%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU389+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:48:40 PM UTC 2026
% Result : Theorem 8.06s 2.16s
% Output : Refutation 9.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 29
% Syntax : Number of formulae : 288 ( 23 unt; 9 def)
% Number of atoms : 1165 ( 31 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 1476 ( 599 ~; 692 |; 119 &)
% ( 29 <=>; 35 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 10 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-3 aty)
% Number of variables : 432 ( 1 sgn 407 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,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/sandbox2/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(f28,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yellow19) ).
fof(f29,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f30,axiom,
! [X0] :
( ( topological_space(X0)
& top_str(X0) )
=> ! [X1,X2] :
( is_a_convergence_point_of_set(X0,X1,X2)
<=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( open_subset(X3,X0)
& in(X2,X3) )
=> in(X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_waybel_7) ).
fof(f32,axiom,
! [X0,X1] :
( ( top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> element(interior(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(f34,axiom,
! [X0,X1] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0)
& element(X1,the_carrier(X0)) )
=> element(neighborhood_system(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow19) ).
fof(f40,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f42,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/sandbox2/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
fof(f62,axiom,
! [X0,X1] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0)
& element(X1,the_carrier(X0)) )
=> ( ~ empty(neighborhood_system(X0,X1))
& filtered_subset(neighborhood_system(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& upper_relstr_subset(neighborhood_system(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& proper_element(neighborhood_system(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_yellow19) ).
fof(f73,axiom,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> open_subset(interior(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_tops_1) ).
fof(f79,axiom,
! [X0,X1,X2] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1)
& element(X2,the_carrier(X1)) )
=> ( in(X0,a_2_0_yellow19(X1,X2))
<=> ? [X3] :
( point_neighbourhood(X3,X1,X2)
& X0 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_yellow19) ).
fof(f117,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f118,axiom,
! [X0,X1] :
( element(X1,powerset(the_carrier(boole_POSet(X0))))
=> ( upper_relstr_subset(X1,boole_POSet(X0))
<=> ! [X2,X3] :
( ( subset(X2,X3)
& subset(X3,X0)
& in(X2,X1) )
=> in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_waybel_7) ).
fof(f119,axiom,
! [X0] :
( one_sorted_str(X0)
=> cast_as_carrier_subset(X0) = the_carrier(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pre_topc) ).
fof(f123,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f124,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( in(X2,neighborhood_system(X0,X1))
<=> point_neighbourhood(X2,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_yellow19) ).
fof(f125,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(interior(X0,X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tops_1) ).
fof(f126,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f127,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( ( upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X0)))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
=> ( is_a_convergence_point_of_set(X0,X2,X1)
<=> subset(neighborhood_system(X0,X1),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_yellow19) ).
fof(f128,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( ( upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X0)))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
=> ( is_a_convergence_point_of_set(X0,X2,X1)
<=> subset(neighborhood_system(X0,X1),X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f127]) ).
fof(f129,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/sandbox2/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(f134,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f117]) ).
fof(f182,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,[],[f27]) ).
fof(f183,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,[],[f182]) ).
fof(f184,plain,
! [X0] :
( ! [X1] :
( neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1)
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f185,plain,
! [X0] :
( ! [X1] :
( neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1)
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f184]) ).
fof(f186,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f187,plain,
! [X0] :
( ! [X1,X2] :
( is_a_convergence_point_of_set(X0,X1,X2)
<=> ! [X3] :
( in(X3,X1)
| ~ open_subset(X3,X0)
| ~ in(X2,X3)
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f188,plain,
! [X0] :
( ! [X1,X2] :
( is_a_convergence_point_of_set(X0,X1,X2)
<=> ! [X3] :
( in(X3,X1)
| ~ open_subset(X3,X0)
| ~ in(X2,X3)
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f187]) ).
fof(f190,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f32]) ).
fof(f191,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f190]) ).
fof(f192,plain,
! [X0,X1] :
( element(neighborhood_system(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(ennf_transformation,[],[f34]) ).
fof(f193,plain,
! [X0,X1] :
( element(neighborhood_system(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(flattening,[],[f192]) ).
fof(f196,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f197,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,[],[f42]) ).
fof(f198,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,[],[f197]) ).
fof(f211,plain,
! [X0,X1] :
( ( ~ empty(neighborhood_system(X0,X1))
& filtered_subset(neighborhood_system(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& upper_relstr_subset(neighborhood_system(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& proper_element(neighborhood_system(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(ennf_transformation,[],[f62]) ).
fof(f212,plain,
! [X0,X1] :
( ( ~ empty(neighborhood_system(X0,X1))
& filtered_subset(neighborhood_system(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& upper_relstr_subset(neighborhood_system(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& proper_element(neighborhood_system(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(flattening,[],[f211]) ).
fof(f230,plain,
! [X0,X1] :
( open_subset(interior(X0,X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f73]) ).
fof(f231,plain,
! [X0,X1] :
( open_subset(interior(X0,X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f230]) ).
fof(f235,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_0_yellow19(X1,X2))
<=> ? [X3] :
( point_neighbourhood(X3,X1,X2)
& X0 = X3 ) )
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(ennf_transformation,[],[f79]) ).
fof(f236,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_0_yellow19(X1,X2))
<=> ? [X3] :
( point_neighbourhood(X3,X1,X2)
& X0 = X3 ) )
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(flattening,[],[f235]) ).
fof(f271,plain,
! [X0,X1] :
( ( upper_relstr_subset(X1,boole_POSet(X0))
<=> ! [X2,X3] :
( in(X3,X1)
| ~ subset(X2,X3)
| ~ subset(X3,X0)
| ~ in(X2,X1) ) )
| ~ element(X1,powerset(the_carrier(boole_POSet(X0)))) ),
inference(ennf_transformation,[],[f118]) ).
fof(f272,plain,
! [X0,X1] :
( ( upper_relstr_subset(X1,boole_POSet(X0))
<=> ! [X2,X3] :
( in(X3,X1)
| ~ subset(X2,X3)
| ~ subset(X3,X0)
| ~ in(X2,X1) ) )
| ~ element(X1,powerset(the_carrier(boole_POSet(X0)))) ),
inference(flattening,[],[f271]) ).
fof(f273,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f119]) ).
fof(f278,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,neighborhood_system(X0,X1))
<=> point_neighbourhood(X2,X0,X1) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f124]) ).
fof(f279,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,neighborhood_system(X0,X1))
<=> point_neighbourhood(X2,X0,X1) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f278]) ).
fof(f280,plain,
! [X0] :
( ! [X1] :
( subset(interior(X0,X1),X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f125]) ).
fof(f281,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f126]) ).
fof(f282,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f281]) ).
fof(f283,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( is_a_convergence_point_of_set(X0,X2,X1)
<~> subset(neighborhood_system(X0,X1),X2) )
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X0)))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(ennf_transformation,[],[f128]) ).
fof(f284,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( is_a_convergence_point_of_set(X0,X2,X1)
<~> subset(neighborhood_system(X0,X1),X2) )
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X0)))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(flattening,[],[f283]) ).
fof(f285,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,[],[f129]) ).
fof(f286,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,[],[f285]) ).
fof(f293,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,[],[f183]) ).
fof(f294,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,[],[f186]) ).
fof(f295,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,[],[f294]) ).
fof(f296,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f295]) ).
fof(f297,plain,
! [X0] :
( ! [X1,X2] :
( ( is_a_convergence_point_of_set(X0,X1,X2)
| ? [X3] :
( ~ in(X3,X1)
& open_subset(X3,X0)
& in(X2,X3)
& element(X3,powerset(the_carrier(X0))) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ open_subset(X3,X0)
| ~ in(X2,X3)
| ~ element(X3,powerset(the_carrier(X0))) )
| ~ is_a_convergence_point_of_set(X0,X1,X2) ) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f188]) ).
fof(f298,plain,
! [X0] :
( ! [X1,X2] :
( ( is_a_convergence_point_of_set(X0,X1,X2)
| ? [X3] :
( ~ in(X3,X1)
& open_subset(X3,X0)
& in(X2,X3)
& element(X3,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( in(X4,X1)
| ~ open_subset(X4,X0)
| ~ in(X2,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ is_a_convergence_point_of_set(X0,X1,X2) ) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(rectify,[],[f297]) ).
fof(f299,plain,
! [X0] :
( ! [X1,X2] :
( ( is_a_convergence_point_of_set(X0,X1,X2)
| ( ~ in(sK2(X0,X1,X2),X1)
& open_subset(sK2(X0,X1,X2),X0)
& in(X2,sK2(X0,X1,X2))
& element(sK2(X0,X1,X2),powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( in(X4,X1)
| ~ open_subset(X4,X0)
| ~ in(X2,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ is_a_convergence_point_of_set(X0,X1,X2) ) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f298]) ).
fof(f308,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_0_yellow19(X1,X2))
| ! [X3] :
( ~ point_neighbourhood(X3,X1,X2)
| X0 != X3 ) )
& ( ? [X3] :
( point_neighbourhood(X3,X1,X2)
& X0 = X3 )
| ~ in(X0,a_2_0_yellow19(X1,X2)) ) )
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(nnf_transformation,[],[f236]) ).
