39,plain,
spl28_4,
inference(rat,[],[s3,s38]) ).
cnf(s40,plain,
spl28_3,
inference(rat,[],[s2,s38]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s31,s36,s5,s39,s38,s40]) ).
fof(f1012,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU372+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 04:58:21 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 4.64/1.58 % (812596)Detected formulas, will run a generic FOF schedule.
% 4.64/1.58 % (812601)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=349871807:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.64/1.58 % (812602)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=1138815993:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.64/1.58 % (812604)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3523184420:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.64/1.58 % (812603)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=1241648071:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.64/1.58 % (812607)dis-21_1_sil=8000:lcm=predicate:random_seed=2221935713: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)
% 4.64/1.58 % (812605)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3885469451:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.64/1.58 % (812606)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1260953160:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.64/1.58 % (812604)Instruction limit reached!
% 4.64/1.58 % (812604)------------------------------
% 4.64/1.58 % (812604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.58 % (812604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.58 % (812604)CaDiCaL version: 2.1.3
% 4.64/1.58 % (812604)Termination reason: Instruction limit
% 4.64/1.58 % (812604)Termination phase: Saturation
% 4.64/1.58 % (812604)Time elapsed: 0.050 s
% 4.64/1.58 % (812604)Peak memory usage: 88 MB
% 4.64/1.58 % (812604)Instructions burned: 109 (million)
% 4.64/1.58 % (812607)Instruction limit reached!
% 4.64/1.58 % (812607)------------------------------
% 4.64/1.58 % (812607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.58 % (812607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.58 % (812607)CaDiCaL version: 2.1.3
% 4.64/1.58 % (812607)Termination reason: Instruction limit
% 4.64/1.58 % (812607)Termination phase: Saturation
% 4.64/1.58 % (812607)Time elapsed: 0.068 s
% 4.64/1.58 % (812607)Peak memory usage: 89 MB
% 4.64/1.58 % (812607)Instructions burned: 131 (million)
% 4.64/1.58 % (812605)Instruction limit reached!
% 4.64/1.58 % (812605)------------------------------
% 4.64/1.58 % (812605)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.58 % (812605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.58 % (812605)CaDiCaL version: 2.1.3
% 4.64/1.58 % (812605)Termination reason: Instruction limit
% 4.64/1.58 % (812605)Termination phase: Saturation
% 4.64/1.58 % (812605)Time elapsed: 0.075 s
% 4.64/1.58 % (812605)Peak memory usage: 88 MB
% 4.64/1.58 % (812605)Instructions burned: 119 (million)
% 4.64/1.58 % (812606)Instruction limit reached!
% 4.64/1.58 % (812606)------------------------------
% 4.64/1.58 % (812606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.58 % (812606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.58 % (812606)CaDiCaL version: 2.1.3
% 4.64/1.58 % (812606)Termination reason: Instruction limit
% 4.64/1.58 % (812606)Termination phase: Saturation
% 4.64/1.58 % (812606)Time elapsed: 0.102 s
% 4.64/1.58 % (812606)Peak memory usage: 90 MB
% 4.64/1.58 % (812606)Instructions burned: 139 (million)
% 4.64/1.58 % (812615)lrs+10_1_sil=8000:sp=occurrence:random_seed=4061342167:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.64/1.58 % (812617)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1818678578:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.64/1.58 % (812616)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1169714869:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.64/1.58 % (812618)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=1209243470:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.64/1.58 % (812616)Instruction limit reached!
% 4.64/1.58 % (812616)------------------------------
% 4.64/1.58 % (812616)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.58 % (812616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.58 % (812616)CaDiCaL version: 2.1.3
% 4.64/1.58 % (812616)Termination reason: Instruction limit
% 4.64/1.58 % (812616)Termination phase: Saturation
% 4.64/1.58 % (812616)Time elapsed: 0.090 s
% 4.64/1.58 % (812616)Peak memory usage: 90 MB
% 4.64/1.58 % (812616)Instructions burned: 157 (million)
% 4.64/1.58 % (812601)First to succeed.
% 4.64/1.58 % (812601)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-812596"
% 4.64/1.58 % (812615)Instruction limit reached!
% 4.64/1.58 % (812615)------------------------------
% 4.64/1.58 % (812615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.58 % (812615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.58 % (812615)CaDiCaL version: 2.1.3
% 4.64/1.58 % (812615)Termination reason: Instruction limit
% 4.64/1.58 % (812615)Termination phase: Saturation
% 4.64/1.58 % (812615)Time elapsed: 0.188 s
% 4.64/1.58 % (812615)Peak memory usage: 92 MB
% 4.64/1.58 % (812615)Instructions burned: 286 (million)
% 4.64/1.58 % (812618)Instruction limit reached!
% 4.64/1.58 % (812618)------------------------------
% 4.64/1.58 % (812618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.58 % (812618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.58 % (812618)CaDiCaL version: 2.1.3
% 4.64/1.58 % (812618)Termination reason: Instruction limit
% 4.64/1.58 % (812618)Termination phase: Saturation
% 4.64/1.58 % (812618)Time elapsed: 0.148 s
% 4.64/1.58 % (812618)Peak memory usage: 92 MB
% 4.64/1.58 % (812618)Instructions burned: 248 (million)
% 4.64/1.58 % (812617)Instruction limit reached!
% 4.64/1.58 % (812617)------------------------------
% 4.64/1.58 % (812617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.58 % (812617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.58 % (812617)CaDiCaL version: 2.1.3
% 4.64/1.58 % (812617)Termination reason: Instruction limit
% 4.64/1.58 % (812617)Termination phase: Saturation
% 4.64/1.58 % (812617)Time elapsed: 0.230 s
% 4.64/1.58 % (812617)Peak memory usage: 91 MB
% 4.64/1.58 % (812617)Instructions burned: 326 (million)
% 4.64/1.58 % (812623)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1829818582:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.64/1.58 % (812624)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4008192777:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.64/1.58 % (812601)Refutation found. Thanks to Tanya!
% 4.64/1.58 % SZS status Theorem for theBenchmark
% 4.64/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 5.66/1.78 % (812601)------------------------------
% 5.66/1.78 % (812601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.78 % (812601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.78 % (812601)CaDiCaL version: 2.1.3
% 5.66/1.78 % (812601)Termination reason: Refutation
% 5.66/1.78 % (812601)Time elapsed: 0.417 s
% 5.66/1.78 % (812601)Peak memory usage: 131 MB
% 5.66/1.78 % (812601)Instructions burned: 1079 (million)
% 5.66/1.78 % (812601)------------------------------
% 5.66/1.78 % (812601)------------------------------
% 5.66/1.78 % (812596)Success in time 0.718 s
% 5.66/1.78 % Vampire exiting
%------------------------------------------------------------------------------