fof(f309,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_0_yellow19(X1,X2))
| ! [X3] :
( ~ point_neighbourhood(X3,X1,X2)
| X0 != X3 ) )
& ( ? [X4] :
( point_neighbourhood(X4,X1,X2)
& X0 = X4 )
| ~ in(X0,a_2_0_yellow19(X1,X2)) ) )
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(rectify,[],[f308]) ).
fof(f310,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_0_yellow19(X1,X2))
| ! [X3] :
( ~ point_neighbourhood(X3,X1,X2)
| X0 != X3 ) )
& ( ( point_neighbourhood(sK10(X0,X1,X2),X1,X2)
& sK10(X0,X1,X2) = X0 )
| ~ in(X0,a_2_0_yellow19(X1,X2)) ) )
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X4,sK10(X0,X1,X2))],[f309]) ).
fof(f347,plain,
! [X0,X1] :
( ( ( upper_relstr_subset(X1,boole_POSet(X0))
| ? [X2,X3] :
( ~ in(X3,X1)
& subset(X2,X3)
& subset(X3,X0)
& in(X2,X1) ) )
& ( ! [X2,X3] :
( in(X3,X1)
| ~ subset(X2,X3)
| ~ subset(X3,X0)
| ~ in(X2,X1) )
| ~ upper_relstr_subset(X1,boole_POSet(X0)) ) )
| ~ element(X1,powerset(the_carrier(boole_POSet(X0)))) ),
inference(nnf_transformation,[],[f272]) ).
fof(f348,plain,
! [X0,X1] :
( ( ( upper_relstr_subset(X1,boole_POSet(X0))
| ? [X2,X3] :
( ~ in(X3,X1)
& subset(X2,X3)
& subset(X3,X0)
& in(X2,X1) ) )
& ( ! [X4,X5] :
( in(X5,X1)
| ~ subset(X4,X5)
| ~ subset(X5,X0)
| ~ in(X4,X1) )
| ~ upper_relstr_subset(X1,boole_POSet(X0)) ) )
| ~ element(X1,powerset(the_carrier(boole_POSet(X0)))) ),
inference(rectify,[],[f347]) ).
fof(f349,plain,
! [X0,X1] :
( ( ( upper_relstr_subset(X1,boole_POSet(X0))
| ( ~ in(sK47(X0,X1),X1)
& subset(sK46(X0,X1),sK47(X0,X1))
& subset(sK47(X0,X1),X0)
& in(sK46(X0,X1),X1) ) )
& ( ! [X4,X5] :
( in(X5,X1)
| ~ subset(X4,X5)
| ~ subset(X5,X0)
| ~ in(X4,X1) )
| ~ upper_relstr_subset(X1,boole_POSet(X0)) ) )
| ~ element(X1,powerset(the_carrier(boole_POSet(X0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46,sK47]),skolemize(X2,sK46(X0,X1)),skolemize(X3,sK47(X0,X1))],[f348]) ).
fof(f352,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f123]) ).
fof(f353,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,neighborhood_system(X0,X1))
| ~ point_neighbourhood(X2,X0,X1) )
& ( point_neighbourhood(X2,X0,X1)
| ~ in(X2,neighborhood_system(X0,X1)) ) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f279]) ).
fof(f354,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ subset(neighborhood_system(X0,X1),X2)
| ~ is_a_convergence_point_of_set(X0,X2,X1) )
& ( subset(neighborhood_system(X0,X1),X2)
| is_a_convergence_point_of_set(X0,X2,X1) )
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X0)))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(nnf_transformation,[],[f284]) ).
fof(f355,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ subset(neighborhood_system(X0,X1),X2)
| ~ is_a_convergence_point_of_set(X0,X2,X1) )
& ( subset(neighborhood_system(X0,X1),X2)
| is_a_convergence_point_of_set(X0,X2,X1) )
& upper_relstr_subset(X2,boole_POSet(cast_as_carrier_subset(X0)))
& element(X2,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(flattening,[],[f354]) ).
fof(f356,plain,
( ( ~ subset(neighborhood_system(sK49,sK50),sK51)
| ~ is_a_convergence_point_of_set(sK49,sK51,sK50) )
& ( subset(neighborhood_system(sK49,sK50),sK51)
| is_a_convergence_point_of_set(sK49,sK51,sK50) )
& upper_relstr_subset(sK51,boole_POSet(cast_as_carrier_subset(sK49)))
& element(sK51,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK49)))))
& element(sK50,the_carrier(sK49))
& ~ empty_carrier(sK49)
& topological_space(sK49)
& top_str(sK49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49,sK50,sK51]),skolemize(X0,sK49),skolemize(X1,sK50),skolemize(X2,sK51)],[f355]) ).
fof(f428,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,[],[f293]) ).
fof(f430,plain,
! [X0,X1] :
( ~ topological_space(X0)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f431,plain,
! [X3,X0,X1] :
( ~ in(X3,X0)
| in(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f296]) ).
fof(f432,plain,
! [X0,X1] :
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f296]) ).
fof(f433,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f296]) ).
fof(f434,plain,
! [X2,X0,X1,X4] :
( ~ is_a_convergence_point_of_set(X0,X1,X2)
| ~ open_subset(X4,X0)
| ~ in(X2,X4)
| ~ element(X4,powerset(the_carrier(X0)))
| in(X4,X1)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f435,plain,
! [X2,X0,X1] :
( element(sK2(X0,X1,X2),powerset(the_carrier(X0)))
| is_a_convergence_point_of_set(X0,X1,X2)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f436,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| in(X2,sK2(X0,X1,X2))
| ~ topological_space(X0)
| is_a_convergence_point_of_set(X0,X1,X2) ),
inference(cnf_transformation,[],[f299]) ).
fof(f437,plain,
! [X2,X0,X1] :
( open_subset(sK2(X0,X1,X2),X0)
| is_a_convergence_point_of_set(X0,X1,X2)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f438,plain,
! [X2,X0,X1] :
( ~ topological_space(X0)
| ~ in(sK2(X0,X1,X2),X1)
| is_a_convergence_point_of_set(X0,X1,X2)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f441,plain,
! [X0,X1] :
( element(interior(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f191]) ).
fof(f442,plain,
! [X0,X1] :
( element(neighborhood_system(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(cnf_transformation,[],[f193]) ).
fof(f447,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f196]) ).
fof(f448,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,[],[f198]) ).
fof(f493,plain,
! [X0,X1] :
( upper_relstr_subset(neighborhood_system(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(cnf_transformation,[],[f212]) ).
fof(f530,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ topological_space(X0)
| open_subset(interior(X0,X1),X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f231]) ).
fof(f565,plain,
! [X2,X0,X1] :
( ~ top_str(X1)
| ~ in(X0,a_2_0_yellow19(X1,X2))
| empty_carrier(X1)
| ~ topological_space(X1)
| sK10(X0,X1,X2) = X0
| ~ element(X2,the_carrier(X1)) ),
inference(cnf_transformation,[],[f310]) ).
fof(f566,plain,
! [X2,X0,X1] :
( ~ top_str(X1)
| ~ in(X0,a_2_0_yellow19(X1,X2))
| empty_carrier(X1)
| ~ topological_space(X1)
| point_neighbourhood(sK10(X0,X1,X2),X1,X2)
| ~ element(X2,the_carrier(X1)) ),
inference(cnf_transformation,[],[f310]) ).
fof(f746,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f134]) ).
fof(f747,plain,
! [X0,X1,X4,X5] :
( ~ upper_relstr_subset(X1,boole_POSet(X0))
| ~ subset(X4,X5)
| ~ subset(X5,X0)
| ~ in(X4,X1)
| in(X5,X1)
| ~ element(X1,powerset(the_carrier(boole_POSet(X0)))) ),
inference(cnf_transformation,[],[f349]) ).
fof(f752,plain,
! [X0] :
( ~ one_sorted_str(X0)
| the_carrier(X0) = cast_as_carrier_subset(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f757,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f352]) ).
fof(f759,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ in(X2,neighborhood_system(X0,X1))
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ topological_space(X0)
| point_neighbourhood(X2,X0,X1) ),
inference(cnf_transformation,[],[f353]) ).
fof(f760,plain,
! [X2,X0,X1] :
( ~ point_neighbourhood(X2,X0,X1)
| in(X2,neighborhood_system(X0,X1))
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f761,plain,
! [X0,X1] :
( subset(interior(X0,X1),X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f762,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| element(X0,X2)
| ~ element(X1,powerset(X2)) ),
inference(cnf_transformation,[],[f282]) ).
fof(f763,plain,
top_str(sK49),
inference(cnf_transformation,[],[f356]) ).
fof(f764,plain,
topological_space(sK49),
inference(cnf_transformation,[],[f356]) ).
fof(f765,plain,
~ empty_carrier(sK49),
inference(cnf_transformation,[],[f356]) ).
fof(f766,plain,
element(sK50,the_carrier(sK49)),
inference(cnf_transformation,[],[f356]) ).
fof(f767,plain,
element(sK51,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK49))))),
inference(cnf_transformation,[],[f356]) ).
fof(f768,plain,
upper_relstr_subset(sK51,boole_POSet(cast_as_carrier_subset(sK49))),
inference(cnf_transformation,[],[f356]) ).
fof(f769,plain,
( subset(neighborhood_system(sK49,sK50),sK51)
| is_a_convergence_point_of_set(sK49,sK51,sK50) ),
inference(cnf_transformation,[],[f356]) ).
fof(f770,plain,
( ~ subset(neighborhood_system(sK49,sK50),sK51)
| ~ is_a_convergence_point_of_set(sK49,sK51,sK50) ),
inference(cnf_transformation,[],[f356]) ).
fof(f771,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ open_subset(X1,X0)
| ~ in(X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| empty_carrier(X0)
| ~ topological_space(X0)
| point_neighbourhood(X1,X0,X2) ),
inference(cnf_transformation,[],[f286]) ).
fof(f778,definition,
( spl52_1
<=> is_a_convergence_point_of_set(sK49,sK51,sK50) ),
introduced(definition,[new_symbols(definition,[spl52_1])],[avatar_definition]) ).
fof(f779,plain,
( is_a_convergence_point_of_set(sK49,sK51,sK50)
| ~ spl52_1 ),
inference(avatar_component_clause,[],[f778]) ).
fof(f781,definition,
( spl52_2
<=> subset(neighborhood_system(sK49,sK50),sK51) ),
introduced(definition,[new_symbols(definition,[spl52_2])],[avatar_definition]) ).
fof(f782,plain,
( subset(neighborhood_system(sK49,sK50),sK51)
| ~ spl52_2 ),
inference(avatar_component_clause,[],[f781]) ).
fof(f783,plain,
( spl52_1
| spl52_2 ),
inference(avatar_split_clause,[],[f769,f781,f778]) ).
fof(f784,plain,
( ~ is_a_convergence_point_of_set(sK49,sK51,sK50)
| spl52_1 ),
inference(avatar_component_clause,[],[f778]) ).
fof(f785,plain,
( ~ subset(neighborhood_system(sK49,sK50),sK51)
| spl52_2 ),
inference(avatar_component_clause,[],[f781]) ).
fof(f786,plain,
( ~ spl52_1
| ~ spl52_2 ),
inference(avatar_split_clause,[],[f770,f781,f778]) ).
fof(f787,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ point_neighbourhood(X2,X0,X1)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ topological_space(X0)
| in(X1,interior(X0,X2)) ),
inference(forward_subsumption_resolution,[],[f428,f448]) ).
fof(f791,plain,
! [X0,X1] :
( in(X0,sK2(sK49,X1,X0))
| ~ topological_space(sK49)
| is_a_convergence_point_of_set(sK49,X1,X0) ),
inference(resolution,[],[f763,f436]) ).
fof(f792,plain,
! [X0,X1] :
( in(X0,sK2(sK49,X1,X0))
| is_a_convergence_point_of_set(sK49,X1,X0) ),
inference(forward_subsumption_resolution,[],[f791,f764]) ).
fof(f793,plain,
! [X0] :
( ~ element(X0,the_carrier(sK49))
| empty_carrier(sK49)
| neighborhood_system(sK49,X0) = a_2_0_yellow19(sK49,X0)
| ~ top_str(sK49) ),
inference(resolution,[],[f764,f430]) ).
fof(f794,plain,
! [X0,X1] :
( ~ in(sK2(sK49,X0,X1),X0)
| is_a_convergence_point_of_set(sK49,X0,X1)
| ~ top_str(sK49) ),
inference(resolution,[],[f764,f438]) ).
fof(f795,plain,
! [X0,X1] :
( ~ in(sK2(sK49,X0,X1),X0)
| is_a_convergence_point_of_set(sK49,X0,X1) ),
inference(forward_subsumption_resolution,[],[f794,f763]) ).
fof(f796,plain,
! [X0] :
( ~ element(X0,the_carrier(sK49))
| neighborhood_system(sK49,X0) = a_2_0_yellow19(sK49,X0)
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f793,f765]) ).
fof(f797,plain,
! [X0] :
( ~ element(X0,the_carrier(sK49))
| neighborhood_system(sK49,X0) = a_2_0_yellow19(sK49,X0) ),
inference(forward_subsumption_resolution,[],[f796,f763]) ).
fof(f798,plain,
neighborhood_system(sK49,sK50) = a_2_0_yellow19(sK49,sK50),
inference(resolution,[],[f797,f766]) ).
fof(f801,plain,
! [X0,X1] :
( ~ in(X0,neighborhood_system(sK49,X1))
| ~ element(X1,the_carrier(sK49))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| point_neighbourhood(X0,sK49,X1) ),
inference(resolution,[],[f759,f763]) ).
fof(f802,plain,
! [X0,X1] :
( ~ in(X0,neighborhood_system(sK49,X1))
| ~ element(X1,the_carrier(sK49))
| ~ topological_space(sK49)
| point_neighbourhood(X0,sK49,X1) ),
inference(forward_subsumption_resolution,[],[f801,f765]) ).
fof(f803,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(sK49))
| ~ in(X0,neighborhood_system(sK49,X1))
| point_neighbourhood(X0,sK49,X1) ),
inference(forward_subsumption_resolution,[],[f802,f764]) ).
fof(f810,plain,
! [X0,X1] :
( ~ open_subset(X0,sK49)
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sK49))
| ~ element(X0,powerset(the_carrier(sK49)))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| point_neighbourhood(X0,sK49,X1) ),
inference(resolution,[],[f771,f763]) ).
fof(f811,plain,
! [X0,X1] :
( ~ open_subset(X0,sK49)
| ~ in(X1,X0)
| ~ element(X0,powerset(the_carrier(sK49)))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| point_neighbourhood(X0,sK49,X1) ),
inference(forward_subsumption_resolution,[],[f810,f762]) ).
fof(f812,plain,
! [X0,X1] :
( ~ open_subset(X0,sK49)
| ~ in(X1,X0)
| ~ element(X0,powerset(the_carrier(sK49)))
| ~ topological_space(sK49)
| point_neighbourhood(X0,sK49,X1) ),
inference(forward_subsumption_resolution,[],[f811,f765]) ).
fof(f813,plain,
! [X0,X1] :
( ~ open_subset(X0,sK49)
| ~ in(X1,X0)
| ~ element(X0,powerset(the_carrier(sK49)))
| point_neighbourhood(X0,sK49,X1) ),
inference(forward_subsumption_resolution,[],[f812,f764]) ).
fof(f814,plain,
! [X2,X0,X1] :
( ~ in(X0,sK2(sK49,X1,X2))
| ~ element(sK2(sK49,X1,X2),powerset(the_carrier(sK49)))
| point_neighbourhood(sK2(sK49,X1,X2),sK49,X0)
| is_a_convergence_point_of_set(sK49,X1,X2)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(resolution,[],[f813,f437]) ).
fof(f815,plain,
! [X2,X0,X1] :
( ~ in(X0,sK2(sK49,X1,X2))
| ~ element(sK2(sK49,X1,X2),powerset(the_carrier(sK49)))
| point_neighbourhood(sK2(sK49,X1,X2),sK49,X0)
| is_a_convergence_point_of_set(sK49,X1,X2)
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f814,f764]) ).
fof(f816,plain,
! [X2,X0,X1] :
( ~ element(sK2(sK49,X1,X2),powerset(the_carrier(sK49)))
| ~ in(X0,sK2(sK49,X1,X2))
| point_neighbourhood(sK2(sK49,X1,X2),sK49,X0)
| is_a_convergence_point_of_set(sK49,X1,X2) ),
inference(forward_subsumption_resolution,[],[f815,f763]) ).
fof(f817,plain,
! [X0,X1] :
( ~ in(X0,a_2_0_yellow19(sK49,X1))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| sK10(X0,sK49,X1) = X0
| ~ element(X1,the_carrier(sK49)) ),
inference(resolution,[],[f565,f763]) ).
fof(f818,plain,
! [X0,X1] :
( ~ in(X0,a_2_0_yellow19(sK49,X1))
| ~ topological_space(sK49)
| sK10(X0,sK49,X1) = X0
| ~ element(X1,the_carrier(sK49)) ),
inference(forward_subsumption_resolution,[],[f817,f765]) ).
fof(f819,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(sK49))
| sK10(X0,sK49,X1) = X0
| ~ in(X0,a_2_0_yellow19(sK49,X1)) ),
inference(forward_subsumption_resolution,[],[f818,f764]) ).
fof(f820,plain,
! [X0] :
( sK10(X0,sK49,sK50) = X0
| ~ in(X0,a_2_0_yellow19(sK49,sK50)) ),
inference(resolution,[],[f819,f766]) ).
fof(f821,plain,
! [X0] :
( ~ in(X0,neighborhood_system(sK49,sK50))
| sK10(X0,sK49,sK50) = X0 ),
inference(forward_demodulation,[],[f820,f798]) ).
fof(f822,plain,
! [X0] :
( subset(neighborhood_system(sK49,sK50),X0)
| sK1(neighborhood_system(sK49,sK50),X0) = sK10(sK1(neighborhood_system(sK49,sK50),X0),sK49,sK50) ),
inference(resolution,[],[f821,f432]) ).
fof(f825,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,cast_as_carrier_subset(sK49))
| ~ in(X0,sK51)
| in(X1,sK51)
| ~ element(sK51,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK49))))) ),
inference(resolution,[],[f747,f768]) ).
fof(f826,plain,
! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,cast_as_carrier_subset(X2))
| ~ in(X0,neighborhood_system(X2,X3))
| in(X1,neighborhood_system(X2,X3))
| ~ element(neighborhood_system(X2,X3),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X2)))))
| empty_carrier(X2)
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,the_carrier(X2)) ),
inference(resolution,[],[f747,f493]) ).
fof(f827,plain,
! [X2,X3,X0,X1] :
( ~ top_str(X2)
| ~ subset(X1,cast_as_carrier_subset(X2))
| ~ in(X0,neighborhood_system(X2,X3))
| in(X1,neighborhood_system(X2,X3))
| empty_carrier(X2)
| ~ topological_space(X2)
| ~ subset(X0,X1)
| ~ element(X3,the_carrier(X2)) ),
inference(forward_subsumption_resolution,[],[f826,f442]) ).
fof(f828,plain,
! [X0,X1] :
( ~ in(X0,sK51)
| ~ subset(X1,cast_as_carrier_subset(sK49))
| ~ subset(X0,X1)
| in(X1,sK51) ),
inference(forward_subsumption_resolution,[],[f825,f767]) ).
fof(f830,plain,
! [X2,X0,X1] :
( ~ subset(X0,cast_as_carrier_subset(sK49))
| ~ in(X1,neighborhood_system(sK49,X2))
| in(X0,neighborhood_system(sK49,X2))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ subset(X1,X0)
| ~ element(X2,the_carrier(sK49)) ),
inference(resolution,[],[f827,f763]) ).
fof(f831,plain,
! [X2,X0,X1] :
( ~ subset(X0,cast_as_carrier_subset(sK49))
| ~ in(X1,neighborhood_system(sK49,X2))
| in(X0,neighborhood_system(sK49,X2))
| ~ topological_space(sK49)
| ~ subset(X1,X0)
| ~ element(X2,the_carrier(sK49)) ),
inference(forward_subsumption_resolution,[],[f830,f765]) ).
fof(f832,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(sK49))
| ~ in(X1,neighborhood_system(sK49,X2))
| in(X0,neighborhood_system(sK49,X2))
| ~ subset(X1,X0)
| ~ subset(X0,cast_as_carrier_subset(sK49)) ),
inference(forward_subsumption_resolution,[],[f831,f764]) ).
fof(f833,plain,
! [X0,X1] :
( ~ in(X0,neighborhood_system(sK49,sK50))
| in(X1,neighborhood_system(sK49,sK50))
| ~ subset(X0,X1)
| ~ subset(X1,cast_as_carrier_subset(sK49)) ),
inference(resolution,[],[f832,f766]) ).
fof(f835,plain,
! [X0] :
( ~ in(X0,neighborhood_system(sK49,sK50))
| point_neighbourhood(X0,sK49,sK50) ),
inference(resolution,[],[f803,f766]) ).
fof(f836,plain,
! [X0] :
( point_neighbourhood(sK1(neighborhood_system(sK49,sK50),X0),sK49,sK50)
| subset(neighborhood_system(sK49,sK50),X0) ),
inference(resolution,[],[f835,f432]) ).
fof(f837,plain,
! [X0,X1] :
( ~ in(X0,a_2_0_yellow19(sK49,X1))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| point_neighbourhood(sK10(X0,sK49,X1),sK49,X1)
| ~ element(X1,the_carrier(sK49)) ),
inference(resolution,[],[f566,f763]) ).
fof(f838,plain,
! [X0,X1] :
( ~ in(X0,a_2_0_yellow19(sK49,X1))
| ~ topological_space(sK49)
| point_neighbourhood(sK10(X0,sK49,X1),sK49,X1)
| ~ element(X1,the_carrier(sK49)) ),
inference(forward_subsumption_resolution,[],[f837,f765]) ).
fof(f839,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(sK49))
| point_neighbourhood(sK10(X0,sK49,X1),sK49,X1)
| ~ in(X0,a_2_0_yellow19(sK49,X1)) ),
inference(forward_subsumption_resolution,[],[f838,f764]) ).
fof(f842,plain,
! [X0] :
( point_neighbourhood(sK10(X0,sK49,sK50),sK49,sK50)
| ~ in(X0,a_2_0_yellow19(sK49,sK50)) ),
inference(resolution,[],[f839,f766]) ).
fof(f843,plain,
! [X0] :
( ~ in(X0,neighborhood_system(sK49,sK50))
| point_neighbourhood(sK10(X0,sK49,sK50),sK49,sK50) ),
inference(forward_demodulation,[],[f842,f798]) ).
fof(f844,plain,
! [X0] :
( point_neighbourhood(sK10(sK1(neighborhood_system(sK49,sK50),X0),sK49,sK50),sK49,sK50)
| subset(neighborhood_system(sK49,sK50),X0) ),
inference(resolution,[],[f843,f432]) ).
fof(f871,plain,
one_sorted_str(sK49),
inference(resolution,[],[f447,f763]) ).
fof(f874,plain,
cast_as_carrier_subset(sK49) = the_carrier(sK49),
inference(resolution,[],[f871,f752]) ).
fof(f917,plain,
! [X0] :
( subset(neighborhood_system(sK49,sK50),X0)
| in(sK10(sK1(neighborhood_system(sK49,sK50),X0),sK49,sK50),neighborhood_system(sK49,sK50))
| ~ element(sK50,the_carrier(sK49))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(resolution,[],[f844,f760]) ).
fof(f919,plain,
! [X0] :
( subset(neighborhood_system(sK49,sK50),X0)
| in(sK10(sK1(neighborhood_system(sK49,sK50),X0),sK49,sK50),neighborhood_system(sK49,sK50))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f917,f766]) ).
fof(f922,plain,
! [X0] :
( subset(neighborhood_system(sK49,sK50),X0)
| in(sK10(sK1(neighborhood_system(sK49,sK50),X0),sK49,sK50),neighborhood_system(sK49,sK50))
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f919,f765]) ).
fof(f925,plain,
! [X0] :
( subset(neighborhood_system(sK49,sK50),X0)
| in(sK10(sK1(neighborhood_system(sK49,sK50),X0),sK49,sK50),neighborhood_system(sK49,sK50))
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f922,f764]) ).
fof(f928,plain,
! [X0] :
( in(sK10(sK1(neighborhood_system(sK49,sK50),X0),sK49,sK50),neighborhood_system(sK49,sK50))
| subset(neighborhood_system(sK49,sK50),X0) ),
inference(forward_subsumption_resolution,[],[f925,f763]) ).
fof(f934,plain,
! [X0,X1] :
( subset(neighborhood_system(sK49,sK50),X0)
| in(X1,neighborhood_system(sK49,sK50))
| ~ subset(sK10(sK1(neighborhood_system(sK49,sK50),X0),sK49,sK50),X1)
| ~ subset(X1,cast_as_carrier_subset(sK49)) ),
inference(resolution,[],[f928,f833]) ).
fof(f939,plain,
! [X0,X1] :
( ~ subset(sK10(sK1(neighborhood_system(sK49,sK50),X0),sK49,sK50),X1)
| subset(neighborhood_system(sK49,sK50),X0)
| in(X1,neighborhood_system(sK49,sK50))
| ~ subset(X1,the_carrier(sK49)) ),
inference(forward_demodulation,[],[f934,f874]) ).
fof(f940,plain,
! [X0] :
( subset(neighborhood_system(sK49,sK50),X0)
| element(sK1(neighborhood_system(sK49,sK50),X0),powerset(the_carrier(sK49)))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| ~ element(sK50,the_carrier(sK49)) ),
inference(resolution,[],[f836,f448]) ).
fof(f944,plain,
! [X0] :
( subset(neighborhood_system(sK49,sK50),X0)
| element(sK1(neighborhood_system(sK49,sK50),X0),powerset(the_carrier(sK49)))
| ~ topological_space(sK49)
| ~ top_str(sK49)
| ~ element(sK50,the_carrier(sK49)) ),
inference(forward_subsumption_resolution,[],[f940,f765]) ).
fof(f946,plain,
! [X0] :
( subset(neighborhood_system(sK49,sK50),X0)
| element(sK1(neighborhood_system(sK49,sK50),X0),powerset(the_carrier(sK49)))
| ~ top_str(sK49)
| ~ element(sK50,the_carrier(sK49)) ),
inference(forward_subsumption_resolution,[],[f944,f764]) ).
fof(f948,plain,
! [X0] :
( subset(neighborhood_system(sK49,sK50),X0)
| element(sK1(neighborhood_system(sK49,sK50),X0),powerset(the_carrier(sK49)))
| ~ element(sK50,the_carrier(sK49)) ),
inference(forward_subsumption_resolution,[],[f946,f763]) ).
fof(f950,plain,
! [X0] :
( element(sK1(neighborhood_system(sK49,sK50),X0),powerset(the_carrier(sK49)))
| subset(neighborhood_system(sK49,sK50),X0) ),
inference(forward_subsumption_resolution,[],[f948,f766]) ).
fof(f968,plain,
! [X0] :
( subset(sK1(neighborhood_system(sK49,sK50),X0),the_carrier(sK49))
| subset(neighborhood_system(sK49,sK50),X0) ),
inference(resolution,[],[f757,f950]) ).
fof(f983,plain,
! [X0,X1] :
( ~ point_neighbourhood(X0,sK49,X1)
| ~ element(X1,the_carrier(sK49))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| in(X1,interior(sK49,X0)) ),
inference(resolution,[],[f787,f763]) ).
fof(f984,plain,
! [X0,X1] :
( ~ point_neighbourhood(X0,sK49,X1)
| ~ element(X1,the_carrier(sK49))
| ~ topological_space(sK49)
| in(X1,interior(sK49,X0)) ),
inference(forward_subsumption_resolution,[],[f983,f765]) ).
fof(f985,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(sK49))
| ~ point_neighbourhood(X0,sK49,X1)
| in(X1,interior(sK49,X0)) ),
inference(forward_subsumption_resolution,[],[f984,f764]) ).
fof(f986,plain,
! [X0] :
( in(sK50,interior(sK49,X0))
| ~ point_neighbourhood(X0,sK49,sK50) ),
inference(resolution,[],[f985,f766]) ).
fof(f988,plain,
! [X0,X1] :
( ~ subset(interior(sK49,X0),X1)
| in(sK50,X1)
| ~ point_neighbourhood(X0,sK49,sK50) ),
inference(resolution,[],[f986,f431]) ).
fof(f998,plain,
! [X0] :
( ~ topological_space(sK49)
| open_subset(interior(sK49,X0),sK49)
| ~ element(X0,powerset(the_carrier(sK49))) ),
inference(resolution,[],[f530,f763]) ).
fof(f999,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK49)))
| open_subset(interior(sK49,X0),sK49) ),
inference(forward_subsumption_resolution,[],[f998,f764]) ).
fof(f1009,plain,
! [X2,X0,X1] :
( ~ in(X0,sK2(sK49,X1,X2))
| point_neighbourhood(sK2(sK49,X1,X2),sK49,X0)
| is_a_convergence_point_of_set(sK49,X1,X2)
| is_a_convergence_point_of_set(sK49,X1,X2)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(resolution,[],[f816,f435]) ).
fof(f1010,plain,
! [X2,X0,X1] :
( ~ in(X0,sK2(sK49,X1,X2))
| point_neighbourhood(sK2(sK49,X1,X2),sK49,X0)
| is_a_convergence_point_of_set(sK49,X1,X2)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(duplicate_literal_removal,[],[f1009]) ).
fof(f1011,plain,
! [X2,X0,X1] :
( ~ in(X0,sK2(sK49,X1,X2))
| point_neighbourhood(sK2(sK49,X1,X2),sK49,X0)
| is_a_convergence_point_of_set(sK49,X1,X2)
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f1010,f764]) ).
fof(f1012,plain,
! [X2,X0,X1] :
( ~ in(X0,sK2(sK49,X1,X2))
| point_neighbourhood(sK2(sK49,X1,X2),sK49,X0)
| is_a_convergence_point_of_set(sK49,X1,X2) ),
inference(forward_subsumption_resolution,[],[f1011,f763]) ).
fof(f1030,plain,
! [X0,X1] :
( point_neighbourhood(sK2(sK49,X0,X1),sK49,X1)
| is_a_convergence_point_of_set(sK49,X0,X1)
| is_a_convergence_point_of_set(sK49,X0,X1) ),
inference(resolution,[],[f1012,f792]) ).
fof(f1032,plain,
! [X0,X1] :
( point_neighbourhood(sK2(sK49,X0,X1),sK49,X1)
| is_a_convergence_point_of_set(sK49,X0,X1) ),
inference(duplicate_literal_removal,[],[f1030]) ).
fof(f1035,plain,
! [X0,X1] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| in(sK2(sK49,X0,X1),neighborhood_system(sK49,X1))
| ~ element(X1,the_carrier(sK49))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(resolution,[],[f1032,f760]) ).
fof(f1036,plain,
! [X0,X1] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| in(sK2(sK49,X0,X1),neighborhood_system(sK49,X1))
| ~ element(X1,the_carrier(sK49))
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f1035,f765]) ).
fof(f1038,plain,
! [X0,X1] :
( is_a_convergence_point_of_set(sK49,X0,X1)
| in(sK2(sK49,X0,X1),neighborhood_system(sK49,X1))
| ~ element(X1,the_carrier(sK49))
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f1036,f764]) ).
fof(f1040,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(sK49))
| in(sK2(sK49,X0,X1),neighborhood_system(sK49,X1))
| is_a_convergence_point_of_set(sK49,X0,X1) ),
inference(forward_subsumption_resolution,[],[f1038,f763]) ).
fof(f1042,plain,
! [X0] :
( in(sK2(sK49,X0,sK50),neighborhood_system(sK49,sK50))
| is_a_convergence_point_of_set(sK49,X0,sK50) ),
inference(resolution,[],[f1040,f766]) ).
fof(f1044,plain,
! [X0] :
( point_neighbourhood(sK10(sK2(sK49,X0,sK50),sK49,sK50),sK49,sK50)
| is_a_convergence_point_of_set(sK49,X0,sK50) ),
inference(resolution,[],[f1042,f843]) ).
fof(f1047,plain,
! [X0] :
( is_a_convergence_point_of_set(sK49,X0,sK50)
| sK2(sK49,X0,sK50) = sK10(sK2(sK49,X0,sK50),sK49,sK50) ),
inference(resolution,[],[f1042,f821]) ).
fof(f1176,plain,
( sK2(sK49,sK51,sK50) = sK10(sK2(sK49,sK51,sK50),sK49,sK50)
| spl52_1 ),
inference(resolution,[],[f784,f1047]) ).
fof(f1259,plain,
! [X0] :
( is_a_convergence_point_of_set(sK49,X0,sK50)
| in(sK10(sK2(sK49,X0,sK50),sK49,sK50),neighborhood_system(sK49,sK50))
| ~ element(sK50,the_carrier(sK49))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(resolution,[],[f1044,f760]) ).
fof(f1261,plain,
! [X0] :
( is_a_convergence_point_of_set(sK49,X0,sK50)
| in(sK10(sK2(sK49,X0,sK50),sK49,sK50),neighborhood_system(sK49,sK50))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f1259,f766]) ).
fof(f1264,plain,
! [X0] :
( is_a_convergence_point_of_set(sK49,X0,sK50)
| in(sK10(sK2(sK49,X0,sK50),sK49,sK50),neighborhood_system(sK49,sK50))
| ~ topological_space(sK49)
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f1261,f765]) ).
fof(f1267,plain,
! [X0] :
( is_a_convergence_point_of_set(sK49,X0,sK50)
| in(sK10(sK2(sK49,X0,sK50),sK49,sK50),neighborhood_system(sK49,sK50))
| ~ top_str(sK49) ),
inference(forward_subsumption_resolution,[],[f1264,f764]) ).
fof(f1270,plain,
! [X0] :
( in(sK10(sK2(sK49,X0,sK50),sK49,sK50),neighborhood_system(sK49,sK50))
| is_a_convergence_point_of_set(sK49,X0,sK50) ),
inference(forward_subsumption_resolution,[],[f1267,f763]) ).
fof(f1279,plain,
! [X0,X1] :
( ~ subset(neighborhood_system(sK49,sK50),X1)
| in(sK10(sK2(sK49,X0,sK50),sK49,sK50),X1)
| is_a_convergence_point_of_set(sK49,X0,sK50) ),
inference(resolution,[],[f1270,f431]) ).
fof(f1310,plain,
( ! [X0] :
( in(sK10(sK2(sK49,X0,sK50),sK49,sK50),sK51)
| is_a_convergence_point_of_set(sK49,X0,sK50) )
| ~ spl52_2 ),
inference(resolution,[],[f1279,f782]) ).
fof(f1318,plain,
( in(sK2(sK49,sK51,sK50),sK51)
| is_a_convergence_point_of_set(sK49,sK51,sK50)
| spl52_1
| ~ spl52_2 ),
inference(superposition,[],[f1310,f1176]) ).
fof(f1319,plain,
( is_a_convergence_point_of_set(sK49,sK51,sK50)
| spl52_1
| ~ spl52_2 ),
inference(forward_subsumption_resolution,[],[f1318,f795]) ).
fof(f1321,plain,
( $false
| spl52_1
| ~ spl52_2 ),
inference(forward_subsumption_resolution,[],[f1319,f784]) ).
fof(f1322,plain,
( spl52_1
| ~ spl52_2 ),
inference(avatar_contradiction_clause,[],[f1321]) ).
fof(f1323,plain,
( ! [X0] :
( ~ open_subset(X0,sK49)
| ~ in(sK50,X0)
| ~ element(X0,powerset(the_carrier(sK49)))
| in(X0,sK51)
| ~ topological_space(sK49)
| ~ top_str(sK49) )
| ~ spl52_1 ),
inference(resolution,[],[f779,f434]) ).
fof(f1324,plain,
( ! [X0] :
( ~ open_subset(X0,sK49)
| ~ in(sK50,X0)
| ~ element(X0,powerset(the_carrier(sK49)))
| in(X0,sK51)
| ~ top_str(sK49) )
| ~ spl52_1 ),
inference(forward_subsumption_resolution,[],[f1323,f764]) ).
fof(f1325,plain,
( ! [X0] :
( ~ open_subset(X0,sK49)
| ~ in(sK50,X0)
| ~ element(X0,powerset(the_carrier(sK49)))
| in(X0,sK51) )
| ~ spl52_1 ),
inference(forward_subsumption_resolution,[],[f1324,f763]) ).
fof(f1327,plain,
( sK1(neighborhood_system(sK49,sK50),sK51) = sK10(sK1(neighborhood_system(sK49,sK50),sK51),sK49,sK50)
| spl52_2 ),
inference(resolution,[],[f785,f822]) ).
fof(f1330,plain,
( ! [X0] :
( ~ subset(sK1(neighborhood_system(sK49,sK50),sK51),X0)
| subset(neighborhood_system(sK49,sK50),sK51)
| in(X0,neighborhood_system(sK49,sK50))
| ~ subset(X0,the_carrier(sK49)) )
| spl52_2 ),
inference(superposition,[],[f939,f1327]) ).
fof(f1333,plain,
( ! [X0] :
( ~ subset(sK1(neighborhood_system(sK49,sK50),sK51),X0)
| in(X0,neighborhood_system(sK49,sK50))
| ~ subset(X0,the_carrier(sK49)) )
| spl52_2 ),
inference(forward_subsumption_resolution,[],[f1330,f785]) ).
fof(f1335,plain,
( in(sK1(neighborhood_system(sK49,sK50),sK51),neighborhood_system(sK49,sK50))
| ~ subset(sK1(neighborhood_system(sK49,sK50),sK51),the_carrier(sK49))
| spl52_2 ),
inference(resolution,[],[f1333,f746]) ).
fof(f1337,definition,
( spl52_24
<=> subset(sK1(neighborhood_system(sK49,sK50),sK51),the_carrier(sK49)) ),
introduced(definition,[new_symbols(definition,[spl52_24])],[avatar_definition]) ).
fof(f1338,plain,
( ~ subset(sK1(neighborhood_system(sK49,sK50),sK51),the_carrier(sK49))
| spl52_24 ),
inference(avatar_component_clause,[],[f1337]) ).
fof(f1340,definition,
( spl52_25
<=> in(sK1(neighborhood_system(sK49,sK50),sK51),neighborhood_system(sK49,sK50)) ),
introduced(definition,[new_symbols(definition,[spl52_25])],[avatar_definition]) ).
fof(f1341,plain,
( in(sK1(neighborhood_system(sK49,sK50),sK51),neighborhood_system(sK49,sK50))
| ~ spl52_25 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f1342,plain,
( ~ spl52_24
| spl52_25
| spl52_2 ),
inference(avatar_split_clause,[],[f1335,f781,f1340,f1337]) ).
fof(f1348,plain,
( subset(neighborhood_system(sK49,sK50),sK51)
| spl52_24 ),
inference(resolution,[],[f1338,f968]) ).
fof(f1350,plain,
( $false
| spl52_2
| spl52_24 ),
inference(forward_subsumption_resolution,[],[f1348,f785]) ).
fof(f1351,plain,
( spl52_2
| spl52_24 ),
inference(avatar_contradiction_clause,[],[f1350]) ).
fof(f1353,plain,
( point_neighbourhood(sK1(neighborhood_system(sK49,sK50),sK51),sK49,sK50)
| ~ spl52_25 ),
inference(resolution,[],[f1341,f835]) ).
fof(f1360,plain,
( element(sK1(neighborhood_system(sK49,sK50),sK51),powerset(the_carrier(sK49)))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| ~ element(sK50,the_carrier(sK49))
| ~ spl52_25 ),
inference(resolution,[],[f1353,f448]) ).
fof(f1364,plain,
( element(sK1(neighborhood_system(sK49,sK50),sK51),powerset(the_carrier(sK49)))
| ~ topological_space(sK49)
| ~ top_str(sK49)
| ~ element(sK50,the_carrier(sK49))
| ~ spl52_25 ),
inference(forward_subsumption_resolution,[],[f1360,f765]) ).
fof(f1366,plain,
( element(sK1(neighborhood_system(sK49,sK50),sK51),powerset(the_carrier(sK49)))
| ~ top_str(sK49)
| ~ element(sK50,the_carrier(sK49))
| ~ spl52_25 ),
inference(forward_subsumption_resolution,[],[f1364,f764]) ).
fof(f1368,plain,
( element(sK1(neighborhood_system(sK49,sK50),sK51),powerset(the_carrier(sK49)))
| ~ element(sK50,the_carrier(sK49))
| ~ spl52_25 ),
inference(forward_subsumption_resolution,[],[f1366,f763]) ).
fof(f1370,plain,
( element(sK1(neighborhood_system(sK49,sK50),sK51),powerset(the_carrier(sK49)))
| ~ spl52_25 ),
inference(forward_subsumption_resolution,[],[f1368,f766]) ).
fof(f1372,plain,
( open_subset(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),sK49)
| ~ spl52_25 ),
inference(resolution,[],[f1370,f999]) ).
fof(f1383,definition,
( spl52_26
<=> in(sK1(neighborhood_system(sK49,sK50),sK51),sK51) ),
introduced(definition,[new_symbols(definition,[spl52_26])],[avatar_definition]) ).
fof(f1384,plain,
( in(sK1(neighborhood_system(sK49,sK50),sK51),sK51)
| ~ spl52_26 ),
inference(avatar_component_clause,[],[f1383]) ).
fof(f1390,plain,
( subset(neighborhood_system(sK49,sK50),sK51)
| ~ spl52_26 ),
inference(resolution,[],[f1384,f433]) ).
fof(f1397,plain,
( $false
| spl52_2
| ~ spl52_26 ),
inference(forward_subsumption_resolution,[],[f1390,f785]) ).
fof(f1398,plain,
( spl52_2
| ~ spl52_26 ),
inference(avatar_contradiction_clause,[],[f1397]) ).
fof(f1416,plain,
( ~ in(sK50,interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)))
| ~ element(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),powerset(the_carrier(sK49)))
| in(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),sK51)
| ~ spl52_1
| ~ spl52_25 ),
inference(resolution,[],[f1372,f1325]) ).
fof(f1418,plain,
( ! [X0] :
( ~ in(X0,interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)))
| ~ element(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),powerset(the_carrier(sK49)))
| point_neighbourhood(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),sK49,X0) )
| ~ spl52_25 ),
inference(resolution,[],[f1372,f813]) ).
fof(f1420,definition,
( spl52_28
<=> element(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),powerset(the_carrier(sK49))) ),
introduced(definition,[new_symbols(definition,[spl52_28])],[avatar_definition]) ).
fof(f1421,plain,
( ~ element(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),powerset(the_carrier(sK49)))
| spl52_28 ),
inference(avatar_component_clause,[],[f1420]) ).
fof(f1423,definition,
( spl52_29
<=> ! [X0] :
( ~ in(X0,interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)))
| point_neighbourhood(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),sK49,X0) ) ),
introduced(definition,[new_symbols(definition,[spl52_29])],[avatar_definition]) ).
fof(f1424,plain,
( ! [X0] :
( ~ in(X0,interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)))
| point_neighbourhood(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),sK49,X0) )
| ~ spl52_29 ),
inference(avatar_component_clause,[],[f1423]) ).
fof(f1425,plain,
( ~ spl52_28
| spl52_29
| ~ spl52_25 ),
inference(avatar_split_clause,[],[f1418,f1340,f1423,f1420]) ).
fof(f1430,definition,
( spl52_31
<=> in(sK50,interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51))) ),
introduced(definition,[new_symbols(definition,[spl52_31])],[avatar_definition]) ).
fof(f1431,plain,
( ~ in(sK50,interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)))
| spl52_31 ),
inference(avatar_component_clause,[],[f1430]) ).
fof(f1434,definition,
( spl52_32
<=> in(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),sK51) ),
introduced(definition,[new_symbols(definition,[spl52_32])],[avatar_definition]) ).
fof(f1435,plain,
( in(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),sK51)
| ~ spl52_32 ),
inference(avatar_component_clause,[],[f1434]) ).
fof(f1436,plain,
( spl52_32
| ~ spl52_28
| ~ spl52_31
| ~ spl52_1
| ~ spl52_25 ),
inference(avatar_split_clause,[],[f1416,f1340,f778,f1430,f1420,f1434]) ).
fof(f1438,plain,
( ~ top_str(sK49)
| ~ element(sK1(neighborhood_system(sK49,sK50),sK51),powerset(the_carrier(sK49)))
| spl52_28 ),
inference(resolution,[],[f1421,f441]) ).
fof(f1440,plain,
( ~ element(sK1(neighborhood_system(sK49,sK50),sK51),powerset(the_carrier(sK49)))
| spl52_28 ),
inference(forward_subsumption_resolution,[],[f1438,f763]) ).
fof(f1441,plain,
( $false
| ~ spl52_25
| spl52_28 ),
inference(forward_subsumption_resolution,[],[f1440,f1370]) ).
fof(f1442,plain,
( ~ spl52_25
| spl52_28 ),
inference(avatar_contradiction_clause,[],[f1441]) ).
fof(f1444,plain,
( point_neighbourhood(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),sK49,sK50)
| ~ point_neighbourhood(sK1(neighborhood_system(sK49,sK50),sK51),sK49,sK50)
| ~ spl52_29 ),
inference(resolution,[],[f1424,f986]) ).
fof(f1445,plain,
( point_neighbourhood(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),sK49,sK50)
| ~ spl52_25
| ~ spl52_29 ),
inference(forward_subsumption_resolution,[],[f1444,f1353]) ).
fof(f1446,plain,
( element(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),powerset(the_carrier(sK49)))
| empty_carrier(sK49)
| ~ topological_space(sK49)
| ~ top_str(sK49)
| ~ element(sK50,the_carrier(sK49))
| ~ spl52_25
| ~ spl52_29 ),
inference(resolution,[],[f1445,f448]) ).
fof(f1451,plain,
( element(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),powerset(the_carrier(sK49)))
| ~ topological_space(sK49)
| ~ top_str(sK49)
| ~ element(sK50,the_carrier(sK49))
| ~ spl52_25
| ~ spl52_29 ),
inference(forward_subsumption_resolution,[],[f1446,f765]) ).
fof(f1454,plain,
( element(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),powerset(the_carrier(sK49)))
| ~ top_str(sK49)
| ~ element(sK50,the_carrier(sK49))
| ~ spl52_25
| ~ spl52_29 ),
inference(forward_subsumption_resolution,[],[f1451,f764]) ).
fof(f1457,plain,
( element(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),powerset(the_carrier(sK49)))
| ~ element(sK50,the_carrier(sK49))
| ~ spl52_25
| ~ spl52_29 ),
inference(forward_subsumption_resolution,[],[f1454,f763]) ).
fof(f1460,plain,
( element(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),powerset(the_carrier(sK49)))
| ~ spl52_25
| ~ spl52_29 ),
inference(forward_subsumption_resolution,[],[f1457,f766]) ).
fof(f1486,plain,
( ! [X0] :
( ~ subset(X0,cast_as_carrier_subset(sK49))
| ~ subset(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),X0)
| in(X0,sK51) )
| ~ spl52_32 ),
inference(resolution,[],[f1435,f828]) ).
fof(f1489,plain,
( ! [X0] :
( ~ subset(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),X0)
| ~ subset(X0,the_carrier(sK49))
| in(X0,sK51) )
| ~ spl52_32 ),
inference(forward_demodulation,[],[f1486,f874]) ).
fof(f1490,plain,
( ~ subset(sK1(neighborhood_system(sK49,sK50),sK51),the_carrier(sK49))
| in(sK1(neighborhood_system(sK49,sK50),sK51),sK51)
| ~ element(sK1(neighborhood_system(sK49,sK50),sK51),powerset(the_carrier(sK49)))
| ~ top_str(sK49)
| ~ spl52_32 ),
inference(resolution,[],[f1489,f761]) ).
fof(f1493,plain,
( in(sK1(neighborhood_system(sK49,sK50),sK51),sK51)
| ~ element(sK1(neighborhood_system(sK49,sK50),sK51),powerset(the_carrier(sK49)))
| ~ top_str(sK49)
| ~ spl52_32 ),
inference(forward_subsumption_resolution,[],[f1490,f757]) ).
fof(f1494,plain,
( in(sK1(neighborhood_system(sK49,sK50),sK51),sK51)
| ~ top_str(sK49)
| ~ spl52_25
| ~ spl52_32 ),
inference(forward_subsumption_resolution,[],[f1493,f1370]) ).
fof(f1495,plain,
( in(sK1(neighborhood_system(sK49,sK50),sK51),sK51)
| ~ spl52_25
| ~ spl52_32 ),
inference(forward_subsumption_resolution,[],[f1494,f763]) ).
fof(f1496,plain,
( spl52_26
| ~ spl52_25
| ~ spl52_32 ),
inference(avatar_split_clause,[],[f1495,f1434,f1340,f1383]) ).
fof(f1775,plain,
! [X0] :
( in(sK50,X0)
| ~ point_neighbourhood(X0,sK49,sK50)
| ~ element(X0,powerset(the_carrier(sK49)))
| ~ top_str(sK49) ),
inference(resolution,[],[f988,f761]) ).
fof(f1778,plain,
! [X0] :
( ~ point_neighbourhood(X0,sK49,sK50)
| in(sK50,X0)
| ~ element(X0,powerset(the_carrier(sK49))) ),
inference(forward_subsumption_resolution,[],[f1775,f763]) ).
fof(f1780,plain,
( in(sK50,interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)))
| ~ element(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),powerset(the_carrier(sK49)))
| ~ spl52_25
| ~ spl52_29 ),
inference(resolution,[],[f1778,f1445]) ).
fof(f1790,plain,
( ~ element(interior(sK49,sK1(neighborhood_system(sK49,sK50),sK51)),powerset(the_carrier(sK49)))
| ~ spl52_25
| ~ spl52_29
| spl52_31 ),
inference(forward_subsumption_resolution,[],[f1780,f1431]) ).
fof(f1791,plain,
( $false
| ~ spl52_25
| ~ spl52_29
| spl52_31 ),
inference(forward_subsumption_resolution,[],[f1790,f1460]) ).
fof(f1792,plain,
( ~ spl52_25
| ~ spl52_29
| spl52_31 ),
inference(avatar_contradiction_clause,[],[f1791]) ).
cnf(s1,plain,
( spl52_1
| spl52_2 ),
inference(sat_conversion,[],[f783]) ).
cnf(s2,plain,
( ~ spl52_1
| ~ spl52_2 ),
inference(sat_conversion,[],[f786]) ).
cnf(s22,plain,
( spl52_1
| ~ spl52_2 ),
inference(sat_conversion,[],[f1322]) ).
cnf(s23,plain,
( spl52_2
| ~ spl52_24
| spl52_25 ),
inference(sat_conversion,[],[f1342]) ).
cnf(s25,plain,
( spl52_2
| spl52_24 ),
inference(sat_conversion,[],[f1351]) ).
cnf(s28,plain,
( spl52_2
| ~ spl52_26 ),
inference(sat_conversion,[],[f1398]) ).
cnf(s29,plain,
( ~ spl52_25
| ~ spl52_28
| spl52_29 ),
inference(sat_conversion,[],[f1425]) ).
cnf(s31,plain,
( ~ spl52_1
| ~ spl52_25
| ~ spl52_28
| ~ spl52_31
| spl52_32 ),
inference(sat_conversion,[],[f1436]) ).
cnf(s33,plain,
( ~ spl52_25
| spl52_28 ),
inference(sat_conversion,[],[f1442]) ).
cnf(s37,plain,
( ~ spl52_25
| spl52_26
| ~ spl52_32 ),
inference(sat_conversion,[],[f1496]) ).
cnf(s58,plain,
( ~ spl52_25
| ~ spl52_29
| spl52_31 ),
inference(sat_conversion,[],[f1792]) ).
cnf(s60,plain,
spl52_1,
inference(rat,[],[s1,s22]) ).
cnf(s62,plain,
~ spl52_2,
inference(rat,[],[s2,s60]) ).
cnf(s63,plain,
~ spl52_26,
inference(rat,[],[s28,s62]) ).
cnf(s64,plain,
spl52_24,
inference(rat,[],[s25,s62]) ).
cnf(s65,plain,
spl52_25,
inference(rat,[],[s23,s62,s64]) ).
cnf(s66,plain,
~ spl52_32,
inference(rat,[],[s37,s63,s65]) ).
cnf(s67,plain,
spl52_28,
inference(rat,[],[s33,s65]) ).
cnf(s69,plain,
spl52_29,
inference(rat,[],[s29,s65,s67]) ).
cnf(s70,plain,
~ spl52_31,
inference(rat,[],[s31,s66,s65,s60,s67]) ).
cnf(s71,plain,
$false,
inference(rat,[],[s58,s65,s70,s69]) ).
fof(f1793,plain,
$false,
inference(avatar_sat_refutation,[],[s71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU389+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n010.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 05:04:02 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 8.06/2.16 % (1567619)Detected formulas, will run a generic FOF schedule.
% 8.06/2.16 % (1567628)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=811883413:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.06/2.16 % (1567628)Instruction limit reached!
% 8.06/2.16 % (1567628)------------------------------
% 8.06/2.16 % (1567628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.06/2.16 % (1567628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.06/2.16 % (1567628)CaDiCaL version: 2.1.3
% 8.06/2.16 % (1567628)Termination reason: Instruction limit
% 8.06/2.16 % (1567628)Termination phase: Saturation
% 8.06/2.16 % (1567628)Time elapsed: 0.041 s
% 8.06/2.16 % (1567628)Peak memory usage: 89 MB
% 8.06/2.16 % (1567628)Instructions burned: 121 (million)
% 8.06/2.16 % (1567624)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=3109820894:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.06/2.16 % (1567626)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=2728228681:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.06/2.16 % (1567625)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=859195579:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.06/2.16 % (1567629)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4202252024:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.06/2.16 % (1567627)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3772927284:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.06/2.16 % (1567630)dis-21_1_sil=8000:lcm=predicate:random_seed=637967676: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)
% 8.06/2.16 % (1567627)Refutation not found, incomplete strategy
% 8.06/2.16 % (1567627)------------------------------
% 8.06/2.16 % (1567627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.06/2.16 % (1567627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.06/2.16 % (1567627)CaDiCaL version: 2.1.3
% 8.06/2.16 % (1567627)Termination reason: Refutation not found, incomplete strategy
% 8.06/2.16 % (1567627)Time elapsed: 0.004 s
% 8.06/2.16 % (1567627)Peak memory usage: 88 MB
% 8.06/2.16 % (1567627)Instructions burned: 4 (million)
% 8.06/2.16 % (1567630)Instruction limit reached!
% 8.06/2.16 % (1567630)------------------------------
% 8.06/2.16 % (1567630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.06/2.16 % (1567630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.06/2.16 % (1567630)CaDiCaL version: 2.1.3
% 8.06/2.16 % (1567630)Termination reason: Instruction limit
% 8.06/2.16 % (1567630)Termination phase: Saturation
% 8.06/2.16 % (1567630)Time elapsed: 0.078 s
% 8.06/2.16 % (1567630)Peak memory usage: 92 MB
% 8.06/2.16 % (1567630)Instructions burned: 130 (million)
% 8.06/2.16 % (1567629)Instruction limit reached!
% 8.06/2.16 % (1567629)------------------------------
% 8.06/2.16 % (1567629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.06/2.16 % (1567629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.06/2.16 % (1567629)CaDiCaL version: 2.1.3
% 8.06/2.16 % (1567629)Termination reason: Instruction limit
% 8.06/2.16 % (1567629)Termination phase: Saturation
% 8.06/2.16 % (1567629)Time elapsed: 0.100 s
% 8.06/2.16 % (1567629)Peak memory usage: 90 MB
% 8.06/2.16 % (1567629)Instructions burned: 140 (million)
% 8.06/2.16 % (1567638)lrs+10_1_sil=8000:sp=occurrence:random_seed=3318041866:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 8.06/2.16 % (1567638)Instruction limit reached!
% 8.06/2.16 % (1567638)------------------------------
% 8.06/2.16 % (1567638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.06/2.16 % (1567638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.06/2.16 % (1567638)CaDiCaL version: 2.1.3
% 8.06/2.16 % (1567638)Termination reason: Instruction limit
% 8.06/2.16 % (1567638)Termination phase: Saturation
% 8.06/2.16 % (1567638)Time elapsed: 0.100 s
% 8.06/2.16 % (1567638)Peak memory usage: 92 MB
% 8.06/2.16 % (1567638)Instructions burned: 287 (million)
% 8.06/2.16 % (1567639)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4158794674:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.06/2.16 % (1567627)------------------------------
% 8.06/2.16 % (1567627)------------------------------
% 8.06/2.16 % (1567640)lrs+1011_1_sil=32000:sp=occurrence:random_seed=198112954:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.06/2.16 % (1567639)Instruction limit reached!
% 8.06/2.16 % (1567639)------------------------------
% 8.06/2.16 % (1567639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.06/2.16 % (1567639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.06/2.16 % (1567639)CaDiCaL version: 2.1.3
% 8.06/2.16 % (1567639)Termination reason: Instruction limit
% 8.06/2.16 % (1567639)Termination phase: Saturation
% 8.06/2.16 % (1567639)Time elapsed: 0.085 s
% 8.06/2.16 % (1567639)Peak memory usage: 89 MB
% 8.06/2.16 % (1567639)Instructions burned: 158 (million)
% 8.06/2.16 % (1567642)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=2879977598:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 8.06/2.16 % (1567645)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3842380415:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.06/2.16 % (1567645)Refutation not found, incomplete strategy
% 8.06/2.16 % (1567645)------------------------------
% 8.06/2.16 % (1567645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.06/2.16 % (1567645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.06/2.16 % (1567645)CaDiCaL version: 2.1.3
% 8.06/2.16 % (1567645)Termination reason: Refutation not found, incomplete strategy
% 8.06/2.16 % (1567645)Time elapsed: 0.015 s
% 8.06/2.16 % (1567645)Peak memory usage: 89 MB
% 8.06/2.16 % (1567645)Instructions burned: 22 (million)
% 8.06/2.16 % (1567642)Instruction limit reached!
% 8.06/2.16 % (1567642)------------------------------
% 8.06/2.16 % (1567642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.06/2.16 % (1567642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.06/2.16 % (1567642)CaDiCaL version: 2.1.3
% 8.06/2.16 % (1567642)Termination reason: Instruction limit
% 8.06/2.16 % (1567642)Termination phase: Saturation
% 8.06/2.16 % (1567642)Time elapsed: 0.084 s
% 8.06/2.16 % (1567642)Peak memory usage: 92 MB
% 8.06/2.16 % (1567642)Instructions burned: 249 (million)
% 8.06/2.16 % (1567646)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4207376036:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 8.06/2.16 % (1567640)Instruction limit reached!
% 8.06/2.16 % (1567640)------------------------------
% 8.06/2.16 % (1567640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.06/2.16 % (1567640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.06/2.16 % (1567640)CaDiCaL version: 2.1.3
% 8.06/2.16 % (1567640)Termination reason: Instruction limit
% 8.06/2.16 % (1567640)Termination phase: Saturation
% 8.06/2.16 % (1567640)Time elapsed: 0.229 s
% 8.06/2.16 % (1567640)Peak memory usage: 92 MB
% 8.06/2.16 % (1567640)Instructions burned: 326 (million)
% 8.06/2.16 % (1567649)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1660181657:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 8.06/2.16 % (1567649)Instruction limit reached!
% 8.06/2.16 % (1567649)------------------------------
% 8.06/2.16 % (1567649)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.06/2.16 % (1567649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.06/2.16 % (1567649)CaDiCaL version: 2.1.3
% 8.06/2.16 % (1567649)Termination reason: Instruction limit
% 8.06/2.16 % (1567649)Termination phase: Saturation
% 8.06/2.16 % (1567649)Time elapsed: 0.043 s
% 8.06/2.16 % (1567649)Peak memory usage: 91 MB
% 8.06/2.16 % (1567649)Instructions burned: 114 (million)
% 8.06/2.16 % (1567645)------------------------------
% 8.06/2.16 % (1567645)------------------------------
% 8.06/2.16 % (1567651)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1758195546:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 8.06/2.16 % (1567653)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3389204979:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 8.06/2.16 % (1567651)Instruction limit reached!
% 8.06/2.16 % (1567651)------------------------------
% 8.06/2.16 % (1567651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.06/2.16 % (1567651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.06/2.16 % (1567651)CaDiCaL version: 2.1.3
% 8.06/2.16 % (1567651)Termination reason: Instruction limit
% 8.06/2.16 % (1567651)Termination phase: Saturation
% 8.06/2.16 % (1567651)Time elapsed: 0.070 s
% 8.06/2.16 % (1567651)Peak memory usage: 89 MB
% 8.06/2.16 % (1567651)Instructions burned: 128 (million)
% 8.06/2.16 % (1567653)Instruction limit reached!
% 8.06/2.16 % (1567653)------------------------------
% 8.06/2.16 % (1567653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.06/2.16 % (1567653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.06/2.16 % (1567653)CaDiCaL version: 2.1.3
% 8.06/2.16 % (1567653)Termination reason: Instruction limit
% 8.06/2.16 % (1567653)Termination phase: Saturation
% 8.06/2.16 % (1567653)Time elapsed: 0.041 s
% 8.06/2.16 % (1567653)Peak memory usage: 90 MB
% 8.06/2.16 % (1567653)Instructions burned: 117 (million)
% 8.06/2.16 % (1567655)lrs+10_1_sil=8000:sp=occurrence:random_seed=1330829976:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 8.06/2.16 % (1567625)First to succeed.
% 8.06/2.16 % (1567625)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1567619"
% 8.06/2.16 % (1567658)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3700202615:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 8.06/2.16 % (1567657)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2567881956:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 8.06/2.16 % (1567624)Also succeeded, but the first one will report.
% 8.06/2.16 % (1567626)Also succeeded, but the first one will report.
% 8.06/2.16 % (1567625)Refutation found. Thanks to Tanya!
% 8.06/2.16 % SZS status Theorem for theBenchmark
% 8.06/2.16 % SZS output start Proof for theBenchmark
% See solution above
% 9.62/2.35 % (1567625)------------------------------
% 9.62/2.35 % (1567625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.62/2.35 % (1567625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.62/2.35 % (1567625)CaDiCaL version: 2.1.3
% 9.62/2.35 % (1567625)Termination reason: Refutation
% 9.62/2.35 % (1567625)Time elapsed: 0.837 s
% 9.62/2.35 % (1567625)Peak memory usage: 133 MB
% 9.62/2.35 % (1567625)Instructions burned: 1229 (million)
% 9.62/2.35 % (1567625)------------------------------
% 9.62/2.35 % (1567625)------------------------------
% 9.62/2.35 % (1567619)Success in time 1.284 s
% 9.62/2.35 % Vampire exiting
%------------------------------------------------------------------------------